74 ·∫∫Ωñ° §≥‘μ»“ μ√æå π◊È ∞“π ¡.2 ¿“§‡√’¬π∑Ë’ 2
3 °“√ª√–¬°ÿ μå¢Õß
¡°“√‡™ß‘ ‡ πâ
μ—«·ª√‡¥’¬«
1. ª√–‚¬§¿“…“·≈–ª√–‚¬§ ≠— ≈—°…≥å
°®‘ °√√¡∑’Ë 1
1. „Àπâ °— ‡√¬’ π‡¢’¬π —≠≈°— …≥·å ∑π¢âÕ§«“¡μàÕ‰ªπ’È
(1) º≈∫«°¢Õß Õ߇∑à“¢Õß®”π«π®”π«πÀπ÷Ëß°—∫À“â ‡∑“à ¢Õß®”π«πππ—È
...................................................................................................................................
(2) x ‡æË¡‘ ¢÷πÈ Õ’° 6
...................................................................................................................................
(3) ®”π«π∑Ë’¡“°°«“à Õ߇∑à“¢Õß x Õ¬Ÿà 5
...................................................................................................................................
(4) º≈∫«°¢Õß®”π«π§à Ÿ “¡®”π«π‡√¬’ ß°π—
...................................................................................................................................
(5) x ≈∫¥â«¬ 5 ‡∑“à °—∫ 2
...................................................................................................................................
(6) º≈∫«°¢Õß x °—∫ 8 ¡§’ à“‡∑à“°—∫ 11
...................................................................................................................................
·∫∫Ωñ° §≥μ‘ »“ μ√åæπÈ◊ ∞“π ¡.2 ¿“§‡√¬’ π∑Ë’ 2 75
(7) ‡»…ÀπßË÷ «à π “¡¢Õß y ‰¡à‡∑à“°—∫ 9
...................................................................................................................................
(8) m ≈∫¥â«¬ 3 πÕâ ¬°«à“ 10
...................................................................................................................................
(9) º≈§≥Ÿ ¢Õß 7 ·≈– n ¡“°°«à“ 21
...................................................................................................................................
(10) “¡‡∑à“¢Õߺ≈∫«°¢Õß®”π«π®”π«πÀπß÷Ë °∫— 5 ‰¡à‡°‘π 20
...................................................................................................................................
(11) º≈∫«° Õ߇∑à“¢Õß®”π«π®”π«πÀπ÷Ëß°∫— 5 ‰¡àμ”Ë °«à“ 15
...................................................................................................................................
(12) º≈∫«°¢Õß®”π«ππ—∫ “¡®”π«π‡√¬’ ß°—π‡∑“à °∫— 21
...................................................................................................................................
(13) ‡»… “¡ «à π ¢’Ë Õß®”π«π®”π«πÀπßË÷ ≈∫¥«â ¬‡»…Àπß÷Ë «à π ¢’Ë Õß®”π«πππÈ— ‡∑“à °∫— 10
...................................................................................................................................
(14) °”≈—ß ÕߢÕß®”π«π®”π«πÀπË÷ß≈∫¥â«¬ 5 ‡∑à“°∫— 20
...................................................................................................................................
(15) ‡’Ë ∑“à ¢Õß®”π«π®”π«πÀπ÷Ëß∫«°¥«â ¬‡»…ÀπË÷ß à«π ’¢Ë Õß®”π«ππÈ—π‡∑“à °∫— 34
...................................................................................................................................
2. „Àâπ°— ‡√¬’ π‡ª≈¬’Ë πª√–‚¬§μàÕ‰ªπ’ȇªìπª√–‚¬§¿“…“
(1) xϪ2 = 3
...................................................................................................................................
(2) xϩ5 = 5
...................................................................................................................................
(3) 3ϫ4 = 12
...................................................................................................................................
(4) 15 = 5
3
...................................................................................................................................
76 ·∫∫Ω°ñ §≥‘μ»“ μ√æå π◊È ∞“π ¡.2 ¿“§‡√’¬π∑’Ë 2
(5) 7x = 35
...................................................................................................................................
(6) x = 3
15
...................................................................................................................................
(7) 2xϩ3x = 25
...................................................................................................................................
(8) 5(xϩ2) = 30
...................................................................................................................................
(9) x2Ϫ6 = 30
...................................................................................................................................
(10) 1 xϪ 1 x = 10
5 10
...................................................................................................................................
3. „Àπâ °— ‡√¬’ π殑 “√≥“«à“¢Õâ §«“¡„¥‡ªìπ ¡°“√·≈–¢Õâ §«“¡„¥‡ªìπÕ ¡°“√
¡°“√ Õ ¡°“√ ‰¡‡à ªπì ∑—Èß ÕßÕ¬à“ß
(1) 17Ϫ5 = 5ϩ7 ..................... ..................... .......................................
(2) 2x Ͻ 10 ..................... ..................... .......................................
(3) 3xϪ2x ..................... ..................... .......................................
(4) 5cϩ2 у 1 ..................... ..................... .......................................
(5) 4m = 0 ..................... ..................... .......................................
(6) 4xϪ3y ..................... ..................... .......................................
(7) 9h = 27 ..................... ..................... .......................................
(8) 4xϪ5 = 19 ..................... ..................... .......................................
(9) 3xϩ2 = xϪ8 ..................... ..................... .......................................
(10) 5xϪ2x = 6 ..................... ..................... .......................................
(11) 5x π 100 ..................... ..................... .......................................
(12) 2xϩ7 = xϩ11 ..................... ..................... .......................................
(13) x ϩ x = 10
..................... ..................... .......................................
32
(14) xϩ5 р xϪ7 ..................... ..................... .......................................
(15) 9xϩ6(34Ϫx) π 207 ..................... ..................... .......................................
·∫∫Ω°ñ §≥μ‘ »“ μ√åæ◊πÈ ∞“π ¡.2 ¿“§‡√¬’ π∑’Ë 2 77
4. „Àπâ —°‡√’¬πÀ“®”π«π¡“·∑πμ—«·ª√‡æÕË◊ ∑”„Àªâ √–‚¬™πåμàÕ‰ªπȇ’ ªìπ®√‘ß
(1) 3x = 12 ..............................................................................................
(2) 4x = Ϫ8 ..............................................................................................
(3) 5x = 4xϩ2 ..............................................................................................
(4) 6xϩ3x = 9 ..............................................................................................
(5) 7xϪ2x = 15 ..............................................................................................
(6) 2xϩ5 = xϩ1 ..............................................................................................
(7) 3xϪ4 = 2xϪ3 ..............................................................................................
(8) xϪ15 = Ϫ8 ..............................................................................................
(9) 1 x = 5 ..............................................................................................
5
(10) xϩ3(xϪ2) = 2xϪ2 ..............................................................................................
(11) 3xϪ4x = 1 ..............................................................................................
(12) Ϫ 1 x = Ϫ3 ..............................................................................................
7
2. §”μÕ∫¢Õß ¡°“√
°‘®°√√¡∑’Ë 2
1. „Àâπ—°‡√’¬π‡¢¬’ πª√–‚¬§ ≠— ≈—°…≥·å ≈«â À“§”μÕ∫¢Õß ¡°“√
(1) ®”π«π®”π«πÀπËß÷ ≈∫¥«â ¬ 2 ‡∑à“°—∫ 3
.....................................................................................................................................
(2) °”≈ß— ÕߢÕß®”π«π®”π«πÀπßË÷ ≈∫¥â«¬ 6 ‡∑à“°∫— 30
.....................................................................................................................................
(3) ®”π«π®”π«πÀπßË÷ À“√¥â«¬ 15 ‡∑“à °∫— 3
.....................................................................................................................................
78 ·∫∫Ω°ñ §≥‘μ»“ μ√åæÈπ◊ ∞“π ¡.2 ¿“§‡√¬’ π∑’Ë 2
(4) À“â ‡∑à“¢Õߺ≈∫«°¢Õß®”π«π®”π«πÀπËß÷ °—∫ 2 ‡∑“à °—∫ 30
.....................................................................................................................................
(5) ‡»…Àπ÷Ëß à«πÀâ“¢Õß®”π«π®”π«πÀπË÷ß≈∫¥â«¬‡»…ÀπË÷ß à«π ‘∫¢Õß®”π«ππ—Èπ‡∑à“°—∫
10
.....................................................................................................................................
2. „Àπâ °— ‡√’¬πμ√«® Õ∫¥«Ÿ à“®”π«π∑°Ë’ ”Àπ¥„À„â π«ß‡≈Á∫ [ ] ‡ªìπ§”μÕ∫¢Õß ¡°“√À√◊Õ‰¡à
(1) 2xϪ5 = 1 [3] .....................................................................................
(2) 3xϪ7 = 11 [6] .....................................................................................
(3) 4xϩ40 = 80 [10] .....................................................................................
(4) 5xϩ9 = 4xϩ10 [1] .....................................................................................
(5) 6xϪ4 = 2xϩ8 [3] .....................................................................................
(6) 7p = 21Ϫ3p [7] .....................................................................................
(7) 8qϪ3q = 6qϪ10 [10] .....................................................................................
(8) 3b = 5bϪ18 [9] .....................................................................................
(9) 2t = 3tϪ11 [11] .....................................................................................
(10) 9x = 7xϪ18 [Ϫ9] .....................................................................................
3. „Àπâ —°‡√¬’ πÀ“§”μÕ∫¢Õß ¡°“√μàÕ‰ªπ’È ‚¥¬«‘∏·’ ∑π§“à
(1) 3x = 12 ........................ (2) 4x = 20 .............................
.............................
(3) 5x = 30 ........................ (4) x = 12 .............................
........................ 3 .............................
(5) x = 20 ........................ .............................
4 ........................ (6) x = 30 .............................
........................ 5
(7) 2 = 3
3a (8) a Ϫ2 = 1
3
(9) a = 1
93 (10) b = 1
73
(11) 2c = 4
55 (12) 3d = 2 1
55
·∫∫Ωñ° §≥‘μ»“ μ√åæπÈ◊ ∞“π ¡.2 ¿“§‡√’¬π∑’Ë 2 79
(13) r ϩ2 = 4 ........................ (14) pϪ p = 1 .............................
3 ........................ 2 .............................
(15) x2 = 9 (16) x3 = 1,000
(17) x2 = 9 ........................ (18) xϪ7 = 3xϪ7 .............................
4
(19) 0.5yϩ3 = 0.3yϩ7 ........................ (20) xϩ 1 x = 4 .............................
3
(21) xϪ 1 x = 4 ........................ (22) yϩ 1 y = 3 yϩ2 .............................
5 44
3. °“√·° â ¡°“√
°‘®°√√¡∑Ë’ 3
1. „Àπâ °— ‡√¬’ π„™ â ¡∫—μ ‘ ¡¡“μ√‡μ‘¡ª√–‚¬§„Àâ ¡∫√Ÿ ≥å
(1) „Àâ 2x = 8 ¥ß— ππÈ— 8 = .....................................................
(2) „Àâ 3(xϩy) = 3xϩ3y ¥—ßππÈ— 3xϩ3y = .....................................................
(3) „Àâ aϩb = bϩa ¥ß— πÈπ— bϩa = .....................................................
(4) „Àâ (2ϩ3)x = 2xϩ3x ¥—ßππÈ— 2xϩ3x = .....................................................
(5) „Àâ Ϫ5xϪ10 = Ϫ5(xϩ2) ¥—ßπÈ—π Ϫ5(xϩ2) = .....................................................
2. „Àâπ°— ‡√¬’ π„™â ¡∫—μ°‘ “√∂“à ¬∑Õ¥‡μ‘¡ª√–‚¬§„Àâ ¡∫Ÿ√≥å
(1) ∂“â a = b ·≈– b = c ·≈â« .............................................................................................
(2) ∂â“ 2xϪx = (2Ϫ1)x ·≈– (2Ϫ1)x = x ·≈«â ....................................................................
(3) ∂“â Ϫ2xϪx = (Ϫ2Ϫ1)x ·≈– (Ϫ2Ϫ1)x = Ϫ3x ·≈«â .......................................................
(4) ∂â“ Ϫ2x = (Ϫ1Ϫ1)x ·≈– (Ϫ1Ϫ1)x = ϪxϪx ·≈â« ........................................................
(5) ∂â“ 3xϩ5x = (3ϩ5)x ·≈– (3ϩ5)x = 8x ·≈â« .................................................................
80 ·∫∫Ωñ° §≥‘μ»“ μ√æå ◊Èπ∞“π ¡.2 ¿“§‡√’¬π∑Ë’ 2
3. „Àπâ °— ‡√¬’ π„™ â ¡∫—μ°‘ “√∫«° ¡∫μ— ‘°“√§≥Ÿ ·≈– ¡∫μ— ‘°“√·®°·®ß‡μ‘¡ª√–‚¬§„À â ¡∫Ÿ√≥å
(1) ∂â“ xϩ5 = 9 ·≈«â xϩ5ϩ(Ϫ5) = ....................................................................................
(2) ∂“â xϩ3 = 5 ·≈â« xϩ3ϩ(Ϫ3) = ..................................................................................
22
(3) ∂“â 5x = 4 ·≈â« 1ϫ5x =...............................................................................................
5
∂“â ·≈â«(4) 2(xϩ2) = 2xϩ4 3(xϩ3) = ..................................................................................
(5) ∂“â 2x = 10 ·≈«â 5 ϫ 2x =.....................................................................................
5 25
4. „Àπâ °— ‡√’¬π„™ â ¡∫—μ‘°“√∫«° ¡∫μ— °‘ “√§Ÿ≥ ·≈– ¡∫μ— ‘°“√·®°·®ß‡μ‘¡ª√–‚¬§„À â ¡∫√Ÿ ≥å
(1) 2xϩ5 = 25
........................................................... ¡∫μ— °‘ “√∫«°
2x = 20
........................................................... ¡∫μ— °‘ “√§≥Ÿ
x = 10
(2) 3xϪ4 = 8
5
........................................................... ¡∫—μ°‘ “√∫«°
3x = 12
5
........................................................... ¡∫μ— ‘°“√§≥Ÿ
x = 20
(3) 3(2xϩ5) = 27
........................................................... ¡∫—μ°‘ “√·®°·®ß
6xϩ15 = 27
........................................................... ¡∫—μ°‘ “√∫«°
6x = 12
........................................................... ¡∫μ— ‘°“√§≥Ÿ
x=2
·∫∫Ωñ° §≥‘μ»“ μ√æå πÈ◊ ∞“π ¡.2 ¿“§‡√’¬π∑Ë’ 2 81
(4) 33 = 3(2xϩ5)
........................................................... ¡∫μ— ‘°“√§≥Ÿ
11 = 2xϩ5
........................................................... ¡∫—μ°‘ “√∫«°
6 = 2x
........................................................... ¡∫μ— °‘ “√§≥Ÿ
3=x
5. „Àπâ —°‡√’¬π·°â ¡°“√μÕà ‰ªπæÈ’ √âÕ¡μ√«® Õ∫§”μÕ∫
(1) 2(xϩ1) = 10
«∏‘ ∑’ ” 2(xϩ1) = 10
xϩ1 = 10
2
......................................................................................................................
......................................................................................................................
......................................................................................................................
μ√«® Õ∫§”μÕ∫ 2(xϩ1) = 10
............................................................................................... .
............................................................................................... .
............................................................................................... .
¥—ßπÈπ— §”μÕ∫¢Õß ¡°“√§◊Õ 4
(2) 3(xϪ1) = Ϫ6
«∏‘ ∑’ ” 3(xϪ1) = Ϫ6
xϪ1 = Ϫ 6
3
......................................................................................................................
......................................................................................................................
......................................................................................................................
82 ·∫∫Ω°ñ §≥‘μ»“ μ√æå π◊È ∞“π ¡.2 ¿“§‡√’¬π∑Ë’ 2
μ√«® Õ∫§”μÕ∫ 3(xϪ1) = Ϫ6
............................................................................................... .
............................................................................................... .
............................................................................................... .
¥ß— π—È𠧔μÕ∫¢Õß ¡°“√§Õ◊ Ϫ1
(3) 7xϪ11 = 6(xϪ1) 7xϪ11 = 6(xϪ1)
«∏‘ ∑’ ”
7xϪ11 = 6xϪ6
......................................................................................................................
......................................................................................................................
μ√«® Õ∫§”μÕ∫ 7xϪ11 = 6(xϪ1)
............................................................................................... .
............................................................................................... .
............................................................................................... .
¥—ßπÈπ— §”μÕ∫¢Õß ¡°“√§Õ◊ 5
(4) 5(xϪ2) = 3(xϩ6)
«∏‘ ∑’ ” 5(xϪ2) = 3(xϩ6)
5xϪ10 = 3xϩ18
......................................................................................................................
......................................................................................................................
......................................................................................................................
μ√«® Õ∫§”μÕ∫ 5(xϪ2) = 3(xϩ6)
............................................................................................... .
............................................................................................... .
............................................................................................... .
¥—ßπÈ—π §”μÕ∫¢Õß ¡°“√§Õ◊ 14
·∫∫Ωñ° §≥‘μ»“ μ√åæ◊Èπ∞“π ¡.2 ¿“§‡√’¬π∑’Ë 2 83
(5) 0.2(xϪ1)ϩ0.3(xϪ2) = 1.2
«∏‘ ∑’ ” 0.2(xϪ1)ϩ0.3(xϪ2) = 1.2
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
μ√«® Õ∫§”μÕ∫ 0.2(xϪ1)ϩ0.3(xϪ2) = 1.2
............................................................................................... .
............................................................................................... .
............................................................................................... .
................................................................................................
¥ß— π—πÈ §”μÕ∫¢Õß ¡°“√§◊Õ 4
(6) 2 xϩ5 = 11
5
«∏‘ ∑’ ” ......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
μ√«® Õ∫§”μÕ∫ ................................................................................................
............................................................................................... .
............................................................................................... .
............................................................................................... .
................................................................................................
......................................................................................................................
84 ·∫∫Ωñ° §≥μ‘ »“ μ√æå Èπ◊ ∞“π ¡.2 ¿“§‡√¬’ π∑Ë’ 2
(7) 2Ϫ x = 1 ϩ x
2 69
«∏‘ ∑’ ” ......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
μ√«® Õ∫§”μÕ∫ ................................................................................................
............................................................................................... .
................................................................................................
......................................................................................................................
(8) x Ϫ 3 ϩ x = 3x ϩ 5
44
«∏‘ ∑’ ” ......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
μ√«® Õ∫§”μÕ∫ ................................................................................................
............................................................................................... .
............................................................................................... .
................................................................................................
......................................................................................................................
·∫∫Ω°ñ §≥‘μ»“ μ√åæπ◊È ∞“π ¡.2 ¿“§‡√’¬π∑Ë’ 2 85
x ϩ11 3 xπ3
xϪ3 2
,(9) =
«∏‘ ∑’ ” ......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
μ√«® Õ∫§”μÕ∫ ................................................................................................
............................................................................................... .
............................................................................................... .
................................................................................................
......................................................................................................................
(10) 7(xϩ4a) = 14(xϪ3a)
«∏‘ ∑’ ” ......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
μ√«® Õ∫§”μÕ∫ ................................................................................................
............................................................................................... .
............................................................................................... .
......................................................................................................................
(11) 3 (3xϩ1) = 8 (4xϪ8)Ϫ11
47
«∏‘ ∑’ ” ......................................................................................................................
......................................................................................................................
86 ·∫∫Ω°ñ §≥‘μ»“ μ√åæÈπ◊ ∞“π ¡.2 ¿“§‡√’¬π∑’Ë 2
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
μ√«® Õ∫§”μÕ∫ 3 (3xϩ1) = 8 (4xϪ8)Ϫ11
47
............................................................................................... .
............................................................................................... .
............................................................................................... .
................................................................................................
......................................................................................................................
(12) 2(x ϩ 4) Ϫ 3(x ϩ1) = 1Ϫ 2(x Ϫ1)
32 3
«∏‘ ∑’ ” ......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
...................................................................................................................................
......................................................................................................................
·∫∫Ωñ° §≥μ‘ »“ μ√åæπ◊È ∞“π ¡.2 ¿“§‡√¬’ π∑Ë’ 2 87
(13) 1 = 1
2x Ϫ1 x ϩ1
«∏‘ ∑’ ” ......................................................................................................................
......................................................................................................................
......................................................................................................................
......................................................................................................................
μ√«® Õ∫§”μÕ∫ ................................................................................................
............................................................................................... .
............................................................................................... .
......................................................................................................................
6. „Àâπ°— ‡√¬’ πÀ“§à“¢Õß x ®“° ¡°“√μÕà ‰ªπÈ’
(1) 25% ¢Õß x = 40
«∏‘ ∑’ ” 25% ¢Õß x = 40
25 x = 40
100
x = ..........................................................................................
........................................................................................................................
(2) xϩ15% ¢Õß x = 3.45
«∏‘ ∑’ ” xϩ 15x = 3.45
100
xϩ0.15x = .................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
88 ·∫∫Ωñ° §≥μ‘ »“ μ√åæ◊Èπ∞“π ¡.2 ¿“§‡√’¬π∑Ë’ 2
(3) xϪ5 = 3ϩ33 1 % ¢Õß x
3 100x
«∏‘ ∑’ ” xϪ5 = 3ϩ 3
100
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
........................................................................................................................
7. °”Àπ¥ A = k(axϩb) ®ßÀ“ x ‡¡ÕË◊ A = 10, k = 5, a = Ϫ1, b = Ϫ3
«∏‘ ∑’ ” A = k(axϩb)
A = axϩb
k
ax = A Ϫb
k
x = 1 Ê A Ϫ bˆ˜¯
a ÁË k
x = ..........................................................................................
........................................................................................................................
........................................................................................................................
·∫∫Ω°ñ §≥‘μ»“ μ√åæ◊Èπ∞“π ¡.2 ¿“§‡√¬’ π∑Ë’ 2 89
4. ‚®∑¬å ¡°“√
°‘®°√√¡∑’Ë 4
1. °”Àπ¥μ«— ·ª√ x „Àâπ—°‡√¬’ π‡¢¬’ π ≠— ≈°— …≥®å “°¢Õâ §«“¡μÕà ‰ªπÈ’
(1) º≈∫«°¢Õß®”π«π®”π«πÀπËß÷ °—∫ 5
.....................................................................................................................................
(2) ®”π«π´ßË÷ ¡“°°«“à ®”π«π®”π«πÀπ÷ËßÕ¬àŸ 7
.....................................................................................................................................
(3) ®”π«π´Ë÷ßπâÕ¬°«“à ®”π«π®”π«πÀπËß÷ Õ¬Ÿà 5
.....................................................................................................................................
(4) º≈§≥Ÿ ¢Õß 3 °∫— ®”π«π®”π«πÀπË÷ß
.....................................................................................................................................
(5) À“â ‡∑à“¢Õß®”π«π®”π«πÀπ÷ßË
.....................................................................................................................................
(6) ·∫ßà ®”π«π®”π«πÀπ÷ËßÕÕ°‡ªìπ 5 «à π‡∑“à Ê °π—
.....................................................................................................................................
(7) 5 ¡“°°«à“®”π«π®”π«πÀπßË÷
.....................................................................................................................................
(8) 35 πâÕ¬°«à“ÀⓇ∑“à ¢Õß®”π«π®”π«πÀπË÷ß
.....................................................................................................................................
2. „Àâπ°— ‡√’¬π‡¢¬’ π ≠— ≈—°…≥å·≈– ¡°“√®“°¢Õâ §«“¡μÕà ‰ªπ’È
(1) Õ߇∑à“¢Õß®”π«π®”π«πÀπË÷ß¡“°°«“à 3 Õ¬àŸ 7
.....................................................................................................................................
90 ·∫∫Ω°ñ §≥μ‘ »“ μ√æå Èπ◊ ∞“π ¡.2 ¿“§‡√¬’ π∑’Ë 2
(2) À“â ‡∑“à ¢Õߺ≈∫«°¢Õß®”π«π®”π«πÀπß÷Ë °—∫ 5 ‡ªπì 20
.....................................................................................................................................
(3) ®”π«π®”π«πÀπË÷߬°°”≈ß— Õ߇∑“à °—∫ 49
.....................................................................................................................................
(4) º≈∫«°¢Õß®”π«π‡μ¡Á ∫«° “¡®”π«π‡√¬’ ß°—π‡ªìπ 63
.....................................................................................................................................
(5) π“¡À≠â“√Ÿª ’ˇÀ≈’ˬ¡º◊πºâ“·ÀàßÀπ÷Ëß¡’¥â“𬓫¬“«°«à“¥â“π°«â“ß 5 ‡¡μ√ ·≈–
π“¡À≠“â π¬È’ “« 25 ‡¡μ√
.....................................................................................................................................
(6) æàÕπ”‡ß‘π®”π«πÀπ÷Ëß√«¡°—∫‡ß‘π 1,000 ∫“∑ ·≈â«·∫àß„Àâ≈Ÿ° 2 §π ‰¥â√—∫§π≈– 300
∫“∑
.....................................................................................................................................
(7) √“¬‰¥¢â Õß™“¬§πÀπ÷Ë߇æ‘Ë¡¢Èπ÷ 5% ‡¢“®–‰¥â‡ß‘π‡æ‘¡Ë ¢Èπ÷ 500 ∫“∑
.....................................................................................................................................
(8) º≈∫«°¢Õß¢π“¥¢Õß¡ÿ¡¿“¬„π¢Õß√Ÿª “¡‡À≈’ˬ¡√ªŸ Àπ÷ßË ¡ÿ¡·√°¡¢’ 𓥇ªπì Õ߇∑à“
¢Õß¡ÿ¡∑’ Ë Õß ·≈–¡¡ÿ ∑’ Ë “¡¡’¢π“¥‡ªπì “¡‡∑“à ¢Õß¡ÿ¡∑’Ë Õß
.....................................................................................................................................
3. º≈∫«°¢Õß®”π«π§àŸ 3 ®”π«π‡√¬’ ß°—π‡ªπì 114 ®ßÀ“®”π«π∑’ËπâÕ¬∑ ’Ë ÿ¥
«∏‘ ∑’ ” „À®â ”π«π§à∑Ÿ Ë’πâÕ¬∑Ë ’ ÿ¥‡ªìπ x
®”π«π§àŸÕ°’ Õß®”π«π∂¥— ‰ª§◊Õ xϩ2 ·≈– ...........................................................
‚®∑¬°å ”Àπ¥º≈∫«°¢Õß®”π«π§à∑Ÿ —Èß “¡®”π«π‡∑“à °—∫ ........................................
¡°“√§Õ◊ ...........................................................................................................
...........................................................................................................
...........................................................................................................
...........................................................................................................
¥ß— ππ—È ®”π«π∑Ëπ’ Õâ ¬∑ Ë’ ¥ÿ §Õ◊ 36
·∫∫Ω°ñ §≥μ‘ »“ μ√æå πÈ◊ ∞“π ¡.2 ¿“§‡√’¬π∑Ë’ 2 91
4. ®”π«π‡μÁ¡∫«° 5 ®”π«π‡√’¬ß°—π√«¡°—π‰¥â 120 ®ßÀ“º≈∫«°¢Õß®”π«π∑’Ë¡“°∑’Ë ÿ¥°—∫
®”π«π∑’πË âÕ¬∑ Ë’ ÿ¥
«∏‘ ∑’ ” „Àâ®”π«π‡μ¡Á ∫«°®”π«π∑ ’Ë “¡ (®”π«π°≈“ß) ‡ªπì x
®”π«π‡μ¡Á ∫«° 5 ®”π«π‡√’¬ß°—π §◊Õ ...................................................................
®”π«π∑Èß— À¡¥√«¡°—π‰¥â .......................................................................................
¡°“√§Õ◊ ...........................................................................................................
...........................................................................................................
...........................................................................................................
º≈∫«°¢Õß®”π«π¡“°∑Ë’ ¥ÿ °∫— ®”π«ππÕâ ¬∑ Ë’ ÿ¥§◊Õ
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
5. ®”π«π®”π«πÀπ÷Ëß¡’ ÕßÀ≈—° ´Ë÷ßμ—«‡≈¢„πÀ≈—°Àπ૬πâÕ¬°«à“μ—«‡≈¢„πÀ≈—° ‘∫Õ¬àŸ 4 ·μà
º≈μ“à ߢÕßμ«— ‡≈¢∑—Èß Õ߇ªìπ 1 ¢Õß®”π«ππÈ—π ®ßÀ“®”π«ππ—Èπ
21
«∏‘ ∑’ ” „ÀâÀ≈—° ∫‘ ‡ªìπ x
À≈—°Àπ«à ¬‡ªìπ .......................................................................................................
®”π«ππÈ—π§◊Õ .........................................................................................................
‚®∑¬å°”Àπ¥ º≈μ“à ߢÕßμ«— ‡≈¢∑ßÈ— Õ߇ªìπ 1 ¢Õß®”π«ππÈ—π
21
¡°“√§◊Õ ...........................................................................................................
...........................................................................................................
...........................................................................................................
...........................................................................................................
...........................................................................................................
μ—«‡≈¢„πÀ≈—° ‘∫§◊Õ ...............................................................................................
μ«— ‡≈¢„πÀ≈°— Àπ૬§Õ◊ ..........................................................................................
¥ß— ππ—È ®”π«ππÈπ— §◊Õ ..............................................................................................
92 ·∫∫Ω°ñ §≥μ‘ »“ μ√åæ◊Èπ∞“π ¡.2 ¿“§‡√¬’ π∑’Ë 2
6. ®”π«π Õß®”π«π√«¡°π— ‰¥â 105 ∂“â π”®”π«ππÕâ ¬‰ªÀ“√®”π«π¡“° ®–‰¥ºâ ≈≈æ— ∏å 7 ‡À≈Õ◊
‡»… 1 ®ßÀ“®”π«π¡“°
«∏‘ ∑’ ” „À®â ”π«π¡“°‡ªπì x
®”π«ππâÕ¬§Õ◊ .......................................................................................................
π”®”π«ππÕâ ¬‰ªÀ“√®”π«π¡“°®–‰¥ºâ ≈≈—æ∏å 7 ‡À≈Õ◊ ‡»… 1
¡°“√§Õ◊ ...........................................................................................................
...........................................................................................................
...........................................................................................................
...........................................................................................................
...............................................................................................................................
7. §«“¡¬“«¢Õߥâ“π∑È—ß “¡¢Õß√Ÿª “¡‡À≈ˬ’ ¡‡ªπì x, xϩ7, xϩ8 ‡´π쇑 ¡μ√ μ“¡≈”¥∫— ·≈–
‡ πâ √Õ∫√Ÿª¬“« 30 ‡´π쇑 ¡μ√ ®ßÀ“§«“¡¬“«¢Õߥ“â π∑È—ß “¡¢Õß√ªŸ “¡‡À≈ˬ’ ¡
«∏‘ ∑’ ”
xϩ7
x
xϩ8
„À¥â â“π∑—Èß “¡¢Õß√ªŸ “¡‡À≈¬’Ë ¡¬“« ................................................... ‡´π쑇¡μ√
‡ πâ √Õ∫√ªŸ ¬“« ..................................................................................... ‡´π쇑 ¡μ√
‚®∑¬å°”À𥇠πâ √Õ∫√ªŸ ¬“« ................................................................ ‡´π쇑 ¡μ√
¡°“√§Õ◊ ...........................................................................................................
...........................................................................................................
...........................................................................................................
¥—ßπÈ—π §«“¡¬“«¢Õߥâ“π∑ßÈ— “¡¢Õß√ªŸ “¡‡À≈¬’Ë ¡‡ªπì ........................................
............................................................................................ ‡´π쑇¡μ√ μ“¡≈”¥∫—
·∫∫Ωñ° §≥μ‘ »“ μ√åæÈπ◊ ∞“π ¡.2 ¿“§‡√¬’ π∑Ë’ 2 93
8. ¥â“π∑ Ë’ ÕߢÕß√Ÿª “¡‡À≈Ë’¬¡√ªŸ ÀπßË÷ È—π°«“à 2 ‡∑“à ¢Õߥâ“π∑’ËÀπßË÷ 5 ‡´π쇑 ¡μ√ ·≈–¥“â π∑Ë’
“¡¬“«°«à“¥“â π∑’ËÀπ÷Ëß 11 ‡´π쇑 ¡μ√ ∂“â §«“¡¬“«‡ πâ √Õ∫√Ÿª 54 ‡´π쇑 ¡μ√ ®ßÀ“§«“¡
¬“«·μà≈–¥â“π
«∏‘ ∑’ ”
x x ϩ 11
2x Ϫ 5
„Àâ¥â“π∑ß—È “¡¢Õß√ªŸ “¡‡À≈¬’Ë ¡¬“« ................................................... ‡´π쑇¡μ√
‡ πâ √Õ∫√ªŸ ¬“« ..................................................................................... ‡´π쇑 ¡μ√
‚®∑¬å°”À𥇠πâ √Õ∫√ªŸ ¬“« ................................................................ ‡´π쑇¡μ√
¡°“√§Õ◊ ...........................................................................................................
...........................................................................................................
...........................................................................................................
¥ß— πÈπ— §«“¡¬“«¢Õߥâ“π∑—ßÈ “¡¢Õß√Ÿª “¡‡À≈ˬ’ ¡‡ªìπ ........................................
............................................................................................ ‡´π쑇¡μ√ μ“¡≈”¥—∫
94 ·∫∫Ωñ° §≥µ‘ »“ µ√æå Èπ◊ ∞“π ¡.2 ¿“§‡√’¬π∑Ë’ 2
·∫∫∑¥ Õ∫º≈ ¡— ƒ∑∏∑Ï‘ “ß°“√‡√¬’ πª√–®”Àπ«à ¬
µÕπ∑Ë’ 1 „Àâπ°— ‡√¬’ π‡≈◊Õ°§”µÕ∫∑∂’Ë °Ÿ µâÕß
1. ∂â“ 2xϩ5 = 38Ϫx ·≈â« 1 xϩ1 ¡’§à“‡∑“à ‰√ 6. ∂â“ Ϫ7(2Ϫx)ϩ4x = 3(2xϪ3) ·≈â« x ¡’
11
1. 1 2. 2 §à“‡∑à“‰√
3. 3 4. 5
1. 1 2. 2
2. ∂â“ 2xϩ 1x = 15 ·≈«â x2Ϫ25 ¡§’ “à ‡∑“à ‰√ 3. 3 4. 4
33
7. ∂â“ 3(8xϩ5)Ϫ5x = xϪ(4xϪ7) ·≈â« x ¡’
1. 95 2. 100 §“à ‡∑“à ‰√
3. 200 4. 225 1. 0 2. 1
3. ∂â“ 7.5Ϫ0.3x = 2.5ϩ0.7x ·≈«â 1xϪ1 ¡’ 3. 3 4. 15
5
§à“‡∑“à ‰√ 8. ∂â“ 11ϪaϪ4a = 1(2Ϫ6a)ϩ3a ·≈«â a ¡’
1. 0 2. 1 2
3. 2 4. 3 §“à ‡∑à“‰√
1. Ϫ5 2. Ϫ3
3. 1 4. 2
4. ∂“â 24Ϫ3x = 4(3Ϫx)ϩ5x ·≈«â x ¡§’ “à ‡∑“à ‰√ 9. ∂“â 13bϪ3(3bϪ3) = 17 ·≈«â b ¡’§à“‡∑à“‰√
1. 1 2. 3 1. Ϫ3 2. 1
3. 4 4. 12
3. 2 4. 4
5. ∂“â 5(3Ϫ3x)Ϫ18 = Ϫ4(5xϪ3) ·≈â« x ¡’ 10. ∂“â 13xϪ3(xϩ5) = 15(1ϩx) ·≈â« x ¡’§à“
§à“‡∑à“‰√
‡∑à“‰√
1. 0 2. 1
3. 2 4. 3 1. 1 2. Ϫ3
3. Ϫ5 4. Ϫ6
·∫∫Ωñ° §≥‘µ»“ µ√åæπ◊È ∞“π ¡.2 ¿“§‡√¬’ π∑’Ë 2 95
µÕπ∑Ë’ 2 „Àπâ °— ‡√¬’ π·° â ¡°“√µàÕ‰ªπ’È
1. 2x Ϫ1 = 3xϩ5
5
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
2. x Ϫ 6 ϩx = 5x ϩ12
33
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
3. 7 Ϫ 1 (xϪ4) = 1 (xϩ1)
48
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
96 ·∫∫Ωñ° §≥‘µ»“ µ√åæÈ◊π∞“π ¡.2 ¿“§‡√’¬π∑’Ë 2
4. π“¡√ªŸ ‡’Ë À≈¬’Ë ¡º◊πºâ“¡¥’ â“𬓫¬“«°«“à ¥â“π°«â“ß 3 ‡¡µ√ ∂“â «—¥§«“¡¬“«√Õ∫ π“¡‰¥â
54 ‡¡µ√ ®ßÀ“æπ◊È ∑¢’Ë Õß π“¡
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
5. Àπ—ß ◊Õ‡≈à¡ÀπË÷ß¡’ 180 Àπâ“ Õà“π‰ª·≈⫇»… Õß à«πÀâ“¢Õß®”π«πÀπâ“∑È—ßÀ¡¥ ®ßÀ“
®”π«πÀπ“â ∑’ˬ—߉¡Õà “à π
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
............................................................................................................................................
The words you are searching are inside this book. To get more targeted content, please make full-text search by clicking here.
เพิ่มเติมม2เทอม2
Discover the best professional documents and content resources in AnyFlip Document Base.
Search
เพิ่มเติมม2เทอม2
- 1 - 23
Pages: