4.2 ALGEBRA(SIMPLE ALGEBRAIC EQUATIONS)

UNIT 4 : ALGEBRA

4.2 SIMPLE ALGEBRAIC EQUATIONS

4.2 SIMPLE ALGEBRAIC EQUATIONS

A) Solving Single Variable Equations

A single variable equation is an equation in which
there is only one variable used.

Example : Solve the equation below.

1. x+2=6 x+2=6
x+2−2=6−2

x=4

x+2−2=6−2 substract 2 from both sides

x=4 simplify

Note : A one-step equation is an algebraic equation you can solve in only one
step. Once you've solved it, you've found the value of the variable that makes the

equation true.

4.2 SIMPLE ALGEBRAIC EQUATIONS

A) Solving Single Variable Equations

A single variable equation is an equation in which
there is only one variable used.

Example : Solve the equation below.

2. x-2=6 x+2=6
x+2−2=6−2

x=4

x-2+2=6+2 add 2 from both sides

x=8 simplify

Note : A one-step equation is an algebraic equation you can solve in only one
step. Once you've solved it, you've found the value of the variable that makes the

equation true.

4.2 SIMPLE ALGEBRAIC EQUATIONS

A) Solving Single Variable Equations

Example : Solve the equation below.

3. 2x = 6

2x = 6 divide 2 from both sides
2
2

x=3 simplify

Note : A one-step equation is an algebraic equation you can solve in only one
step. Once you've solved it, you've found the value of the variable that makes the

equation true.

4.2 SIMPLE ALGEBRAIC EQUATIONS

A) Solving Single Variable Equations

Example : Solve the equation below.

4. -2x = -6

= 2x 6
 2 divide -2 from both sides
2

x=3 simplify

Note : A one-step equation is an algebraic equation you can solve in only one
step. Once you've solved it, you've found the value of the variable that makes the

equation true.

4.2 SIMPLE ALGEBRAIC EQUATIONS

A) Solving Single Variable Equations

Example : Solve the equation below.

5. -2x = 6

= 2x 6 divide -2 from both sides
2
2

x=-3 simplify

Note : A one-step equation is an algebraic equation you can solve in only one
step. Once you've solved it, you've found the value of the variable that makes the

equation true.

4.2 SIMPLE ALGEBRAIC EQUATIONS

A) Solving Single Variable Equations
Example : Solve the equation below.

6. 3x + 2 = 8
3x + 2 - 2 = 8-2 substract 2 from both sides
3x = 6
3x = 6
divide 3 from both sides
33

x=2 simplify

Note : Two step math equations are algebraic problems that require you to make
two moves to find the value of the unknown variable.

4.2 SIMPLE ALGEBRAIC EQUATIONS

B) Solving Equations with Fraction Coefficient

Example : Solve the equation below.

1. x = 12

4

x  4 =12x4 multiply both sides by 4.

4

x=48 simplify

Note : A one-step equation is an algebraic equation you can solve in only one
step. Once you've solved it, you've found the value of the variable that makes the

equation true.

4.2 SIMPLE ALGEBRAIC EQUATIONS

B) Solving Equations with Fraction Coefficient

Example : Solve the equation below.

2.  x = 12

4

=12x-4x4 multiply both sides by -4.

4

x=-48 simplify

Note : A one-step equation is an algebraic equation you can solve in only one
step. Once you've solved it, you've found the value of the variable that makes the

equation true.

4.2 SIMPLE ALGEBRAIC EQUATIONS

B) Solving Equations with Fraction Coefficient

Example : Solve the equation below.

3.  x  12

x 4

 4  4   12  4 multiply both sides by -4.
simplify
x  48

Note : A one-step equation is an algebraic equation you can solve in only one
step. Once you've solved it, you've found the value of the variable that makes the

equation true.

4.2 SIMPLE ALGEBRAIC EQUATIONS

B) Solving Equations with Fraction Coefficient

Example : Solve the equation below.

4. 1 x  1  1
8 2 4

1 x  1  1  11 To isolate the x-term, substract
8 2 2 42 both sides by 1 .

1 x  1 2
8 4
1 simplify
(8  1 )x  4  8
8 multiply both sides by 8.
simplify
x 2

Note : Two / more steps math equations are algebraic problems that require
you to make two/more moves to find the value of the unknown variable.

4.2 SIMPLE ALGEBRAIC EQUATIONS

C)Solving Equation with Variable on Both Sides
Example : Solve the equation below.

1. 2x + 4 = x +12 substract 4 from both sides
2x + 4 - 4 = x+12-4
Substract x from both sides
2x = x+8 simplify
2x-x = x-x+8

x=8

Note : More step math equations are algebraic problems that require you to
make more moves to find the value of the unknown variable.

4.2 SIMPLE ALGEBRAIC EQUATIONS

C)Solving Equation with Variable on Both Sides
Example : Solve the equation below.

2. 2x - 3 = x -12 add 3 from both sides
2x - 3 + 3 = x-12+3
Substract x from both sides
2x = x-9 Simplify
2x-x = x-x-9

x=-9

Note : More step math equations are algebraic problems that require you to
make more moves to find the value of the unknown variable.

4.2 SIMPLE ALGEBRAIC EQUATIONS

C)Solving Equation with Variable on Both Sides
Example : Solve the equation below.

3. 2x + 3 = 12 - x
2x + 3 - 3 = 12-3-x substract 3 from both sides
2x = 9-x
2x+x = 9-x+x
Add x from both sides

3x=9
3x  9
divide both sides by 3.
33 Simplify

x 3
Note : More step math equations are algebraic problems that require you to
make more moves to find the value of the unknown variable.

4.2 SIMPLE ALGEBRAIC EQUATIONS
Exercise 4.2