Solve equations using the distributive property 

Learn to solve equations using the distributive property with the following three good examples. 

Example #1

Solve 2(x - 4) = 10 using the distributive property

2(x - 4) = 10

Use the distributive property

2x - 8 = 10

Isolate x by adding 8 to both sides of the equation

2x - 8 = 10

2x - 8 + 8 = 10 + 8

2x = 18

Divide each side by 2

2x/2 = 18/2

x = 9

Example #2

Solve 6(x - 2) = 2(9 - 2x) using the distributive property

6(x - 2) = 2(9 - 2x)

Use the distributive property

6x - 12 = 18 - 4x

Isolate x by adding 12 to both sides of the equations and by adding 4x to both sides of the equations.

6x + 4x - 12 + 12 = 18 + 12 - 4x + 4x 

6x + 4x = 18 + 12  

Simplify 

10x = 30

Divide both sides by 10

10x/10 = 30/10

x = 3

Example #3

Solve -2x + 4(x + 3) = 2(-3x + -6) using the distributive property

-2x + 4(x + 3) = 2(-3x + -6)

Use the distributive property

-2x + 4x + 12 = -6x + -12

Isolate x by subtracting 12 from each side of the equation and by adding 6x to both sides of the equation

-2x + 4x + 12 - 12 + 6x = -6x + 6x + -12 - 12

-2x + 4x + 6x = -12 - 12

Simplify

8x = -24

Divide both sides by 8

8x/8 = -24/8

x = -3