Math 7 (Period 4)

Solving Equations Using the Distributive Property 4.4

You may need to use the Distributive Property in solving some equations.

Solve

 5y + 2(y-3) = 92

Use the distributive property to obtain

5y + 2y – 6 = 92

Combine like terms

7y – 6 = 92

Add six to both sides

7y = 98

 

y = 14

Solve 13 = 4(3x-7) +5

Again use the Distributive Property

13 = 12x – 28 + 5

Combine like terms

13 = 12x – 23

You will need to add 23 to both sides

36 = 12x

3= x

Solving with a Negative Coefficient

3 –(x-2) = 4

First realize this is really

3 -1(x-2) =4

In Algebra we call this The Inverse Property of a SUM. When you distribute the negative 1, everything inside the parentheses becomes it’s opposite.

So 3 -1(x-2) =4 becomes

3 –x + 2 = 4

Combine like terms

5 –x = 4

Using the methods from our previous lesson,

you could add x to bother sides, first

5 =4 + x

1 = x

Solving a multi-step problem often using the Distributive Property as well.