Digits, Grade 8, Volume 2, Homework Helper

# Unit G: Step-Up Lessons

## Topic 15: Step-Up Lessons

### 15-1: Solving Equations Using the Distributive Property

#### Part 1

Intro

You can use the Distributive Property to simplify the expressions a(b+c) and a(b−c), where a, b, and c are numbers.

table with 1 row and 3 columns , row1 column 1 , eh . open . b plus c . close . equals eh middle dot b plus eh middle dot c , column 2 , column 3 eh . open . b minus c . close . equals eh middle dot b minus eh middle dot c , end table

Some equations are easier to solve if you use the Distributive Property to simplify them.

Example Using the Distributive Property to Solve Equations

Use the Distributive Property to solve 4(8−c)=8c+16−6c.

Solution

table with 9 rows and 3 columns , row1 column 1 , cap usethecap distributivecap property. , column 2 4 , open 8 close , minus 4 , open c close , column 3 equals 8 c plus 16 minus 6 c , row2 column 1 , cap multiply , . , column 2 32 minus 4 c , column 3 equals 8 c plus 16 minus 6 c , row3 column 1 , cap combine . like , , terms , . , column 2 32 minus 4 c , column 3 equals 2 c plus 16 , row4 column 1 , cap add 4 bold italic c . toeachside. , column 2 32 minus 4 c plus 4 c , column 3 equals 2 c plus 4 c plus 16 , row5 column 1 , cap combineliketerms. , column 2 32 , column 3 equals 6 c plus 16 , row6 column 1 , cap subtract16fromeachside. , column 2 32 minus 16 , column 3 equals 6 c plus 16 minus 16 , row7 column 1 , cap simplify. , column 2 16 , column 3 equals 6 c , row8 column 1 , cap divideeachsideby6. , column 2 fraction 16 , over 6 end fraction , column 3 equals , fraction 6 c , over 6 end fraction , row9 column 1 , cap simplify. , column 2 fraction 8 , over 3 end fraction , column 3 equals c , end table

When 4 open 8 minus c close equals 8 c plus 16 minus 6 c comma c equals , 8 thirds .

Check

table with 5 rows and 2 columns , row1 column 1 , 4 . open . 8 minus c . close , column 2 equals 8 c plus 16 minus 6 c , row2 column 1 , 4 . open . 8 minus , 8 thirds . close , column 2 modified modified question mark with under bar below with under bar below , 8 . open , 8 thirds , close . plus 16 minus 6 . open , 8 thirds , close , row3 column 1 , 4 . open , 16 over 3 , close , column 2 modified modified question mark with under bar below with under bar below , , 64 over 3 , plus 16 minus , 48 over 3 , row4 column 1 , 64 , column 2 modified modified question mark with under bar below with under bar below , 64 plus 48 minus 48 , row5 column 1 , 64 , column 2 equals 64 u 2 , end table

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