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Envision Math 2.0: Grade 7, Volume 1

EM

Envision Math 2.0: Grade 7, Volume 1 View details

Review

Exercise 2 Page 246

Remember, only like terms can be combined.

14x - 11y

Practice makes perfect

Before we try to simplify the given expression, let's use the Distributive Property so that we can get rid of the parentheses.

(6x - 2y - 5) - (- 5 + 9y - 8x)

Remove parentheses

6x - 2y - 5 - (- 5 + 9y - 8x)

Distribute - 1

6x - 2y - 5 + (- 1)(- 5) + (- 1)(9y) + (- 1)(- 8x)

MultNegNegOnePar

- a(- b)=a* b

6x - 2y - 5 + (1)(5) + (- 1)(9y) + (1)(8x)

a * 1=a

6x - 2y - 5 + 5 + (- 1)(9y) + 8x

(- a)b = - ab

6x - 2y - 5 + 5 + (- 9y) + 8x

a+(- b)=a-b

6x - 2y - 5 + 5 - 9y + 8x

To simplify this expression is to identify which, if any, terms can be combined. Remember, only like terms — constant terms or terms with the same variable — can be combined. 6x - 2y - 5 + 5 - 9y + 8x In this case, we have two x-terms, two y-terms and two constants. To simplify the expression we will rearrange it according to the Commutative Property of Addition and Associative Property of Addition.

6x - 2y - 5 + 5 - 9y + 8x

CommutativePropAdd

Commutative Property of Addition

6x + 8x - 2y - 9y - 5 + 5

AssociativePropAdd

Associative Property of Addition

(6x + 8x) +(- 2y - 9y) +(- 5 + 5)

Add terms

14x + (- 2y - 9y)

Subtract term

14x + (- 11y)

a+(- b)=a-b

14x - 11y

Subchapter links

Topic Essential Question p.243

Vocabulary Review p.243

Use Vocabulary in Writing p.243

1 Write and Evaluate Algebraic Expressions p.244

2-3 Generate Equivalent Expressions and Simplify Expressions p.244

4 Expand Expressions p.245

5 Factor Expressions p.245

6-7 Add and Subtract Expressions p.246

8 Analyze Equivalent Expressions p.246