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Envision Math 2.0: Grade 8, Volume 1

EM

Envision Math 2.0: Grade 8, Volume 1 View details

Review

Exercise 2 Page 149

Gather all of the variable terms on one side of the equation and all of the constant terms on the other side.

x=27/11

Practice makes perfect

To solve an equation, we should first gather all of the variable terms on one side and all of the constant terms on the other side using the Properties of Equality. In this case, we need to start by using the Distributive Property to simplify the left-hand side of the equation.

8(2x+3x+2)=- 4x+124

Distribute 8

16x+24x+16=- 4x+124

Now, we can continue to solve using the Properties of Equality.

16x+24x+16=- 4x+124

LHS+4x=RHS+4x

16x+24x+16+4x=- 4x+124+4x

CommutativePropAdd

Commutative Property of Addition

16x+24x+4x+16=- 4x+4x+124

Add and subtract terms

44x+16=124

LHS-16=RHS-16

44x+16-16=124-16

Subtract terms

44x=108

.LHS /44.=.RHS /44.

44x/44=108/44

CancelCommonFac

Cancel out common factors

44x/44=108/44

Simplify quotient

x=108/44

a/b=.a /4./.b /4.

x=27/11

The solution to the equation is x= 2711.

Subchapter links

Topic Essential Questions p.147

Vocabulary Review p.147

Use Vocabulary in Writing p.147

1 Combine Like Terms to Solve Equations p.148

2 Solve Equations with Variables on Both Sides p.148

3 Solve Multistep Equations p.149

4 Equations with No Solutions or Infinitely Many Solutions p.149

5 Compare Proportional Relationships p.150

6 Connect Proportional Relationships and Slope p.151

7 Analyze Linear Equations: y=mx p.151

8 Understand the y-Intercept of a Line p.152

9 Analyze Linear Equations: y=mx+b p.152