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Envision Math 2.0: Grade 8, Volume 1

EM

Envision Math 2.0: Grade 8, Volume 1 View details

4. Equations with No Solutions or Infinitely Many Solutions

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Exercise 16 Page 109

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

One solution

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 inverse operations. In this case, we need to start by using the Distributive Property to simplify the left- and right-hand sides of the equation.

6(x+2)=5(x+7)

Distribute 6

6x+12=5(x+7)

Distribute 5

6x+12=5x+35

Now, we can continue to solve using inverse operations.

6x+12=5x+35

LHS-5x=RHS-5x

6x+12-5x=5x+35-5x

CommutativePropAdd

Commutative Property of Addition

6x-5x+12=5x-5x+35

Subtract terms

x+12=35

LHS-12=RHS-12

x+12-12=35-12

Subtract terms

x=23

The solution to the equation is x=23. Therefore, the equation has exactly one solution.

Subchapter links

Do You Understand? p.107

Do You Know How? p.107

Practice & Problem Solving p.108-110

Assessment Practice p.110