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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 24 Page 110

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

B

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-hand side of the equation.

4(2x+3)=16x+12-8x

Distribute 4

8x+12=16x+12-8x

CommutativePropAdd

Commutative Property of Addition

8x+12=16x-8x+12

Subtract term

8x+12=8x+12

We can see that both sides of the equation are the same. Simplifying the equation resulted in an identity. Therefore, the equation has infinitely many solutions. This corresponds to option B.

Subchapter links

Do You Understand? p.107

Do You Know How? p.107

Practice & Problem Solving p.108-110

Assessment Practice p.110