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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 21 Page 110

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

No 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 right-hand side of the equation.

6x+26x-10=8(4x+10)

Distribute 8

6x+26x-10=32x+80

Now, we can continue to solve using inverse operations.

6x+26x-10=32x+80

LHS+10=RHS+10

6x+26x-10+10=32x+80+10

Add and subtract terms

32x=32x+90

LHS-32x=RHS-32x

32x-32x=32x+90-32x

CommutativePropAdd

Commutative Property of Addition

32x-32x=32x-32x+90

Subtract terms

0≠ 90 *

Simplifying the equation resulted in a contradiction. Therefore, the equation has no solution.

Subchapter links

Do You Understand? p.107

Do You Know How? p.107

Practice & Problem Solving p.108-110

Assessment Practice p.110