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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 4 Page 107

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 left-hand side of the equation.

3(2.4x+4)=4.1x+7+3.1x

Distribute 3

7.2x+12=4.1x+7+3.1x

Now, we can continue to solve using inverse operations.

7.2x+12=4.1x+7+3.1x

LHS-7.2x=RHS-7.2x

7.2x+12-7.2x=4.1x+7+3.1x-7.2x

CommutativePropAdd

Commutative Property of Addition

7.2x-7.2x+12=4.1x+3.1x-7.2x+7

Add and subtract terms

12≠ 7 *

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