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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 18 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 right-hand side of the equation.

170x-1000=30(5x-30)

Distribute 30

170x-1000=150x-900

Now, we can continue to solve using inverse operations.

170x-1000=150x-900

LHS-150x=RHS-150x

170x-1000-150x=150x-900-150x

CommutativePropAdd

Commutative Property of Addition

170x-150x-1000=150x-150x-900

Subtract terms

20x-1000=- 900

LHS+1000=RHS+1000

20x-1000+1000=- 900+1000

Add terms

20x=100

.LHS /20.=.RHS /20.

20x/20=100/20

CancelCommonFac

Cancel out common factors

20x/20=100/20

Simplify quotient

x=100/20

Calculate quotient

x=5

The solution to the equation is x=5. 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