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Big Ideas Math: Modeling Real Life, Grade 7

BI

Big Ideas Math: Modeling Real Life, Grade 7 View details

5. Solving Inequalities Using Addition or Subtraction

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Exercise 3 Page 152

Use the Addition Property of Inequality.

Solution: z < - 1/4
Graph:

Practice makes perfect

Inequalities can be solved in the same way as equations, by performing inverse operations on both sides until the variable is isolated. Let's use the Addition Property of Inequality to solve the inequality.

- 1/2 > z - 1/4

LHS+1/4>RHS+1/4

- 1/2 + 1/4 > z - 1/4 + 1/4

a/b=a * 2/b * 2

- 2/4 + 1/4 > z

Add terms

- 1/4 > z

Rearrange inequality

z < - 1/4

The above tells us that all values of z that are less than - 14 will satisfy the inequality. Below we demonstrate the inequality by graphing the solution set on a number line. Notice that z can not equal - 14, which we show with an opened circle on the number line.

Subchapter links

Try It p.152-153

Self-Assessment for Concept & Skills p.153

Self-Assessment for Problem Solving p.154

Review & Refresh p.155

Concept, Skills, & Problem Solving p.155-156