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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

6. Solving Absolute Value Inequalities

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Exercise 40 Page 92

The solution set of an and compound inequality is the intersection of the solution sets of the individual inequalities.

Inequality: 6 Steps: See solution.

Practice makes perfect

We have been given a compound inequality that is composed of two absolute value inequalities. Let's start by rewriting and graphing each of the absolute value inequalities.

First Inequality

The first absolute value inequality can be rewritten as an and compound inequality. |x-3|<4 ⇒ -4

-4 < x-3 < 4

Add 3 to each expression

-4+3 < x-3+3 < 4+3

Add terms

-1 < x <7

We can graph this solution set on a number line.

Second Inequality

The second absolute value inequality can be rewritten as an or compound inequality. |x+2|>8 ⇒ x+2>8 or x+2<-8 Let's solve this inequality!

x+2>8 or x+2<-8

Subtract 2 from each expression

x+2-2>8-2 or x+2-2<-8-2

Subtract terms

x>6 or x<-10

We can graph this solution on a number line.

Compound Inequality

To find the solution set of the compound inequality, we can graph both solution sets on the same number line.

Since the compound inequality is an and compound inequality, the solution set to the compound inequality is the intersection of the solution sets of the absolute value inequalities.

The solution set is the overlapping interval between 6 and 7. 6 < x < 7

Subchapter links

Communicate Your Answer p.87

Monitoring Progress p.89-90

Exercises p.91-92