BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.7, Problem 98E
To determine

To find:an inequality involving an absolute value that describes the sets.

Expert Solution

Answer to Problem 98E

  |x+2|>1 .

Explanation of Solution

Given:

A set of real number is graphed on the number line:

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 98E , additional homework tip  1

Concept used:

Properties of absolute value inequalities:

    Inequality Equivalent formGraph
    |x|<cc<x<cPrecalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 98E , additional homework tip  2
    |x|ccxcPrecalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 98E , additional homework tip  3
    |x|>cx<c or c<xPrecalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 98E , additional homework tip  4
    |x|cxc or cxPrecalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 98E , additional homework tip  5

Calculation:

According to the properties of absolute value inequalities, theequivalent form of the given set of real number is

  x<3 or 1<x{add 2 on both the sides}x+3<0 or 2<x+3|x+2|<1or |x+2|>1|x+2|>1

Therefore, the inequality is |x+2|>1

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