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 86E
To determine

To solve: the absolute value inequality. Express the solution using interval notation and graph the solution set.

Expert Solution

Answer to Problem 86E

  x(,3][1,) .

Explanation of Solution

Given:

The given inequality is 3|2x+4|1 .

Concept used:

Properties of absolute value inequalities:

    Inequality Equivalent formGraph
    |x|<cc<x<cPrecalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 86E , additional homework tip  1
    |x|ccxcPrecalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 86E , additional homework tip  2
    |x|>cx<c or c<xPrecalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 86E , additional homework tip  3
    |x|cxc or cxPrecalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 86E , additional homework tip  4

Calculation:

The given inequalitycan be expressed as

  3|2x+4|1{isolate the absolute value}|2x+4|31|2x+4|2

According to the properties of absolute value inequalities, the given inequality is expressed as

  2x+42or2x+42{subtract both sides by 4}2x2or2x6{divide both sides by 2}x1orx3i.ex(,3][1,)

Hence,the solution set is x(,3][1,) .

The solution set of the inequality graphed on the number line.

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 86E , additional homework tip  5

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