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 87E
To determine

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

Expert Solution

Answer to Problem 87E

  x[12,32] .

Explanation of Solution

Given:

The given inequality is 8|2x1|6 .

Concept used:

Properties of absolute value inequalities:

    Inequality Equivalent formGraph
    |x|<cc<x<cPrecalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 87E , additional homework tip  1
    |x|ccxcPrecalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 87E , additional homework tip  2
    |x|>cx<c or c<xPrecalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 87E , additional homework tip  3
    |x|cxc or cxPrecalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 87E , additional homework tip  4

Calculation:

The given inequality can be expressed as

  8|2x1|6{isolate the absolute value}|2x1|86|2x1|2

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

  22x12{add 1 on both the sides}12x3divide  both sides by 2}12x32i.ex[12,32] .

Hence,the solution set is x[12,32] .

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

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 87E , additional homework tip  5

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