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 79E
To determine

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

Expert Solution

Answer to Problem 79E

  [1.3,1.7] .

Explanation of Solution

Given:

The given inequality is |2x3|0.4 .

Concept used:

Properties of absolute value inequalities:

    Inequality Equivalent formGraph
    |x|<cc<x<cPrecalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 79E , additional homework tip  1
    |x|ccxcPrecalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 79E , additional homework tip  2
    |x|>cx<c or c<xPrecalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 79E , additional homework tip  3
    |x|cxc or cxPrecalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 79E , additional homework tip  4

Calculation:

The given inequalityis |2x3|0.4 .

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

  0.42x30.4{add 3 on both the sides}2.62x3.4 .

  divide  both sides by 2}1.32x1.7i.ex[1.3,1.7]

Hence,the solution set is [1.3,1.7] .

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

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 79E , additional homework tip  5

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