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 74E
To determine

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

Expert Solution

Answer to Problem 74E

  x(5,5) .

Explanation of Solution

Given:

The given inequality is |3x|<15 .

Concept used:

Properties of absolute value inequalities:

    Inequality Equivalent formGraph
    |x|<cc<x<cPrecalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 74E , additional homework tip  1
    |x|ccxcPrecalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 74E , additional homework tip  2
    |x|>cx<c or c<xPrecalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 74E , additional homework tip  3
    |x|cxc or cxPrecalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 74E , additional homework tip  4

Calculation:

The given inequalityis expressed as

  |3x3|<153{divide both side by 3}|x|<5

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

  5<x5i.ex(5,5) .

Hence,the solution set is x(5,5) .

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

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.7, Problem 74E , additional homework tip  5

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!