PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Chapter P.7, Problem 45E
Solution

The solution set of the absolute value inequality x2≤1 .

  D. −1,1

Given:

The absolute value inequality x2≤1 .

Concept used:

  • Absolute value inequality states that, if x<a , then the solutions are −a<x<a .
  • The value of an absolute value function is always greater than or equal to 0.
  • If there is the strict inequality symbol < or> , then use a parenthesis on the interval
  • If there is the inequality symbol ≤ or≥ , then use a bracket on the interval
  • To graph the endpoint with strict inequality < or> , use the open parenthesis or a hollow circle at that endpoint.
  • To graph the endpoint with inequality symbol ≤ or≥ , use the bracket or a solid circle at that endpoint.
  • Multiplying or dividing an inequality by a negative number reverse the inequality sign.

Calculation:

In order to solve the given absolute value inequality, use the definition of absolute value function and simplify further as shown below

  x2≤1x2−1≤1−1x2−1≤0x+1x−1≤0⇒x≥−1 or x≤1

Thus, the solution set of the given absolute value inequality is −1,1 .

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Chapter P.7, Problem 44E
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Chapter P.7, Problem 46E

Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

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