Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition
Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition
10th Edition
ISBN: 9780134673301
Author: Waits, Foley, Kennedy, Bock Demana
Publisher: PEARSON
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Chapter P.7, Problem 42E
Solution

The solution set of the absolute value inequality x−2<3 .

  E. −1,5

Given:

The absolute value inequality x−2<3 .

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

  x−2<3−3<x−2<3−3+2<x−2+2<3+2−1<x<5

Thus, the solution set of the given absolute value inequality is −1,5 .

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Chapter P.7, Problem 41E
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Chapter P.7, Problem 43E

Chapter P Solutions

Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition

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