## Algebra and Trigonometry 10th Edition

Published by Cengage Learning

# Prerequisites - P.1 - Review of Real Numbers and Their Properties - Exercises - Page 12: 47

#### Answer

$|x-5| \leq 3$ or $2 \leq x \leq 8$

#### Work Step by Step

To find the absolute value of a given expression we need to define what is the absolute value function. The absolute value of a number is its distance from the origin. |x| = 0 if x = 0; |x| = -x if x < 0; |x| = x if x > 0; The distance between x and 5 is |x-5| and since this distance is less than 3 implies $|x-5| \leq 3$

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