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Chapter 1: Problem 60

Solve each absolute value inequality. $$|x|<5$$

Short Answer

Expert verified
The solution to the inequality is \( -5 < x < 5 \).

Step by step solution

01

Rewrite as a compound inequality

First, an absolute value inequality \( |x| < 5 \) is equivalent to an inequality -5 < x < 5. This is because the absolute value of a number is the distance of the number from zero on a number line, and all points x within 5 units of zero can be written as -5 < x < 5.
02

Solve the inequality

The inequality -5 < x < 5 does not require any further steps to solve. The solution is just that x can be any number that is larger than -5 and less than 5.

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