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Chapter 1: Problem 141

Describe the solution set of \(|x|>-4\).

Short Answer

Expert verified
The solution set of \(|x|>-4\) is all real numbers, represented as \(-\infty < x < \infty\).

Step by step solution

01

Understand the absolute value

The absolute value of any number, including x, is its distance from zero. It is always positive or zero, and never negative.
02

Analyze the inequality

The exercise asks for \(|x|>-4\). Since the absolute value is never negative, it's always greater than any negative number.
03

Formulate the solution set

Since the absolute value of x is always greater than -4 (and any other negative number), all real numbers are part of the solution. This can be represented as \(-\infty < x < \infty\).

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