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Chapter 0: Problem 131

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

Short Answer

Expert verified
The solution set of the inequality \(|x|>-4\) is the set of all real numbers, or \(\mathbb{R}\).

Step by step solution

01

Understanding the inequality

The inequality in the question is \(|x|>-4\). It implies that the absolute value or magnitude of x is greater than -4. Since the absolute value (distance from zero) of any real number is always non-negative, this inequality holds true for all real numbers.
02

Visualizing on a number line

To better understand the solution, you may visualize it on a number line. Every real number is at a distance from zero that is greater than -4, so every point on the number line satisfies this inequality.
03

Writing the solution

Since any real number would satisfy this inequality, the solution set is the set of all real numbers which is generally noted as \(\mathbb{R}\).

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