Problem 141 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: Analyze the inequality

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

Step 3: 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 \(-\infty < x < \infty\).