Problem 119 - College Algebra

Question

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

Step-by-Step Solution

Answer

The solution set to the inequality \(|x|>-4\) is all real numbers, represented as (-∞, ∞).

Step 1: Understanding Absolute Values

Before jumping into the solution, it's crucial to understand what absolute values indicate. The absolute value of a number represents its distance from zero, regardless of direction. Therefore, it cannot be a negative number. It's denoted as \(|x|\) where x can be any real number.

Step 2: Applying Absolute Value Understanding to Problem

Since the absolute value can never be negative, that means \(|x|\) will always be more than -4. This makes every real number a valid answer.

Step 3: Formulating the Solution

As it was established in Step 2, every real number will satisfy this inequality. We can express this solution set as (-∞, ∞), which denotes the set of all real numbers.