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Chapter 1: Problem 119

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

Short Answer

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

Step by step solution

01

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.
02

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.
03

Formulating the Solution

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

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Most popular questions from this chapter

Writing in Mathematics What is a quadratic inequality?

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$5 \sqrt{-8}+3 \sqrt{-18}$$

Solve each rational inequality in Exercises \(29-48,\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ \frac{3}{x+3}>\frac{3}{x-2} $$

In Exercises \(21-28,\) divide and express the result in standard form. $$\frac{-6 i}{3+2 i}$$

In Exercises \(1-16,\) solve and check each linear equation. $$ 7 x-5=72 $$
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