Chapter 1: Q1. (page 30)

Explain why the absolute value of a number is always nonnegative, $| a |$ can equal $- a$ .

Short Answer

Expert verified

The absolute value of a number is always nonnegative.

Step by step solution

Step 1- Apply the concept of absolute value.

Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

Step 2- Step description.

Let $x \in ℝ$ be a real number, then its absolute value is denoted by $| x |$ and defined as $| x | = {\begin{matrix} x & x \geq 0 \\ - x & x < 0 \end{matrix}$

Step 3- Step description.

The absolute value of a negative numbers is $| - x | = x$

For example: The absolute value of some negative numbers is as follows:

$\begin{array}{l} | - 4 | = 4 \\ | - 10 | = 10 \\ | - 152 | = 152 \end{array}$

Therefore, the absolute value of a number is always nonnegative..

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Explain why the absolute value of a number is always nonnegative, $| a |$ can equal $- a$ .

Short Answer

Step by step solution

Step 1- Apply the concept of absolute value.

Step 2- Step description.

Step 3- Step description.

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Explain why the absolute value of a number is always nonnegative, |a|can equal -a.

Short Answer

Step by step solution

Step 1- Apply the concept of absolute value.

Step 2- Step description.

Step 3- Step description.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

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Pure Maths

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Study anywhere. Anytime. Across all devices.

Explain why the absolute value of a number is always nonnegative, $| a |$ can equal $- a$ .