# Show that |b | \leq a if and only if -a \leq b \leq a

## Question:

Show that {eq}|b | \leq a {/eq} if and only if {eq}-a \leq b \leq a {/eq}

## Absolute Value:

The definition of absolute value tells us that the absolute value of a positive number is the number itself and if it is negative it is the opposite value.

That is to say:

{eq}\left| b \right| = \left\{ \begin{array}{l} - b\quad b < 0\\ b\quad b \ge 0 \end{array} \right. {/eq}

## Answer and Explanation:

Remembering the definition of absolute value:

{eq}\left| b \right| = \left\{ \begin{array}{l} - b\quad b < 0\\ b\quad b \ge 0 \end{array}...

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The Absolute-Value Inequality: Definition & Example

from Remedial Algebra I

Chapter 25 / Lesson 9
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