Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Jan 22, 2024

Find the absolute value of $w$ given $|w| = 5$ .

STEP 1

Assumptions
1. We are given the absolute value equation $|w| = 5$ .
2. We need to solve for the variable $w$ .

STEP 2

Understand the definition of absolute value. The absolute value of a number is its distance from zero on the number line, without considering direction. Therefore, the absolute value of a number is always non-negative.
$|x| = \begin{cases} x & \text{if } x \geq 0 \\ -x & \text{if } x < 0 \end{cases}$

STEP 3

Apply the definition of absolute value to the given equation. Since $|w| = 5$ , $w$ can be either $5$ or $-5$ because both numbers are at a distance of $5$ from zero on the number line.

STEP 4

Write down the two possible equations that come from the absolute value equation.
$w = 5 \quad \text{or} \quad w = -5$

STEP 5

Conclude that the solution to the equation $|w| = 5$ is $w = 5$ or $w = -5$ .
The solution to the equation is $w = 5$ or $w = -5$ .

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