Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Jan 22, 2024

Solve the absolute value equation $-3|x| = 15$ to find the value of $x$ .

STEP 1

Assumptions
1. We are given the equation $-3|x| = 15$ .
2. We need to solve for the variable $x$ .
3. The absolute value function $|x|$ yields a non-negative result for any real number $x$ .

STEP 2

First, we need to isolate the absolute value expression by dividing both sides of the equation by $-3$ .
$\frac{-3|x|}{-3} = \frac{15}{-3}$

STEP 3

Perform the division to simplify the equation.
$|x| = -5$

STEP 4

Recognize that the absolute value of any real number is always non-negative. Therefore, the equation $|x| = -5$ has no solution because the absolute value cannot equal a negative number.
The solution to the equation $-3|x| = 15$ is that there is no real number $x$ that satisfies the equation.

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