Question

solve the equation.
|x| = -27
use a comma to separate solutions, as needed. if there is no solution, type dne in the answer box.
x =
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Explanation:

Step1: Recall absolute value definition

The absolute value of a real number $|x|$ is defined as $|x| =

$$\begin{cases} x & \text{if } x \geq 0, \\ -x & \text{if } x < 0 \end{cases}$$

$, so $|x| \geq 0$ for all real $x$.

Step2: Compare to given equation

The equation is $|x| = -27$, but $-27 < 0$, which contradicts the property that absolute value is non-negative.

Answer:

DNE