Question

solve |x| = 2
x =
to give multiple answers, list your answers separated by a comma
question help: video

Explanation:

Step1: Recall absolute - value definition

The absolute - value of a number \(x\), \(|x|\), is defined as \(|x|=

$$\begin{cases}x, & x\geq0\\-x, & x < 0\end{cases}$$

\). If \(|x| = 2\), then we have two cases.

Step2: Case 1: When \(x\geq0\)

If \(x\geq0\), then \(|x|=x\). So, \(x = 2\) is a solution since when \(x = 2\), \(|2|=2\).

Step3: Case 2: When \(x<0\)

If \(x<0\), then \(|x|=-x\). Setting \(-x = 2\), we solve for \(x\) by multiplying both sides by \(- 1\) to get \(x=-2\). Since when \(x=-2\), \(|-2| = 2\).

Answer:

\(2,-2\)