Question

which number line represents the solutions to $-2|x| = -6$? (four number line options are shown, each with blue dots on different positions)

Explanation:

Step1: Solve the equation for \(|x|\)

We start with the equation \(-2|x| = -6\). To isolate \(|x|\), we divide both sides of the equation by \(-2\).
\[
\frac{-2|x|}{-2}=\frac{-6}{-2}
\]
Simplifying both sides, we get \(|x| = 3\).

Step2: Solve for \(x\) from the absolute - value equation

The absolute - value equation \(|x| = 3\) means that \(x\) can be either \(3\) or \(- 3\) because the absolute value of a number is its distance from \(0\) on the number line, and both \(3\) and \(-3\) are \(3\) units away from \(0\).

Step3: Identify the number line with solutions at - 3 and 3

We look at the number lines. The fourth number line has blue dots at \(-3\) and \(3\), which are the solutions to the equation \(-2|x|=-6\).

Answer:

The fourth number line (the one with blue dots at - 3 and 3)