Question

linear equations and inequalities
which number line represents the solutions to -2|x| = -6?

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 \(x\) is a number whose distance from 0 on the number line is 3. By the definition of absolute value, if \(|x|=a\) (\(a\geq0\)), then \(x = a\) or \(x=-a\). So, when \(|x| = 3\), we have \(x = 3\) or \(x=-3\).

Step3: Analyze the number - line representation

The solutions to the equation are \(x = 3\) and \(x=-3\). So, the number line that represents the solutions should have points marked at \(-3\) and \(3\).

Answer:

The number line with points marked at \(-3\) and \(3\) (assuming the number lines are labeled with integers and have marks at \(-3\) and \(3\))