Question

which number line represents the solutions to |x + 4| = 2?

Explanation:

Step1: Recall absolute - value property

If \(|a| = b\) (\(b\geq0\)), then \(a = b\) or \(a=-b\). So for \(|x + 4|=2\), we have \(x + 4=2\) or \(x + 4=-2\).

Step2: Solve \(x + 4=2\)

Subtract 4 from both sides: \(x=2 - 4=-2\).

Step3: Solve \(x + 4=-2\)

Subtract 4 from both sides: \(x=-2 - 4=-6\).

Answer:

The number line with points at -6 and -2 represents the solutions. So the first number - line (with points at -6 and -2) is the correct one.