which number line represents the solutions to |x - 5| = 1?

Explanation:

Step1: Recall absolute - value definition

The equation (|x - 5|=1) means (x−5 = 1) or (x−5=-1).

Step2: Solve (x−5 = 1)

Add 5 to both sides: (x=1 + 5=6).

Step3: Solve (x−5=-1)

Add 5 to both sides: (x=-1 + 5 = 4).

Answer:

The number line with points at (x = 4) and (x = 6) (the second number - line in the given options where points are at 4 and 6 on the number line).