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

Explanation:

Step1: Solve the absolute - value equation

Given (|x + 4|=2). By the definition of absolute value, if (|a| = b) ((b\geq0)), then (a=b) or (a=-b). So (x + 4=2) or (x + 4=-2).

Step2: Solve (x + 4=2)

Subtract 4 from both sides of the equation (x+4 = 2). We get (x=2 - 4=-2).

Step3: Solve (x + 4=-2)

Subtract 4 from both sides of the equation (x + 4=-2). We get (x=-2-4=-6).

Answer:

The number line with blue dots at (-6) and (-2) (the first option in the given number - line choices) represents the solutions.