Question

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

option 1:
<---|---|---|---|---|---|---|---|---|---|---|---|---|--->
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
(blue dots at -6 and -2)

option 2:
<---|---|---|---|---|---|---|---|---|---|---|---|---|--->
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
(blue dots at 2 and 4)

option 3:
<---|---|---|---|---|---|---|---|---|---|---|---|---|--->
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
(blue dots at 2 and 6)

option 4:
<---|---|---|---|---|---|---|---|---|---|---|---|---|--->
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
(blue dots at -4 and -2)

Explanation:

Step1: Solve the absolute value equation

The equation is \(|x + 4| = 2\). By the definition of absolute value, this means \(x + 4 = 2\) or \(x + 4 = -2\).

Step2: Solve for \(x\) in each case

For \(x + 4 = 2\), subtract 4 from both sides: \(x = 2 - 4 = -2\).
For \(x + 4 = -2\), subtract 4 from both sides: \(x = -2 - 4 = -6\).
So the solutions are \(x = -6\) and \(x = -2\). Now we look at the number lines. The first number line has blue dots at -6 and -2, which matches our solutions.

Answer:

The first number line (with blue dots at -6 and -2)