Question

the solution to $\frac{1}{2}|x + 6|-4>-1$ is $x < - 12$ or $x>0$. select the number line that represents the solution.

Explanation:

Step1: Analyze the solution set

The solution is $x < - 12$ or $x>0$. This means we need an open - circle at $x = - 12$ (since $x
eq - 12$) and the line goes to the left, and an open - circle at $x = 0$ (since $x
eq0$) and the line goes to the right.

Step2: Match with number - line options

We look for a number line with open - circles at $x=-12$ and $x = 0$ and arrows pointing left from $x=-12$ and right from $x = 0$.

Answer:

The second number line (from the top - left in the original image) which has open - circles at $x=-12$ and $x = 0$ and arrows pointing left from $x=-12$ and right from $x = 0$.