Question

solve for q and graph the solution.
5 ≤ |q + 5|
click two endpoints to graph a line segment, an endpoint and an arrowhead to graph a ray, or two arrowheads to graph a line. to change endpoints from filled - in circles to empty circles, click on them.

Explanation:

Step1: Split absolute - value inequality

We know that if $5\leq|q + 5|$, then $q+5\geq5$ or $q + 5\leq - 5$.

Step2: Solve $q+5\geq5$

Subtract 5 from both sides: $q+5 - 5\geq5 - 5$, so $q\geq0$.

Step3: Solve $q + 5\leq - 5$

Subtract 5 from both sides: $q+5 - 5\leq-5 - 5$, so $q\leq - 10$.

Answer:

The solution is $q\leq - 10$ or $q\geq0$. On the number - line, we graph a ray starting at $q=-10$ with a filled - in circle (since the inequality is $\leq$) and going to the left, and a ray starting at $q = 0$ with a filled - in circle (since the inequality is $\geq$) and going to the right.