Question

solve for q and graph the solution. 24 ≥ |q + 60| - 1 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: Isolate the absolute - value expression

Add 1 to both sides of the inequality $24\geq|q + 60|-1$.
$24+1\geq|q + 60|$, so $25\geq|q + 60|$, which can be written as $|q + 60|\leq25$.

Step2: Rewrite the absolute - value inequality as a compound inequality

If $|x|\leq a$ ($a\geq0$), then $-a\leq x\leq a$. Here $x = q + 60$ and $a = 25$, so $-25\leq q+60\leq25$.

Step3: Solve the compound inequality for $q$

Subtract 60 from all parts of the compound inequality:
$-25-60\leq q+60 - 60\leq25-60$.
$-85\leq q\leq - 35$.

To graph the solution on the number - line:

• The endpoints are $q=-85$ and $q = - 35$.
• Since the inequality is $\leq$, we use filled - in circles at $q=-85$ and $q=-35$.
• Then we draw a line segment between these two points.

Answer:

The solution of the inequality is $-85\leq q\leq - 35$. On the number - line, there are filled - in circles at $-85$ and $-35$ with a line segment connecting them.