Question

solve for q and graph the solution.
524 ≥ 3|5q + 825| - 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.
← -200 -190 -180 -170 -160 -150 -140 -130 -120 -110 -100 -90 -80 →

Explanation:

Step1: Isolate the absolute value

Add 1 to both sides: $524 + 1 \geq 3|5q + 825|$
$525 \geq 3|5q + 825|$

Step2: Divide by 3

Divide both sides by 3: $\frac{525}{3} \geq |5q + 825|$
$175 \geq |5q + 825|$

Step3: Rewrite as compound inequality

This is equivalent to $-175 \leq 5q + 825 \leq 175$

Step4: Subtract 825

Subtract 825 from all parts: $-175 - 825 \leq 5q \leq 175 - 825$
$-1000 \leq 5q \leq -650$

Step5: Divide by 5

Divide all parts by 5: $\frac{-1000}{5} \leq q \leq \frac{-650}{5}$
$-200 \leq q \leq -130$

Answer:

The solution for \( q \) is \( -200 \leq q \leq -130 \). To graph, plot a line segment with filled - in circles at \( -200 \) and \( -130 \) on the number line.