Question

solve for q and graph the solution.
12 ≥ q + 20 ≥ 4
plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, ray, or line to delete it.
-22 -20 -18 -16 -14 -12 -10 -8 -6

Explanation:

Step1: Subtract 20 from all parts

To solve the compound inequality \(12 \geq q + 20 \geq 4\), we subtract 20 from each part of the inequality. This is based on the property of inequalities that if we perform the same operation (subtraction of 20 here) on all parts of a compound inequality, the inequality relations remain valid.
So we have:
\(12 - 20 \geq q + 20 - 20 \geq 4 - 20\)

Step2: Simplify each part

Simplify the left - hand side: \(12-20=-8\)
Simplify the middle part: \(q + 20-20 = q\)
Simplify the right - hand side: \(4 - 20=-16\)
After simplification, the inequality becomes \(-8\geq q\geq - 16\) or we can rewrite it as \(-16\leq q\leq - 8\)

Answer:

The solution for \(q\) is \(-16\leq q\leq - 8\)