Question

1. -24 ≤ -2x - 10 < -22
2. 10 - 8x ≥ 58 or 9 - 4x ≤ -11

Explanation:

Step1: Solve the compound - inequality $-24\leq - 2x-10\lt - 22$

Add 10 to all parts of the inequality:
$-24 + 10\leq-2x-10 + 10\lt-22 + 10$
$-14\leq-2x\lt - 12$
Divide all parts by - 2. Remember to reverse the inequality signs when dividing by a negative number:
$\frac{-14}{-2}\geq\frac{-2x}{-2}>\frac{-12}{-2}$
$7\geq x>6$

Step2: Solve the compound - inequality $10 - 8x\geq58$ or $9 - 4x\leq - 11$

For $10 - 8x\geq58$:
Subtract 10 from both sides:
$10-10 - 8x\geq58 - 10$
$-8x\geq48$
Divide both sides by - 8 and reverse the inequality sign:
$x\leq - 6$
For $9 - 4x\leq - 11$:
Subtract 9 from both sides:
$9-9 - 4x\leq-11 - 9$
$-4x\leq - 20$
Divide both sides by - 4 and reverse the inequality sign:
$x\geq5$

Answer:

The solution to $-24\leq - 2x-10\lt - 22$ is $6 < x\leq7$. The solution to $10 - 8x\geq58$ or $9 - 4x\leq - 11$ is $x\leq - 6$ or $x\geq5$.