Question

1. solve the compound inequality: $n - 10 \geq -20$ and $n + 1 \leq 6$

a. $-10 \leq n \leq 5$
b. $-4 < n < 9$
c. $n \geq -10$
d. $n > -4$

Explanation:

Step1: Solve \( n - 10 \geq -20 \)

Add 10 to both sides of the inequality:
\( n - 10 + 10 \geq -20 + 10 \)
\( n \geq -10 \)

Step2: Solve \( n + 1 \leq 6 \)

Subtract 1 from both sides of the inequality:
\( n + 1 - 1 \leq 6 - 1 \)
\( n \leq 5 \)

Step3: Find the intersection

The compound inequality requires both \( n \geq -10 \) and \( n \leq 5 \) to be true. So the solution is \( -10 \leq n \leq 5 \).

Answer:

A. \( -10 \leq n \leq 5 \)