Question

module 6 lesson 3 practice
examples 1, 3, and 4
solve each compound inequality. then graph the solution set.

1. $f - 6 < 5$ and $f - 4 \geq 2$
2. $n + 2 \leq -5$ and $n + 6 \geq -6$
3. $y - 1 \geq 7$ or $y + 3 < -1$
4. $t + 14 \geq 15$ or $t - 9 < -10$
5. $-5 < 3p + 7 \leq 22$
6. $-3 \leq 7c + 4 < 18$
7. $5h - 4 \geq 6$ and $7h + 11 < 32$
8. $22 \geq 4m - 2$ or $5 - 3m \leq -13$

examples 5 and 6
rite a compound inequality that describes each graph.
(graphs: number lines with points at -3 (open), 3 (closed); -2 (open), 1 (closed); -2 (open); -1 (open))

Explanation:

Step1: Solve \( f - 6 < 5 \)

Add 6 to both sides: \( f - 6 + 6 < 5 + 6 \) → \( f < 11 \)

Step2: Solve \( f - 4 \geq 2 \)

Add 4 to both sides: \( f - 4 + 4 \geq 2 + 4 \) → \( f \geq 6 \)

Step3: Find the intersection

The solution is \( 6 \leq f < 11 \)

Answer:

\( 6 \leq f < 11 \)