Question

1. $f - 6 < 5$ and $f - 4 \geq 2$
2. $y - 1 \geq 7$ or $y + 3 < -1$
3. $-5 < 3p + 7 \leq 22$

Explanation:

Step1: Solve the left inequality

Subtract 7 from all parts of the compound inequality \(-5 < 3p + 7 \leq 22\).
We get \(-5 - 7 < 3p + 7 - 7 \leq 22 - 7\), which simplifies to \(-12 < 3p \leq 15\).

Step2: Solve for \(p\)

Divide all parts of the inequality \(-12 < 3p \leq 15\) by 3.
We have \(\frac{-12}{3} < \frac{3p}{3} \leq \frac{15}{3}\), which simplifies to \(-4 < p \leq 5\).

Answer:

\(-4 < p \leq 5\)