Question: Solve $2 < \frac{q-6}{5} \leq 7$
1. **State the problem:** Solve the compound inequality $$2 < \frac{q-6}{5} \leq 7$$ for $q$.
2. **Recall the rule:** To solve inequalities involving fractions, multiply all parts of the inequality by the denominator (if positive) to eliminate the fraction without changing inequality directions.
3. Multiply all parts by $5$ (positive, so inequality signs remain):
$$2 \times 5 < \frac{q-6}{5} \times 5 \leq 7 \times 5$$
which simplifies to
$$10 < q - 6 \leq 35$$
4. Add $6$ to all parts to isolate $q$:
$$10 + 6 < q - 6 + 6 \leq 35 + 6$$
$$16 < q \leq 41$$
5. **Final solution:**
$$\boxed{16 < q \leq 41}$$
This means $q$ is greater than $16$ and less than or equal to $41$.