Compound Inequality Bdbdbc

1. **State the problem:** Solve the compound inequality $$12 \leq \frac{x}{4} + 8 \leq 20$$. 2. **Isolate the variable term:** Subtract 8 from all parts of the inequality: $$12 - 8 \leq \frac{x}{4} + 8 - 8 \leq 20 - 8$$ which simplifies to $$4 \leq \frac{x}{4} \leq 12$$. 3. **Eliminate the fraction:** Multiply all parts of the inequality by 4 to solve for $x$: $$4 \times 4 \leq \frac{x}{4} \times 4 \leq 12 \times 4$$ which is $$16 \leq x \leq 48$$. 4. **Final answer:** The solution to the inequality is $$\boxed{16 \leq x \leq 48}$$. This means $x$ can be any number between 16 and 48, inclusive.