1. **State the problem:** Solve the inequality $$-6u - 17 \leq 7$$ for the variable $u$. 2. **Add 17 to both sides** to isolate the term with $u$: $$-6u - 17 + 17 \leq 7 + 17$$ which simplifies to $$-6u \leq 24$$ 3. **Divide both sides by -6** to solve for $u$. Remember, dividing by a negative number reverses the inequality sign: $$\frac{-6u}{\cancel{-6}} \geq \frac{24}{\cancel{-6}}$$ which simplifies to $$u \geq -4$$ 4. **Final answer:** $$u \geq -4$$ This means $u$ can be any number greater than or equal to $-4$.