1. **State the problem:** Solve the equation $$-6x - 7 = 17$$ for $x$. 2. **Add 7 to both sides** to isolate the term with $x$: $$-6x - 7 + 7 = 17 + 7$$ $$-6x = 24$$ 3. **Divide both sides by -6** to solve for $x$: $$\cancel{-6}x \div \cancel{-6} = \frac{24}{-6}$$ $$x = -4$$ 4. **Final answer:** $$x = -4$$ This means the value of $x$ that satisfies the equation is $-4$.