1. **State the problem:** Solve the linear equation $$-5x - 7 = 13$$ for $$x$$. 2. **Write the formula and rules:** To solve for $$x$$, isolate $$x$$ by performing inverse operations step-by-step. 3. **Add 7 to both sides:** $$-5x - 7 + 7 = 13 + 7$$ $$-5x = 20$$ 4. **Divide both sides by $$-5$$ to isolate $$x$$:** $$x = \frac{20}{-5}$$ 5. **Simplify the fraction:** $$x = \frac{\cancel{20}}{\cancel{5}} \times \frac{1}{-1} = -4$$ 6. **Final answer:** $$x = -4$$