1. **State the problem:** Solve for $x$ in the equation $x - 7(2x + 1) = 2(6 - 5x) - 13$. 2. **Write the equation and apply distributive property:** $$x - 7(2x + 1) = 2(6 - 5x) - 13$$ Distribute $-7$ and $2$: $$x - 14x - 7 = 12 - 10x - 13$$ 3. **Simplify both sides:** Left side: $x - 14x - 7 = -13x - 7$ Right side: $12 - 10x - 13 = -10x - 1$ 4. **Rewrite the simplified equation:** $$-13x - 7 = -10x - 1$$ 5. **Bring all $x$ terms to one side and constants to the other:** Add $13x$ to both sides: $$-13x - 7 + 13x = -10x - 1 + 13x$$ $$-7 = 3x - 1$$ Add $1$ to both sides: $$-7 + 1 = 3x - 1 + 1$$ $$-6 = 3x$$ 6. **Solve for $x$ by dividing both sides by 3:** $$x = \frac{-6}{3}$$ Show cancellation: $$x = \frac{\cancel{-6}}{\cancel{3}} = -2$$ 7. **Final answer:** $$\boxed{-2}$$