1. **State the problem:** Solve for $x$ in the equation $$-x - (-7x - 4) = 8x + 6(-x + 5).$$ 2. **Apply the distributive property and remove parentheses:** $$-x + 7x + 4 = 8x + 6(-x) + 6(5)$$ 3. **Simplify both sides:** $$(-x + 7x) + 4 = 8x - 6x + 30$$ $$6x + 4 = 2x + 30$$ 4. **Isolate variable terms on one side and constants on the other:** $$6x - 2x = 30 - 4$$ 5. **Simplify both sides:** $$4x = 26$$ 6. **Solve for $x$ by dividing both sides by 4:** $$x = \frac{26}{4}$$ 7. **Simplify the fraction by canceling common factors:** $$x = \frac{\cancel{26}^{13}}{\cancel{4}^{2}} = \frac{13}{2}$$ **Final answer:** $$x = \frac{13}{2}$$