1. **State the problem:** Solve the linear equation $$-(3x + 8) + 6 = -(7x - 9)$$ for $x$. 2. **Apply the distributive property:** Distribute the negative signs inside the parentheses. $$-(3x + 8) = -3x - 8$$ $$-(7x - 9) = -7x + 9$$ So the equation becomes: $$-3x - 8 + 6 = -7x + 9$$ 3. **Simplify both sides:** Combine like terms on the left side. $$-3x - 2 = -7x + 9$$ 4. **Isolate variable terms on one side:** Add $7x$ to both sides to bring all $x$ terms to the left. $$-3x + \cancel{7x} - 2 = \cancel{-7x} + 9 + 7x$$ Simplifies to: $$4x - 2 = 9$$ 5. **Isolate the constant term:** Add $2$ to both sides. $$4x - \cancel{2} + 2 = 9 + \cancel{2}$$ Simplifies to: $$4x = 11$$ 6. **Solve for $x$:** Divide both sides by $4$. $$\frac{4x}{\cancel{4}} = \frac{11}{\cancel{4}}$$ Simplifies to: $$x = \frac{11}{4}$$ **Final answer:** $$x = \frac{11}{4}$$