1. **State the problem:** Solve the linear equation $$-4(-6u+6) - 5u = 7(u-1) - 2$$ for the variable $u$. 2. **Apply the distributive property:** Multiply inside the parentheses. $$-4(-6u+6) = -4 \times -6u + (-4) \times 6 = 24u - 24$$ $$7(u-1) = 7u - 7$$ So the equation becomes: $$24u - 24 - 5u = 7u - 7 - 2$$ 3. **Combine like terms on each side:** Left side: $$24u - 5u = 19u$$ Right side: $$-7 - 2 = -9$$ So the equation is: $$19u - 24 = 7u - 9$$ 4. **Isolate variable terms on one side and constants on the other:** Subtract $7u$ from both sides: $$19u - \cancel{7u} - 24 = \cancel{7u} - 9 - 7u$$ which simplifies to: $$12u - 24 = -9$$ Add 24 to both sides: $$12u - 24 + 24 = -9 + 24$$ which simplifies to: $$12u = 15$$ 5. **Solve for $u$ by dividing both sides by 12:** $$u = \frac{15}{12}$$ Simplify the fraction by dividing numerator and denominator by 3: $$u = \frac{\cancel{15}^5}{\cancel{12}^4}$$ 6. **Final answer:** $$u = \frac{5}{4}$$