1. **State the problem:** Solve the linear equation $$-(8w - 3) + 2 = 4 + w - 4$$ for $w$. 2. **Apply the distributive property:** The negative sign before the parentheses means we distribute $-1$ to both terms inside: $$-(8w - 3) = -1 \times 8w + (-1) \times (-3) = -8w + 3$$ So the equation becomes: $$-8w + 3 + 2 = 4 + w - 4$$ 3. **Combine like terms on each side:** Left side: $3 + 2 = 5$ Right side: $4 - 4 = 0$ So the equation is: $$-8w + 5 = w$$ 4. **Collect like terms:** Move all terms involving $w$ to one side and constants to the other. Subtract $w$ from both sides: $$-8w + 5 - w = w - w$$ $$-8w - w + 5 = 0$$ $$-9w + 5 = 0$$ 5. **Isolate $w$:** Subtract 5 from both sides: $$-9w + 5 - 5 = 0 - 5$$ $$-9w = -5$$ 6. **Solve for $w$ by dividing both sides by $-9$:** $$w = \frac{-5}{-9}$$ Use cancellation notation: $$w = \frac{\cancel{-5}}{\cancel{-9}} = \frac{5}{9}$$ 7. **Final answer:** $$w = \frac{5}{9}$$ **Summary:** Jamaal's mistake was in Step 1 where he incorrectly distributed the negative sign. The correct distribution changes $- (8w - 3)$ to $-8w + 3$, not $-8w - 3$.