1. **State the problem:** Solve the linear equation $$2 = 5(5w - 21) - 9(3w - 2)$$. 2. **Apply the distributive property:** Multiply inside the parentheses: $$2 = 5 \times 5w - 5 \times 21 - 9 \times 3w + 9 \times 2$$ $$2 = 25w - 105 - 27w + 18$$ 3. **Combine like terms on the right side:** $$2 = (25w - 27w) + (-105 + 18)$$ $$2 = -2w - 87$$ 4. **Isolate the variable term:** Add 87 to both sides: $$2 + 87 = -2w - 87 + 87$$ $$89 = -2w$$ 5. **Solve for $w$ by dividing both sides by $-2$:** $$w = \frac{89}{\cancel{-2}} \times \frac{\cancel{-1}}{1} = -\frac{89}{2}$$ 6. **Final answer:** $$w = -\frac{89}{2}$$