Question: Solve for $w$ in the equation $- \frac{1}{2} = \frac{1}{5} w - \frac{1}{3}$. Simplify your answer as much as possible.
1. **State the problem:** Solve the two-step equation $$- \frac{1}{2} = \frac{1}{5} w - \frac{1}{3}$$ for $w$.
2. **Add $\frac{1}{3}$ to both sides** to isolate the term with $w$:
$$- \frac{1}{2} + \frac{1}{3} = \frac{1}{5} w - \frac{1}{3} + \frac{1}{3}$$
3. **Simplify the left side:** Find common denominator 6:
$$- \frac{3}{6} + \frac{2}{6} = - \frac{1}{6}$$
So,
$$- \frac{1}{6} = \frac{1}{5} w$$
4. **Multiply both sides by 5** to solve for $w$:
$$5 \times \left(- \frac{1}{6}\right) = 5 \times \frac{1}{5} w$$
Intermediate step showing cancellation:
$$\cancel{5} \times \left(- \frac{1}{6}\right) = \cancel{5} \times \frac{1}{\cancel{5}} w$$
Simplifies to:
$$- \frac{5}{6} = w$$
5. **Final answer:**
$$w = - \frac{5}{6}$$