Question: Solve for $c$. Express your answer as a proper or improper fraction in simplest terms.
$-\frac{5}{6} = \frac{1}{2} - \frac{2}{3} c$
1. **State the problem:** Solve for $c$ in the equation $$-\frac{5}{6} = \frac{1}{2} - \frac{2}{3} c$$.
2. **Isolate the term with $c$:** Subtract $\frac{1}{2}$ from both sides:
$$-\frac{5}{6} - \frac{1}{2} = - \frac{2}{3} c$$
3. **Find a common denominator to combine the left side:** The denominators are 6 and 2, common denominator is 6.
$$-\frac{5}{6} - \frac{3}{6} = - \frac{2}{3} c$$
Simplify the left side:
$$-\frac{5}{6} - \frac{3}{6} = -\frac{8}{6}$$
4. **Rewrite the equation:**
$$-\frac{8}{6} = - \frac{2}{3} c$$
5. **Divide both sides by $-\frac{2}{3}$ to solve for $c$:**
$$c = \frac{-\frac{8}{6}}{-\frac{2}{3}}$$
6. **Simplify the division of fractions:**
$$c = \left(-\frac{8}{6}\right) \times \left(-\frac{3}{2}\right)$$
7. **Multiply numerators and denominators:**
$$c = \frac{8 \times 3}{6 \times 2}$$
8. **Simplify the fraction:**
$$c = \frac{24}{12}$$
9. **Reduce the fraction to simplest terms:**
$$c = 2$$
**Final answer:**
$$c = 2$$