Question: Solve for $q$.
$\frac{5}{6} q - \frac{1}{2} = \frac{3}{8}$
1. **State the problem:** Solve the equation $$\frac{5}{6} q - \frac{1}{2} = \frac{3}{8}$$ for $q$.
2. **Add $\frac{1}{2}$ to both sides** to isolate the term with $q$:
$$\frac{5}{6} q - \frac{1}{2} + \frac{1}{2} = \frac{3}{8} + \frac{1}{2}$$
which simplifies to
$$\frac{5}{6} q = \frac{3}{8} + \frac{1}{2}$$
3. **Find a common denominator** to add the fractions on the right side. The common denominator of 8 and 2 is 8:
$$\frac{3}{8} + \frac{1}{2} = \frac{3}{8} + \frac{4}{8} = \frac{7}{8}$$
So now we have
$$\frac{5}{6} q = \frac{7}{8}$$
4. **Solve for $q$ by dividing both sides by $\frac{5}{6}$**. Dividing by a fraction is the same as multiplying by its reciprocal:
$$q = \frac{7}{8} \div \frac{5}{6} = \frac{7}{8} \times \frac{6}{5}$$
5. **Multiply the fractions:**
$$q = \frac{7 \times 6}{8 \times 5} = \frac{42}{40}$$
6. **Simplify the fraction by canceling common factors:**
$$q = \frac{\cancel{42}^{6 \times 7}}{\cancel{40}^{8 \times 5}} = \frac{21}{20}$$
7. **Final answer:**
$$q = \frac{21}{20}$$