Question: Solve for $j$.
$\frac{5}{8} j + \frac{3}{4} = \frac{1}{2}$
$j = [ ]$
1. **State the problem:** Solve for $j$ in the equation $$\frac{5}{8} j + \frac{3}{4} = \frac{1}{2}$$.
2. **Isolate the term with $j$:** Subtract $\frac{3}{4}$ from both sides:
$$\frac{5}{8} j + \frac{3}{4} - \frac{3}{4} = \frac{1}{2} - \frac{3}{4}$$
which simplifies to
$$\frac{5}{8} j = \frac{1}{2} - \frac{3}{4}$$
3. **Calculate the right side:** Find a common denominator (4):
$$\frac{1}{2} = \frac{2}{4}$$
So,
$$\frac{5}{8} j = \frac{2}{4} - \frac{3}{4} = -\frac{1}{4}$$
4. **Solve for $j$:** Divide both sides by $\frac{5}{8}$:
$$j = \frac{-\frac{1}{4}}{\frac{5}{8}}$$
Rewrite division as multiplication by reciprocal:
$$j = -\frac{1}{4} \times \frac{8}{5}$$
5. **Simplify:**
$$j = -\frac{1 \times 8}{4 \times 5} = -\frac{8}{20}$$
Simplify fraction by dividing numerator and denominator by 4:
$$j = -\frac{\cancel{8}^{2}}{\cancel{20}^{5}} = -\frac{2}{5}$$
**Final answer:**
$$j = -\frac{2}{5}$$