Question: Solve for $j$.
$$\frac{2}{5}\left(j + \frac{7}{2}\right) = 5$$
1. **State the problem:** Solve the equation $$\frac{2}{5}\left(j + \frac{7}{2}\right) = 5$$ for $j$.
2. **Identify the formula and rules:** This is a two-step equation involving fractions. To solve, first eliminate the fraction by multiplying both sides by the reciprocal of $$\frac{2}{5}$$, which is $$\frac{5}{2}$$.
3. **Multiply both sides by $$\frac{5}{2}$$:**
$$\frac{5}{2} \times \frac{2}{5}\left(j + \frac{7}{2}\right) = 5 \times \frac{5}{2}$$
4. **Simplify the left side by canceling common factors:**
$$\cancel{\frac{5}{2}} \times \cancel{\frac{2}{5}}\left(j + \frac{7}{2}\right) = \frac{25}{2}$$
This simplifies to:
$$j + \frac{7}{2} = \frac{25}{2}$$
5. **Isolate $j$ by subtracting $$\frac{7}{2}$$ from both sides:**
$$j + \frac{7}{2} - \frac{7}{2} = \frac{25}{2} - \frac{7}{2}$$
6. **Simplify the right side:**
$$j = \frac{25 - 7}{2} = \frac{18}{2}$$
7. **Simplify the fraction:**
$$j = 9$$
**Final answer:**
$$j = 9$$