Question: Solve the equation.
$$\frac{3}{5} (x - 15) = \frac{1}{2} (x + 20)$$
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The solution to the equation is x = □.
1. **State the problem:** Solve the linear equation $$\frac{3}{5} (x - 15) = \frac{1}{2} (x + 20)$$.
2. **Distribute the fractions:**
$$\frac{3}{5}x - \frac{3}{5} \times 15 = \frac{1}{2}x + \frac{1}{2} \times 20$$
3. Calculate the products:
$$\frac{3}{5}x - \frac{45}{5} = \frac{1}{2}x + 10$$
Simplify $$\frac{45}{5}$$:
$$\frac{3}{5}x - 9 = \frac{1}{2}x + 10$$
4. **Bring all terms involving $$x$$ to one side and constants to the other:**
Subtract $$\frac{1}{2}x$$ from both sides:
$$\frac{3}{5}x - \frac{1}{2}x - 9 = 10$$
5. Find common denominator for $$\frac{3}{5}x - \frac{1}{2}x$$ which is 10:
$$\frac{6}{10}x - \frac{5}{10}x - 9 = 10$$
Simplify:
$$\frac{1}{10}x - 9 = 10$$
6. Add 9 to both sides:
$$\frac{1}{10}x = 19$$
7. Multiply both sides by 10 to solve for $$x$$:
$$\cancel{10} \times \frac{1}{\cancel{10}}x = 19 \times 10$$
Simplify:
$$x = 190$$
**Final answer:** $$x = 190$$