1. **Problem:** Solve the equation $$\frac{2}{3}x + \frac{3}{8} = \frac{3}{4}$$ for $$x$$. 2. **Formula and rules:** To solve for $$x$$, isolate $$x$$ by subtracting and dividing. Remember to find a common denominator when subtracting fractions. 3. **Step 1:** Subtract $$\frac{3}{8}$$ from both sides: $$\frac{2}{3}x + \frac{3}{8} - \frac{3}{8} = \frac{3}{4} - \frac{3}{8}$$ 4. **Step 2:** Simplify the right side by finding a common denominator (8): $$\frac{3}{4} = \frac{6}{8}$$ So, $$\frac{6}{8} - \frac{3}{8} = \frac{3}{8}$$ 5. **Step 3:** Now the equation is: $$\frac{2}{3}x = \frac{3}{8}$$ 6. **Step 4:** To solve for $$x$$, divide both sides by $$\frac{2}{3}$$, which is the same as multiplying by its reciprocal $$\frac{3}{2}$$: $$x = \frac{3}{8} \times \frac{3}{2}$$ 7. **Step 5:** Multiply numerators and denominators: $$x = \frac{3 \times 3}{8 \times 2} = \frac{9}{16}$$ 8. **Final answer:** $$x = \frac{9}{16}$$