1. **Problem:** Solve for $x$ in the equation $$\frac{3x}{4} + \frac{5}{8} = \frac{3}{8}$$. 2. **Formula and rules:** To solve equations involving fractions, first find a common denominator to combine terms or isolate $x$. Remember to perform the same operation on both sides of the equation. 3. **Step-by-step solution:** - Subtract $\frac{5}{8}$ from both sides: $$\frac{3x}{4} = \frac{3}{8} - \frac{5}{8}$$ - Simplify the right side: $$\frac{3x}{4} = -\frac{2}{8} = -\frac{1}{4}$$ - Multiply both sides by 4 to clear the denominator: $$3x = -1$$ - Divide both sides by 3: $$x = -\frac{1}{3}$$ 4. **Answer:** $x = -\frac{1}{3}$ --- **Example questions:** 1) $$\frac{2x}{5} + \frac{1}{10} = \frac{3}{10}$$ Options: (a) $\frac{1}{2}$ (b) $\frac{1}{5}$ (c) $\frac{2}{5}$ (d) $\frac{3}{5}$ 2) $$\frac{5x}{6} + \frac{1}{3} = \frac{7}{6}$$ Options: (a) $\frac{2}{5}$ (b) $\frac{3}{5}$ (c) $\frac{4}{5}$ (d) $\frac{1}{2}$ 3) $$\frac{4x}{7} + \frac{2}{7} = 1$$ Options: (a) $\frac{3}{4}$ (b) $\frac{5}{4}$ (c) $\frac{1}{2}$ (d) $\frac{1}{4}$ 4) $$\frac{3x}{8} + \frac{1}{4} = \frac{5}{8}$$ Options: (a) $\frac{1}{2}$ (b) $\frac{1}{4}$ (c) $\frac{3}{4}$ (d) $\frac{1}{8}$ 5) $$\frac{7x}{10} + \frac{3}{5} = 1$$ Options: (a) $\frac{1}{7}$ (b) $\frac{2}{7}$ (c) $\frac{3}{7}$ (d) $\frac{4}{7}$ 6) $$\frac{6x}{9} + \frac{1}{3} = \frac{5}{6}$$ Options: (a) $\frac{1}{2}$ (b) $\frac{1}{3}$ (c) $\frac{2}{3}$ (d) $\frac{1}{6}$ 7) $$\frac{5x}{12} + \frac{1}{4} = \frac{7}{12}$$ Options: (a) $\frac{1}{2}$ (b) $\frac{1}{3}$ (c) $\frac{2}{3}$ (d) $\frac{1}{4}$