1. **Problem:** Find the value of $x$ in the equation $$9x + \frac{7}{8} = \frac{1}{8}$$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by moving constants to the other side and then divide by the coefficient of $x$. 3. **Step-by-step solution:** - Subtract $\frac{7}{8}$ from both sides: $$9x = \frac{1}{8} - \frac{7}{8}$$ - Simplify the right side: $$9x = \frac{1 - 7}{8} = \frac{-6}{8} = -\frac{3}{4}$$ - Divide both sides by 9: $$x = -\frac{3}{4} \times \frac{1}{9} = -\frac{3}{36} = -\frac{1}{12}$$ 4. **Answer:** The value of $x$ is $-\frac{1}{12}$.