1. **State the problem:** Solve the equation $$\frac{1}{x} + \frac{1}{4} = \frac{7}{12}$$ for $x$. 2. **Identify the formula and rules:** To solve for $x$, we need to isolate $x$ by combining fractions and then solving the resulting equation. Remember, to combine fractions, find a common denominator. 3. **Find a common denominator for the fractions on the left side:** The denominators are $x$ and $4$. The common denominator is $4x$. 4. **Rewrite each term with the common denominator:** $$\frac{1}{x} = \frac{4}{4x}, \quad \frac{1}{4} = \frac{x}{4x}$$ 5. **Rewrite the equation:** $$\frac{4}{4x} + \frac{x}{4x} = \frac{7}{12}$$ 6. **Combine the fractions on the left:** $$\frac{4 + x}{4x} = \frac{7}{12}$$ 7. **Cross-multiply to solve for $x$:** $$12(4 + x) = 7(4x)$$ 8. **Expand both sides:** $$48 + 12x = 28x$$ 9. **Bring all terms involving $x$ to one side:** $$48 = 28x - 12x$$ $$48 = 16x$$ 10. **Solve for $x$:** $$x = \frac{48}{16} = 3$$ **Final answer:** $x = 3$