1. **State the problem:** Solve the equation $$\frac{x}{2} = 25 + \frac{x}{12}$$ for $x$. 2. **Formula and rules:** To solve equations with fractions, first eliminate the denominators by multiplying both sides by the least common denominator (LCD). Here, the denominators are 2 and 12, so the LCD is 12. 3. **Multiply both sides by 12:** $$12 \times \frac{x}{2} = 12 \times \left(25 + \frac{x}{12}\right)$$ 4. **Simplify each term:** $$12 \times \frac{x}{2} = \cancel{12} \times \frac{x}{\cancel{2}} = 6x$$ $$12 \times 25 = 300$$ $$12 \times \frac{x}{12} = \cancel{12} \times \frac{x}{\cancel{12}} = x$$ So the equation becomes: $$6x = 300 + x$$ 5. **Isolate $x$ terms:** Subtract $x$ from both sides: $$6x - x = 300$$ $$\cancel{6x} - \cancel{x} = 5x$$ 6. **Solve for $x$:** $$5x = 300$$ Divide both sides by 5: $$\frac{5x}{\cancel{5}} = \frac{300}{\cancel{5}}$$ $$x = 60$$ **Final answer:** $$x = 60$$