1. **State the problem:** Solve the equation $$\frac{x}{2} + x + \frac{97}{12} = 0$$ for $x$. 2. **Combine like terms:** To combine the terms with $x$, express all terms with a common denominator. The denominators are 2 and 1 (for $x$), so rewrite $x$ as $\frac{2x}{2}$: $$\frac{x}{2} + \frac{2x}{2} + \frac{97}{12} = 0$$ 3. **Add the $x$ terms:** $$\frac{x + 2x}{2} + \frac{97}{12} = 0$$ $$\frac{3x}{2} + \frac{97}{12} = 0$$ 4. **Isolate $x$:** Subtract $\frac{97}{12}$ from both sides: $$\frac{3x}{2} = -\frac{97}{12}$$ 5. **Solve for $x$:** Multiply both sides by the reciprocal of $\frac{3}{2}$, which is $\frac{2}{3}$: $$x = -\frac{97}{12} \times \frac{2}{3}$$ 6. **Simplify the multiplication:** $$x = -\frac{97 \times 2}{12 \times 3} = -\frac{194}{36}$$ 7. **Reduce the fraction:** Both numerator and denominator are divisible by 2: $$x = -\frac{\cancel{194}^{97}}{\cancel{36}^{18}}$$ So, $$x = -\frac{97}{18}$$ **Final answer:** $$x = -\frac{97}{18}$$