1. **State the problem:** Solve the equation $$\frac{50}{x} + 7 = 107$$ for $x$. 2. **Isolate the fraction:** Subtract 7 from both sides to get $$\frac{50}{x} = 107 - 7$$ 3. **Simplify the right side:** $$\frac{50}{x} = 100$$ 4. **Solve for $x$:** Multiply both sides by $x$ to get rid of the denominator: $$50 = 100x$$ 5. **Divide both sides by 100:** $$x = \frac{50}{100}$$ 6. **Simplify the fraction:** $$x = \frac{1}{2}$$ **Final answer:** $$x = \frac{1}{2}$$