1. **State the problem:** Solve the inequality $$\frac{683+x}{718+x} > 0.955$$. 2. **Rewrite the inequality:** Multiply both sides by the positive denominator $(718+x)$ (assuming $718+x > 0$) to avoid reversing the inequality: $$683 + x > 0.955(718 + x)$$ 3. **Distribute the right side:** $$683 + x > 0.955 \times 718 + 0.955x$$ Calculate $0.955 \times 718$: $$0.955 \times 718 = 685.69$$ So the inequality becomes: $$683 + x > 685.69 + 0.955x$$ 4. **Isolate $x$ terms:** $$x - 0.955x > 685.69 - 683$$ Simplify: $$0.045x > 2.69$$ 5. **Solve for $x$:** $$x > \frac{2.69}{0.045}$$ Calculate: $$x > 59.78$$ 6. **Check domain:** Since we multiplied by $718 + x$, we must ensure $718 + x > 0$: $$x > -718$$ This is always true for $x > 59.78$, so no conflict. **Final answer:** $$x > 59.78$$