1. **State the problem:** Solve the equation $$\frac{x + 6}{x - 5} = \frac{5}{4}$$ for $x$. 2. **Use the cross-multiplication method:** When two fractions are equal, their cross products are equal. So, $$4(x + 6) = 5(x - 5)$$ 3. **Expand both sides:** $$4x + 24 = 5x - 25$$ 4. **Isolate $x$ terms on one side and constants on the other:** $$4x + 24 = 5x - 25$$ $$24 + 25 = 5x - 4x$$ $$49 = x$$ 5. **Final answer:** $$x = 49$$ This means the value of $x$ that satisfies the equation is 49.