1. **State the problem:** Solve the equation $$\frac{2}{3}x + 5 = 4 - \frac{3}{4}x$$ for $x$. 2. **Write down the equation:** $$\frac{2}{3}x + 5 = 4 - \frac{3}{4}x$$ 3. **Goal:** Isolate $x$ on one side. 4. **Add $\frac{3}{4}x$ to both sides:** $$\frac{2}{3}x + \frac{3}{4}x + 5 = 4$$ 5. **Subtract 5 from both sides:** $$\frac{2}{3}x + \frac{3}{4}x = 4 - 5$$ $$\frac{2}{3}x + \frac{3}{4}x = -1$$ 6. **Find common denominator for fractions:** Denominators are 3 and 4, common denominator is 12. 7. **Rewrite fractions:** $$\frac{2}{3}x = \frac{8}{12}x, \quad \frac{3}{4}x = \frac{9}{12}x$$ 8. **Add fractions:** $$\frac{8}{12}x + \frac{9}{12}x = \frac{17}{12}x$$ 9. **Equation becomes:** $$\frac{17}{12}x = -1$$ 10. **Multiply both sides by the reciprocal of $\frac{17}{12}$, which is $\frac{12}{17}$:** $$x = -1 \times \frac{12}{17}$$ $$x = -\frac{12}{17}$$ **Final answer:** $$x = -\frac{12}{17}$$