1. **State the problem:** Solve the equation $$\frac{2) - 3x - 7}{4} + x + \frac{17}{5} = 0.$$ 2. **Rewrite the equation clearly:** The expression seems to be $$\frac{2 - 3x - 7}{4} + x + \frac{17}{5} = 0.$$ Simplify the numerator first: $$2 - 3x - 7 = -3x - 5.$$ So the equation becomes $$\frac{-3x - 5}{4} + x + \frac{17}{5} = 0.$$ 3. **Find a common denominator to combine terms:** The denominators are 4 and 5. The common denominator is 20. Multiply each term by 20 to clear denominators: $$20 \times \left(\frac{-3x - 5}{4}\right) + 20 \times x + 20 \times \frac{17}{5} = 20 \times 0$$ 4. **Simplify each term:** $$5(-3x - 5) + 20x + 4(17) = 0$$ $$-15x - 25 + 20x + 68 = 0$$ 5. **Combine like terms:** $$(-15x + 20x) + (-25 + 68) = 0$$ $$5x + 43 = 0$$ 6. **Isolate $x$:** $$5x = -43$$ 7. **Divide both sides by 5:** $$x = \frac{-43}{5}$$ 8. **Final answer:** $$\boxed{x = -\frac{43}{5}}$$