1. **State the problem:** Simplify the expression $$\left(\frac{2}{11}x - 3 - 5y\right) + \left(-\frac{3}{11}x + 5y + 5.5\right)$$. 2. **Write down the expression:** $$\frac{2}{11}x - 3 - 5y - \frac{3}{11}x + 5y + 5.5$$ 3. **Group like terms:** $$\left(\frac{2}{11}x - \frac{3}{11}x\right) + (-3 + 5.5) + (-5y + 5y)$$ 4. **Simplify each group:** - For the $x$ terms: $$\frac{2}{11}x - \frac{3}{11}x = \frac{2-3}{11}x = -\frac{1}{11}x$$ - For the constants: $$-3 + 5.5 = 2.5$$ - For the $y$ terms: $$-5y + 5y = 0$$ 5. **Combine all simplified parts:** $$-\frac{1}{11}x + 2.5 + 0 = -\frac{1}{11}x + 2.5$$ **Final answer:** $$-\frac{1}{11}x + 2.5$$