1. **State the problem:** Simplify the expression $x - \frac{2}{3} + x + \frac{4}{4}$. 2. **Combine like terms:** The terms with $x$ are $x$ and $x$, so add them: $$x + x = 2x$$ 3. **Simplify the constants:** Note that $\frac{4}{4} = 1$. So the constants are $-\frac{2}{3} + 1$. 4. **Find a common denominator for the constants:** The common denominator is 3. Rewrite 1 as $\frac{3}{3}$. $$-\frac{2}{3} + \frac{3}{3} = \frac{-2 + 3}{3} = \frac{1}{3}$$ 5. **Write the simplified expression:** $$2x + \frac{1}{3}$$ **Final answer:** $2x + \frac{1}{3}$