Linear Inequality 0598F7

1. **State the problem:** Solve the inequality $$2x - \frac{1}{3} - x + \frac{2}{4} > 1$$. 2. **Combine like terms:** Group the terms with $x$ and the constants separately. $$2x - x - \frac{1}{3} + \frac{2}{4} > 1$$ Simplify the $x$ terms: $$x - \frac{1}{3} + \frac{1}{2} > 1$$ 3. **Combine the constants:** Find a common denominator for $-\frac{1}{3} + \frac{1}{2}$. Common denominator is $6$: $$-\frac{2}{6} + \frac{3}{6} = \frac{1}{6}$$ So the inequality becomes: $$x + \frac{1}{6} > 1$$ 4. **Isolate $x$:** Subtract $\frac{1}{6}$ from both sides. $$x + \frac{1}{6} - \frac{1}{6} > 1 - \frac{1}{6}$$ $$x > \frac{6}{6} - \frac{1}{6}$$ $$x > \frac{5}{6}$$ 5. **Final answer:** The solution to the inequality is: $$\boxed{x > \frac{5}{6}}$$