1. **State the problem:** Solve the equation $$\frac{11}{10}x - \frac{2}{15}x - \frac{7}{10} = \frac{11}{5}$$ for $x$. 2. **Combine like terms on the left side:** Find a common denominator for the $x$ terms, which is 30. $$\frac{11}{10}x = \frac{33}{30}x, \quad \frac{2}{15}x = \frac{4}{30}x$$ So, $$\frac{33}{30}x - \frac{4}{30}x = \frac{29}{30}x$$ The equation becomes: $$\frac{29}{30}x - \frac{7}{10} = \frac{11}{5}$$ 3. **Isolate the $x$ term:** Add $\frac{7}{10}$ to both sides: $$\frac{29}{30}x = \frac{11}{5} + \frac{7}{10}$$ Find common denominator 10 for the right side: $$\frac{11}{5} = \frac{22}{10}$$ So, $$\frac{29}{30}x = \frac{22}{10} + \frac{7}{10} = \frac{29}{10}$$ 4. **Solve for $x$ by dividing both sides by $\frac{29}{30}$:** $$x = \frac{\frac{29}{10}}{\frac{29}{30}} = \frac{29}{10} \times \frac{30}{29}$$ Cancel $29$: $$x = \frac{\cancel{29}}{10} \times \frac{30}{\cancel{29}} = \frac{30}{10} = 3$$ 5. **Final answer:** $$\boxed{3}$$