1. **State the problem:** Simplify the expression $$\frac{2}{5} + \left(-\frac{3}{2} + \frac{1}{4}\right) - \left(3 - \left(-\frac{7}{10}\right)\right)$$. 2. **Simplify inside the parentheses:** - Calculate $$-\frac{3}{2} + \frac{1}{4}$$. - Calculate $$3 - \left(-\frac{7}{10}\right)$$. 3. **Calculate $$-\frac{3}{2} + \frac{1}{4}$$:** - Find common denominator 4: $$-\frac{3}{2} = -\frac{6}{4}$$ - So, $$-\frac{6}{4} + \frac{1}{4} = -\frac{5}{4}$$ 4. **Calculate $$3 - \left(-\frac{7}{10}\right)$$:** - Subtracting a negative is addition: $$3 + \frac{7}{10}$$ - Convert 3 to tenths: $$3 = \frac{30}{10}$$ - So, $$\frac{30}{10} + \frac{7}{10} = \frac{37}{10}$$ 5. **Rewrite the expression:** $$\frac{2}{5} + \left(-\frac{5}{4}\right) - \frac{37}{10}$$ 6. **Convert all fractions to a common denominator:** - Denominators are 5, 4, and 10. - Least common denominator is 20. - Convert each: $$\frac{2}{5} = \frac{8}{20}$$ $$-\frac{5}{4} = -\frac{25}{20}$$ $$-\frac{37}{10} = -\frac{74}{20}$$ 7. **Combine all terms:** $$\frac{8}{20} - \frac{25}{20} - \frac{74}{20} = \frac{8 - 25 - 74}{20} = \frac{-91}{20}$$ 8. **Final answer:** $$\boxed{-\frac{91}{20}}$$