1. Stating the problem: Simplify the expression $$\frac{7}{10} - \left( \frac{3}{5} - \frac{1}{2} \right)$$. 2. Use the rule for subtraction inside parentheses: $$a - (b - c) = a - b + c$$. 3. Apply this to the expression: $$\frac{7}{10} - \frac{3}{5} + \frac{1}{2}$$. 4. Find a common denominator for the fractions. The denominators are 10, 5, and 2. The least common denominator (LCD) is 10. 5. Convert each fraction to have denominator 10: $$\frac{7}{10} = \frac{7}{10}$$ $$\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}$$ $$\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}$$ 6. Substitute back: $$\frac{7}{10} - \frac{6}{10} + \frac{5}{10}$$ 7. Perform the subtraction and addition step by step: $$\frac{7}{10} - \frac{6}{10} = \frac{\cancel{7} - \cancel{6}}{10} = \frac{1}{10}$$ 8. Now add $$\frac{1}{10} + \frac{5}{10} = \frac{1 + 5}{10} = \frac{6}{10}$$ 9. Simplify $$\frac{6}{10}$$ by dividing numerator and denominator by 2: $$\frac{\cancel{6} \div 2}{\cancel{10} \div 2} = \frac{3}{5}$$ Final answer: $$\frac{3}{5}$$.