When \( 2\left(\frac{3}{5} x+2 \frac{3}{4} y-\frac{1}{4} x-1 \frac{1}{2} y+3\right) \) is simplified, what is the resulting expression? \( 1 \frac{7}{10} x+2 \frac{1}{2} y+6 \) \( \frac{7}{10} x+2 \frac{1}{2} y+6 \) \( \frac{7}{10} x+8 \frac{1}{2} y+6 \) \( 1 \frac{7}{10} x+4 \frac{1}{4} y+3 \)

To simplify the expression \( 2\left(\frac{3}{5} x + 2 \frac{3}{4} y - \frac{1}{4} x - 1 \frac{1}{2} y + 3\right) \), we will first convert the mixed numbers into improper fractions where necessary and then combine like terms. 1. **Convert mixed numbers**: - \( 2 \frac{3}{4} y = \frac{8}{4} y + \frac{3}{4} y = \frac{11}{4} y \) - \( 1 \frac{1}{2} y = \frac{2}{2} y + \frac{1}{2} y = \frac{3}{2} y \) - \( 1 \frac{7}{10} x = \frac{10}{10} x + \frac{7}{10} x = \frac{17}{10} x \) Now, simplifying the expression inside the parentheses: \[ \frac{3}{5} x - \frac{1}{4} x = \frac{12}{20} x - \frac{5}{20} x = \frac{7}{20} x \] Next, simplify \( 2 \frac{3}{4} y - 1 \frac{1}{2} y + 3 \): \[ \frac{11}{4} y - \frac{3}{2} y + 3 = \frac{11}{4} y - \frac{6}{4} y + 3 = \frac{5}{4} y + 3 \] Now combine everything inside the parentheses: \[ 2\left(\frac{7}{20} x + \frac{5}{4} y + 3\right) \] Distributing the 2: \[ \frac{14}{20} x + \frac{10}{4} y + 6 = \frac{7}{10} x + \frac{5}{2} y + 6 \] Now we check the final answer against the options: - \( \frac{7}{10} x + 2 \frac{1}{2} y + 6 \) is equivalent to \( \frac{7}{10} x + \frac{5}{2} y + 6 \). - Therefore, the correct answer is: \[ \frac{7}{10} x + 2 \frac{1}{2} y + 6 \]