To simplify the expression \( \frac{3}{4}x + \frac{3}{5}y - \frac{1}{2}x + \frac{7}{10}y \), we first combine the \( x \)-terms and the \( y \)-terms separately.
Step 1: Combine the \( x \)-terms
The \( x \)-terms are: \[ \frac{3}{4}x - \frac{1}{2}x \]
To combine these, we need a common denominator. The least common multiple of 4 and 2 is 4. We can rewrite \( \frac{1}{2}x \) as \( \frac{2}{4}x \): \[ \frac{3}{4}x - \frac{2}{4}x = \frac{1}{4}x \]
Step 2: Combine the \( y \)-terms
The \( y \)-terms are: \[ \frac{3}{5}y + \frac{7}{10}y \]
Again, we need a common denominator. The least common multiple of 5 and 10 is 10. We can rewrite \( \frac{3}{5}y \) as \( \frac{6}{10}y \): \[ \frac{6}{10}y + \frac{7}{10}y = \frac{13}{10}y \]
Step 3: Combine both results
Putting it all together, we have: \[ \frac{1}{4}x + \frac{13}{10}y \]
Final Answer:
The simplified expression is: \[ \frac{1}{4}x + \frac{13}{10}y \]
So the correct response is: 1/4x + 13/10y.