Question

Simplify the expression.

3/4x + 3/5y −1/2x +7/10y


(1 point)
Responses

4/6x + 10/15y
46x + 1015y

1/4x + 13/10y
14x + 1310y

1/2x + 6/10y
12x + 610y

1 1/4x + 1y

Answer 1

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**.