Question

Which expression is equivalent to 38x+85y+38+12−72x−25y?
Responses
318x + 2y − 18


118x − 65y − 78


−258x + 65y + 78
-19/10 + 7/8x - 1/40y

Answer 1

To simplify the expression \(38x + 85y + 38 + 12 - 72x - 25y\), we can combine like terms.

1. **Combine the \(x\) terms**:
- \(38x - 72x = -34x\)

2. **Combine the \(y\) terms**:
- \(85y - 25y = 60y\)

3. **Combine the constant terms**:
- \(38 + 12 = 50\)

Now, putting it all together, we get:
\[
-34x + 60y + 50
\]

Now, let's check each of the provided responses to see if any are equivalent to \(-34x + 60y + 50\):

1. **Response 1**: \(318x + 2y - 18\) - Not equivalent.
2. **Response 2**: \(118x - 65y - 78\) - Not equivalent.
3. **Response 3**: \(-258x + 65y + 78\) - Not equivalent.
4. **Response 4**: \(-19/10 + 7/8x - 1/40y\) - Not equivalent.

None of the provided options are equivalent to the simplified expression \(-34x + 60y + 50\).

If you need further assistance or corrections to the choices, please let me know!