Question

7. Which equation has the same first step to solve as this equation: 2x+12−3x=27
(1 point)
Responses

2x+12=−3x−27
2 x plus 12 is equal to negative 3 x minus 27

2(x−5)+2x=10
2 times open paren x minus 5 close paren plus 2 x is equal to 10

2x+12=27
2 x plus 12 is equal to 27

4x−17+2x=9

Answer 1

To find which equation has the same first step as \( 2x + 12 - 3x = 27 \), we need to analyze the first step in solving it.

1. **Original equation**: \( 2x + 12 - 3x = 27 \)
2. **Combine like terms on the left side**:
- Combine \( 2x \) and \( -3x \):
\[
(2x - 3x) + 12 = 27
\]
\[
-x + 12 = 27
\]

Now we can review the given equations to see which one can also be simplified in a similar way (specifically, combining like terms or moving terms to the same side).

1. **\( 2x + 12 = -3x - 27 \)**: Cannot combine like terms easily.
2. **\( 2(x - 5) + 2x = 10 \)**: This involves distributing which is different from our first step.
3. **\( 2x + 12 = 27 \)**: Direct comparison, but this does not involve similar operation.
4. **\( 4x - 17 + 2x = 9 \)**: Combine like terms \( (4x + 2x) - 17 = 9 \).

The only equation that follows the same first step of combining like terms is \( 4x - 17 + 2x = 9 \).

So the answer is **\( 4x - 17 + 2x = 9 \)**.