Which equation has the same first step to solve as this equation: 2x+12−3x=27

\( 4x - 17 + 2x = 9 \): Combine like terms on the left side, will yield \( 6x - 17 = 9 \).
\( 2x + 12 = 27 \): This is already simplified and doesn't involve combining like terms.
\( 2x + 12 = -3x - 27 \): Involves moving terms around, not just combining like terms.
\( 2(x - 5) + 2x = 10 \): Would require distribution as the first step.

Question

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

4x−17+2x=9

2x+12=27

2x+12=−3x−27

2(x−5)+2x=10

GPT-4o mini · Answer

To solve the equation $ 2x + 12 - 3x = 27 $, the first step is to combine like terms on the left side. This simplifies the equation to $ -x + 12 = 27 $. Now, let's analyze the options: 1. **$ 4x - 17 + 2x = 9 $**: Combine like terms on the left side, will yield $ 6x - 17 = 9 $. 2. **$ 2x + 12 = 27 $**: This is already simplified and doesn't involve combining like terms. 3. **$ 2x + 12 = -3x - 27 $**: Involves moving terms around, not just combining like terms. 4. **$ 2(x - 5) + 2x = 10 $**: Would require distribution as the first step. The only equation that involves combining like terms, similar to the original equation, is the first option: **$ 4x - 17 + 2x = 9 $** combines like terms right away. So, the correct answer is: **4x−17+2x=9**.