To solve the equation \(2x + 12 - 3x = 27\), the first step typically involves isolating the variable \(x\) by combining like terms.
In this case, we first combine \(2x\) and \(-3x\):
\[ 2x - 3x + 12 = 27 \implies -x + 12 = 27 \]
Now, we can look at the provided responses for an equation that requires the same first step of combining like terms.
- \(2x + 12 = -3x - 27\) - This does not apply as it is already an equation without like terms on the left side.
- \(4x - 17 + 2x = 9\) - Here, we combine \(4x\) and \(2x\) as the first step.
- \(2(x - 5) + 2x = 10\) - This requires distribution first and doesn’t match our step.
- \(2x + 12 = 27\) - This further isolates \(x\) directly, not a like terms equation.
The second option, \(4x - 17 + 2x = 9\), has the same first step by combining like terms (specifically, combining \(4x\) and \(2x\)) as in the original equation.
Thus, the answer is:
4x - 17 + 2x = 9