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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 4x−17+2x=9 4 x minus 17 plus 2 x is equal to 9 2(x−5)+2x=10 2 times open paren x minus 5 close paren plus 2 x is equal to 10 2x+12=27

1 answer

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.

  1. \(2x + 12 = -3x - 27\) - This does not apply as it is already an equation without like terms on the left side.
  2. \(4x - 17 + 2x = 9\) - Here, we combine \(4x\) and \(2x\) as the first step.
  3. \(2(x - 5) + 2x = 10\) - This requires distribution first and doesn’t match our step.
  4. \(2x + 12 = 27\) - 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