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

Question

Responses

2x+12=272 x plus 12 is equal to 27

4x−17+2x=94 x minus 17 plus 2 x is equal to 9

2(x−5)+2x=102 times open paren x minus 5 close paren plus 2 x is equal to 10

2x+12=−3x−27

Answer 1

To solve the equation \(2x + 12 - 3x = 27\), the first step involves simplifying the left side of the equation by combining like terms.

Now, let's analyze the options provided to see which one also involves the same initial step of combining like terms:

1. \(2x + 12 = 27\): This does not require combining like terms on the left side.

2. \(4x - 17 + 2x = 9\): This can be combined as \(6x - 17 = 9\), so it involves combining like terms.

3. \(2(x - 5) + 2x = 10\): This requires distributing and combination of terms, but it is not an initial like-term combination step.

4. \(2x + 12 = -3x - 27\): This equation still involves simplifying one side, but it's not about combining terms on the same side as the first equation.

The equation that has the same first step as \(2x + 12 - 3x = 27\) is:

\(4x - 17 + 2x = 9\) (because you also need to combine like terms).