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+123x=27, the first step typically involves isolating the variable x by combining like terms.

In this case, we first combine 2x and 3x:

2x3x+12=27x+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=3x27 - This does not apply as it is already an equation without like terms on the left side.
  2. 4x17+2x=9 - Here, we combine 4x and 2x as the first step.
  3. 2(x5)+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, 4x17+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