Ask a New Question
Menu

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

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

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

4x−17+2x=9

1 answer

To find which equation has the same first step as \( 2x + 12 - 3x = 27 \), we need to analyze the first step in solving it.

  1. Original equation: \( 2x + 12 - 3x = 27 \)
  2. Combine like terms on the left side:
    • Combine \( 2x \) and \( -3x \): \[ (2x - 3x) + 12 = 27 \] \[ -x + 12 = 27 \]

Now we can review the given equations to see which one can also be simplified in a similar way (specifically, combining like terms or moving terms to the same side).

  1. \( 2x + 12 = -3x - 27 \): Cannot combine like terms easily.
  2. \( 2(x - 5) + 2x = 10 \): This involves distributing which is different from our first step.
  3. \( 2x + 12 = 27 \): Direct comparison, but this does not involve similar operation.
  4. \( 4x - 17 + 2x = 9 \): Combine like terms \( (4x + 2x) - 17 = 9 \).

The only equation that follows the same first step of combining like terms is \( 4x - 17 + 2x = 9 \).

So the answer is \( 4x - 17 + 2x = 9 \).