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

Question

4x−17+2x=9

2(x−5)+2x=10

2x+12=27

2x+12=−3x−27

Answer 1

To determine which equation has the same first step to solve as the equation \( 2x + 12 - 3x = 27 \), we will first simplify this equation.

The first step to solving \( 2x + 12 - 3x = 27 \) is to combine the \( x \) terms on the left side:

\[ 2x - 3x + 12 = 27 \quad \Rightarrow \quad -x + 12 = 27 \]

Now, we can analyze the options given:

1. \( 4x - 17 + 2x = 9 \):

   • Combine \( 4x \) and \( 2x \): \( 6x - 17 = 9 \) (first step is combining \( x \) terms)

2. \( 2(x - 5) + 2x = 10 \):

   • Distribute the \( 2 \): \( 2x - 10 + 2x = 10 \) (first step is distributing)

3. \( 2x + 12 = 27 \):

   • No \( x \) terms to combine on the left (first step would be subtracting 12)

4. \( 2x + 12 = -3x - 27 \):

   • Rearranging terms would be the first step (not combining)

From this analysis, the only equation that has the same first step—combining like terms involving \( x \)—as the original equation is:

Option 1: \( 4x - 17 + 2x = 9 \).

So that would be the answer.