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Which equation has the same first step to solve as this equation:

2x + 12 - 3x = 27
A. 2x + 12 = 27
B. 2(x - 5) + 2x = 10
C. 4x - 17 + 2x = 9
D. 2x + 12 = -3x - 27

3 answers

To solve the equation \(2x + 12 - 3x = 27\), the first step would be to combine like terms on the left side. This involves combining the \(2x\) and the \(-3x\).

Let's examine each option to see which one has the same first step:

A. \(2x + 12 = 27\)

Here, there are no like terms to combine, so this does not have the same first step.

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

In this equation, there are no like terms to combine right away either.

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

In this equation, we can combine \(4x\) and \(2x\) on the left side. This option has a similar first step since we are combining like terms.

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

In this equation, there are no like terms to combine directly on the left side.

After reviewing each option, the correct answer is:

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

This equation also requires combining the like terms \(4x\) and \(2x\) as a first step, just like the original equation does with \(2x\) and \(-3x\).

are you sure this answer is correct

Let's analyze each equation again to determine the correct answer clearly.

The original equation is:

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

The first step is to combine like terms, specifically \(2x - 3x\), which gives:

\[ -1x + 12 = 27 \]

Now, let's break down each of the answer choices based on whether it involves combining like terms in the same way.

A. \(2x + 12 = 27\)
Here, \(2x + 12\) remains as is, and there are no like terms to combine on the left side, so this option does not match the original.

B. \(2(x - 5) + 2x = 10\)
This equation does not have like terms to combine right away; it involves distributing first.

C. \(4x - 17 + 2x = 9\)
In this equation, combining \(4x\) and \(2x\) (which gives \(6x - 17 = 9\)) is indeed similar to the original since it also involves combining coefficients of \(x\).

D. \(2x + 12 = -3x - 27\)
No like terms to combine directly on the left side; instead, you would move terms around.

Upon reevaluation, my previous conclusion appears to have mistakenly indicated option C without considering other aspects thoroughly.

Therefore, the correct answer that involves the same first step of combining like terms (coefficients of x) in the left side by reducing or removing like terms is option C: \(4x + 2x - 17 = 9\). This requires similar manipulation to the original equation.

Thank you for your patience, and I appreciate your bringing it to my attention!