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Which equation has the same solution for x as this equation:

x - 12 = 40?
A. 12 - x = 40
B. x/4 = 13
C. x/2 = 14
D. x + 12 = -40

3 answers

Let's first solve the given equation:

\[ x - 12 = 40 \]

To find \( x \), we can add 12 to both sides of the equation:

\[ x = 40 + 12 \] \[ x = 52 \]

Now, let's check each of the options to see which one also has \( x = 52 \) as a solution.

A. \( 12 - x = 40 \)

Rearranging gives: \[ -x = 40 - 12 \] \[ -x = 28 \] \[ x = -28 \] (not equal to 52)

B. \( \frac{x}{4} = 13 \)

Multiplying both sides by 4 gives: \[ x = 13 \times 4 \] \[ x = 52 \] (this is a match)

C. \( \frac{x}{2} = 14 \)

Multiplying both sides by 2 gives: \[ x = 14 \times 2 \] \[ x = 28 \] (not equal to 52)

D. \( x + 12 = -40 \)

Rearranging gives: \[ x = -40 - 12 \] \[ x = -52 \] (not equal to 52)

The only equation that has the same solution as the original equation \( x - 12 = 40 \) is:

B. x/4 = 13

are you sure this is correct

Let's verify the calculations step by step to be sure about the solution:

  1. Original equation:
    \( x - 12 = 40 \)
    Adding 12 to both sides:
    \[ x = 40 + 12 \]
    \[ x = 52 \]

Now let's check each option to see if it also results in \( x = 52 \).

A. \( 12 - x = 40 \)
Rearranging gives:
\[ -x = 40 - 12 \]
\[ -x = 28 \]
\[ x = -28 \] (not equal to 52)

B. \( \frac{x}{4} = 13 \)
Multiplying both sides by 4:
\[ x = 13 \times 4 \]
\[ x = 52 \] (this is a match)

C. \( \frac{x}{2} = 14 \)
Multiplying both sides by 2:
\[ x = 14 \times 2 \]
\[ x = 28 \] (not equal to 52)

D. \( x + 12 = -40 \)
Rearranging gives:
\[ x = -40 - 12 \]
\[ x = -52 \] (not equal to 52)

The only equation that has the same solution \( x = 52 \) as the original equation \( x - 12 = 40 \) is indeed:

B. \( \frac{x}{4} = 13 \)

So yes, I can confirm that the answer is correct.