Question

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

Answer 1

are you sure this is correct

Answer 2

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**

Answer 3

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.