Let's solve the equation \( x - 12 = 40 \) first:
\[ x - 12 = 40 \] \[ x = 40 + 12 \] \[ x = 52 \]
Now, we need to check which of the given equations has the same solution \( x = 52 \):
A. \( x + 12 = -40 \)
\[ x + 12 = -40 \] \[ x = -40 - 12 \] \[ x = -52 \quad (\text{Not equal to } 52) \]
B. \( \frac{x}{4} = 13 \)
\[ \frac{x}{4} = 13 \] \[ x = 13 \times 4 \] \[ x = 52 \quad (\text{Equal to } 52) \]
C. \( \frac{x}{2} = 14 \)
\[ \frac{x}{2} = 14 \] \[ x = 14 \times 2 \] \[ x = 28 \quad (\text{Not equal to } 52) \]
D. \( 12 - x = 40 \)
\[ 12 - x = 40 \] \[ -x = 40 - 12 \] \[ -x = 28 \] \[ x = -28 \quad (\text{Not equal to } 52) \]
The equation that has the same solution \( x = 52 \) is:
B. \( \frac{x}{4} = 13 \)