1. Which equation has the same solution for x as this equation: x−12=40 ?(1 point)Responses12−x=4012 minus x is equal to 40x4=13x over 4 is equal to 13x+12=−40x plus 12 is equal to negative 40x2=14

Answer 1

To find an equation that has the same solution for \( x \) as the equation \( x - 12 = 40 \), we first solve the original equation:

\[ x - 12 = 40 \]

Adding 12 to both sides, we get:

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

Now, we need to check which of the given options also leads to \( x = 52 \).

1. \( 12 - x = 40 \)

   Solving this: \[ -x = 40 - 12 \] \[ -x = 28 \quad \Rightarrow \quad x = -28 \quad (\text{not equal to 52}) \]

2. \( x/4 = 13 \)

   Solving this: \[ x = 4 \times 13 \] \[ x = 52 \quad (\text{this one works}) \]

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

   Solving this: \[ x = -40 - 12 \] \[ x = -52 \quad (\text{not equal to 52}) \]

4. \( x^2 = 14 \)

   Solving this: \[ x = \sqrt{14} \quad \text{or} \quad x = -\sqrt{14} \quad (\text{not equal to 52}) \]

Therefore, the equation that has the same solution for \( x \) as \( x - 12 = 40 \) is:

\( x/4 = 13 \).