Which equation has the same solution for x as this equation: x−12=40

Question

?(1 point)
Responses

x4=13
x over 4 is equal to 13

12−x=40
12 minus x is equal to 40

x2=14
x over 2 is equal to 14

x+12=−40

Answer 1

To solve the original equation \( x - 12 = 40 \), we can add 12 to both sides:

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

Now, we need to determine which of the given equations also has the solution \( x = 52 \).

Let's evaluate each option:

1. \( x/4 = 13 \) \[ x = 13 \cdot 4 = 52 \quad \text{(This has the same solution)} \]

2. \( 12 - x = 40 \) \[ -x = 40 - 12 \ -x = 28 \ x = -28 \quad \text{(Different solution)} \]

3. \( x/2 = 14 \) \[ x = 14 \cdot 2 = 28 \quad \text{(Different solution)} \]

4. \( x + 12 = -40 \) \[ x = -40 - 12 \ x = -52 \quad \text{(Different solution)} \]

The only equation that has the same solution \( x = 52 \) is: \[ x/4 = 13 \]

So, the answer is:

\( x/4 = 13 \)