Which equation has the same solution for x as this equation: x−12=40 ?(1 point)

Question

Responses

x+12=−40x plus 12 is equal to negative 40

x4=13x over 4 is equal to 13

x2=14x over 2 is equal to 14

12−x=40

Answer 1

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

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

Now we will check which of the given equations has the same solution \( x = 52 \).

1. Equation: \( x + 12 = -40 \) \[ x + 12 = -40 \ x = -40 - 12 \ x = -52 \quad \text{(not 52)} \]

2. Equation: \( \frac{x}{4} = 13 \) \[ \frac{x}{4} = 13 \ x = 13 \times 4 \ x = 52 \quad \text{(this is 52)} \]

3. Equation: \( \frac{x}{2} = 14 \) \[ \frac{x}{2} = 14 \ x = 14 \times 2 \ x = 28 \quad \text{(not 52)} \]

4. Equation: \( 12 - x = 40 \) \[ 12 - x = 40 \ -x = 40 - 12 \ -x = 28 \ x = -28 \quad \text{(not 52)} \]

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

\[ \frac{x}{4} = 13 \]

So the answer is: x/4 = 13.