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

Question

?(1 point)
Responses

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

x4=13
x over 4 is equal to 13

x2=14
x over 2 is equal to 14

12−x=40

Answer 1

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

1. Start with the equation \( x - 12 = 40 \).
2. Add 12 to both sides to isolate \( x \): \[ x = 40 + 12 \]
3. Simplifying gives: \[ x = 52 \]

Now, let's analyze each of the given equations to see if any yield \( x = 52 \):

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

2. \( \frac{x}{4} = 13 \): \[ x = 13 \times 4 = 52 \quad (\text{same solution}) \]

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

4. \( 12 - x = 40 \): \[ -x = 40 - 12 \implies -x = 28 \implies x = -28 \quad (\text{not the same solution}) \]

The equation that has the same solution for \( x = 52 \) is:

\( \frac{x}{4} = 13 \).