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

12−x=40
12 minus x is equal to 40

x2=14

Answer 1

To solve the equation \( x - 12 = 40 \), we can isolate \( x \):

1. Add 12 to both sides: \[ x - 12 + 12 = 40 + 12 \] \[ x = 52 \]

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

1. Option 1: \( x + 12 = -40 \) \[ x + 12 = -40 \implies x = -40 - 12 = -52 \quad \text{(Not a match)} \]

2. Option 2: \( \frac{x}{4} = 13 \) \[ \frac{x}{4} = 13 \implies x = 13 \times 4 = 52 \quad \text{(This is a match)} \]

3. Option 3: \( 12 - x = 40 \) \[ 12 - x = 40 \implies -x = 40 - 12 \implies -x = 28 \implies x = -28 \quad \text{(Not a match)} \]

4. Option 4: \( x^2 = 14 \) \[ x = \sqrt{14} \text{ or } x = -\sqrt{14} \quad \text{(Not a match)} \]

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

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