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

12−x=40
12 minus x is equal to 40

x/2=14
x over 2 is equal to 14

x/4=13

Answer 1

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

1. Start with the original equation: \[ x - 12 = 40 \]

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

Now, let's check each of the response options to see which one also gives \( x = 52 \):

1. Option A: \( x + 12 = -40 \)

   • Subtract 12 from both sides: \[ x = -40 - 12 = -52 \quad \text{(not 52)} \]

2. Option B: \( 12 - x = 40 \)

   • Rearranging gives: \[ -x = 40 - 12 \] \[ -x = 28 \quad \Rightarrow \quad x = -28 \quad \text{(not 52)} \]

3. Option C: \( \frac{x}{2} = 14 \)

   • Multiply both sides by 2: \[ x = 14 \times 2 = 28 \quad \text{(not 52)} \]

4. Option D: \( \frac{x}{4} = 13 \)

   • Multiply both sides by 4: \[ x = 13 \times 4 = 52 \quad \text{(is 52!)} \]

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

Option D: \( \frac{x}{4} = 13 \).