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

x2=14
x over 2 is equal to 14

x4=13

Answer 1

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

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

Now we'll check each of the provided options to see which one also equals \( x = 52 \).

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

2. Option: \( 12 - x = 40 \) \[ 12 - x = 40 \ -x = 40 - 12 \ -x = 28 \ x = -28 \quad (\text{Not equal to } 52) \]

3. Option: \( \frac{x}{2} = 14 \) \[ \frac{x}{2} = 14 \ x = 14 \times 2 \ x = 28 \quad (\text{Not equal to } 52) \]

4. Option: \( \frac{x}{4} = 13 \) \[ \frac{x}{4} = 13 \ x = 13 \times 4 \ x = 52 \quad (\text{Equal to } 52) \]

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

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

So, the answer is \( x \div 4 = 13 \).