Question

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

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