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: $x+12=-40$ $$x+12=-40⟹x=-40-12=-52\text{(Not a match)}$$

2. Option 2: $\frac{x}{4}=13$ $$\frac{x}{4}=13⟹x=13\times 4=52\text{(This is a match)}$$

3. Option 3: $12-x=40$ $$12-x=40⟹-x=40-12⟹-x=28⟹x=-28\text{(Not a match)}$$

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

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

$\frac{x}{4}=13$.