Suppose that e and f are points on the number line. if ef=12 and e lies at −4, where could f be located?
if there are several locations, separate them with commas.

The distance between two points is defined as

We know that the distance between E and F is 12 units.
The point E is at the point -4.

I'll use X for the point F.

Now we have the equation

Solve for X.

We have two possible equations: and

Solve each of them.

-4 - X = 12

Using the Addition Principle of Equality, we can add 4 to each side of the equation and will still get an equation with the same solution.

-4 - X + 4 = 12 + 4
X = 16

Now for the second equation.

-4 - X = -12

Just like with the equation above, we can use the Addition Principle of Equality to add 4 to each side of the equation and still get an equation with the same solution.

-4 - X + 4 = -12 + 4
-X = -8

-X = -8 is the same thing as X = 8 because we can divide both sides -1 to get X = 8.

So, the two points where X could be are the points -16 and 8.