Well, if we are taking the absolute value, of |x - 3| = 7, then you have a total of two cases. 7 can be either positive or negitive.
Knowing this, we can write out our two cases as:
|x - 3| = 7, or
|x - 3| = -7
Using these two equations, we can solve the equations for our values of x:
First Case:
|x - 3| = 7
x - 3 = 7
x = 10
Second Case:
|x - 3| = -7
x - 3 = -7
x = -4
So, our two cases show us that x can equal -4, or 10.
