Hi Seth,
There are 2 parts to your problem. First lets figure the answer to the right of the equals.
1/2 - 1 = ?
What does 1 equal?
1 = 2/2
so 1/2 - 2/2 = 1-2 halves.
1/2 - 1 = -1/2
Now...
How can we substract 1/4x from 1/3x?
We need a common denominator.
Our lowest common denominator is 12.
1/3 = 4/12
1/4 = 3/12
So...
4/12x - 3/12x = -1/12x
Now we know this:
1/12x = -1/2
Let's solve for x by isolating x. We do this by multiplying both sides by 12 (which is the inverse of 1/12).
1/12x = -1/2
(12)(1/12)x = (-1/2)(12)
x = (-1/2)(12)
What is half of 12?
x = -6
Let's check our work.
1/3x - 1/4x = -1/2
What is 1/3 of -6 and 1/4 of -6?
1/3 * -6 = -2
1/4 * -6 = -1.5 (3/2)
-2 + 1.5 = -1/2
This is true so our answer is correct. x = -6