[linz06]

I wrote this down quickly so I'm not sure if it's the right answer but it was a nice quick break from work (I love math, I'm a geek)

Since you know what y is, you insert that value for y and you get:

-1/2-3 = 3/4x-8

First, you need common denominators if you want to add/subtract fractions. since the only fraction we need to worry about right now has a 2 on the bottom, put a 2 on the bottom of the other numbers we need to add an subtract. 3 becomes 6/2 and 8 becomes 16/2. Same value, just a common denominator. I'll put brackets around the fractions so they're easier to decipher in computer type. You end up with:

-(1/2) - (6/2) = (3/4x) - (16/2)

Now you can easily simplify the left side. You add or subtract the top numbers, so -1 - 6 = -7. Your new value for that side becomes -7/2:

-7/2 = (3/4x) - (16/2)

Simply add the 16/2 to both sides, which cancels it out on the right side and adds it to the left side. The bolded numbers cancel each other out and equal 0:

-(7/2) + (16/2) = (3/4x) - (16/2) + (16/2)

Add the -7 + 16 to end up with 9/2 on the left side:

9/2 = 3/4x

If you multiply 4x (in fraction form, 4x/1), the 4x will cancel out on the right side:

(9/2) * (4x/1) = (3/4x) * (4x/1)

When multiplying fractions, you can multiply straight across - top number times top number, over bottom number times bottom number. 9 * 4x = 36x, and 2 * 1 = 2. You end up with 36x/2:

36x/2 = 3

Now you can divide 36 by 2 and you end up simplifying to 12x:

12x = 3

To get x alone, you must divide both sides by 12:

x = 3/12, or simplified to x = 1/4