inequalities

Fairly certain that isn't an inequality. Looks to me like a simple algebraic equation for solving "x." Did you list the wrong equation or enter the wrong title? I'll just assume that you miss-dubbed the title and help you with the answer to the problem as written.

5/9+3/4x=2/3x-1/6x

Get all of the fractions with x beside them to have the least common denominator, in this case, 24 (24 is the lowest number 4, 3, and 6 can go into).

You will end up with: 5/9 + 18/24x = 16/24x - 4/24x

Adding the fractions with "x" attached on the right side, we get 5/9 + 18/24x = 12/24

Then subtract 18/24 from the both sides so we can get all the "x fractions" together. We end up with: 5/9 = -6/24x

Now that we have all the "x fractions" added together, we can simplify the "x fraction" we have left so it will be easier to get rid off what is attached to the x. The result is 5/9 = -1/4x.

Now we have to get x by itself. To do this, we multiply both sides by the reciprocal of -1/4 (-4 or -4/1). This leaves us with -20/9 = x.

Thus, -20/9 is your answer. (Ugly, I know.) Plugging -20/9 back into the equation, you will find that everything works so the answer is assured to be correct. Hope that helps! (If it's actually an inequality, repost it and I'll try to help you out as soon as possible.)

Jay:

5/9+3/4x=2/3x-1/6x

Hi Jay and GrammarFascist,

That is a great answer there, I am impressed.
I would just do it a little bit diferently.
You have denominators of 9,4,3,6 (that's assuming all the x's are on the top)
now, the lowest common denominator of all these is 36.
If you multiply everything on both sides by 36 you will get rid of all the fractions in one fell swoop.
Then it will be much easier to deal with,

also,
Why don't you both join up properly,

There are some big benefits to joining up.
1) It is a little easier to make a post.
2) Once you have made a post you can edit it if you are a member. I edit my post all the time. I would hate not to be able to do that.
3) You can also delete your post so long as no-one has answered you yet.
4) No-one else can use your username
5) You can send and receive private messages to other people and make real friends. I know that I have.

---------------------------------------------------------------------------------------------------------------------------------