basically, its more simple algebra, except with a few of them it can be tricky.
The main point is you've got a single unknown variable (x in this case), and you want to manipulate the equation so that it's just the variable with no constants by it on one side and having that equal a constant.
For example: 3x = 3. Divide both sides by 3 and you get x = 1, yay.
Now, lets take a look at the first sample problem (1 / x) + (7 / 3x) = -4. So first you need to look for something common to manipulate without making the problem horribly messed up. In this case, its 1 / x. So we can just multiple both sides by X (whatever you do to one side of the equation, must follow through with the other side) and get 1 + (7/3) = -4x; 10/3 = -4x. Then it's easy from there. But I prefer this way as well.
Take out a factor of (1/x) so it now looks like (1/x)[1 + (7/3)] = -4. And do the rest.
The third one I suspect will be in the Ax^2 + Bx + C = 0 format. Can still be done but you may have to do some completing the squares in the end. No clue on the fourth one, can't read it well.