Why do some equations have the same variable on both sides?

Some equations have the same variable on both sides because you are supposed to solve for that number. for example 5x+4=11-2x for this example, so you dont have to deal with negatives, you would add 2x to both sides first. and you would do that so that you can cancel out the variable on the right side so that it is only on the left side so you end up with, 7x+4=11. the next thing you would do is subtract 4 from both sides so that you can get the variable by itself on one side so it would look like this, 7x=7. and to finish it off, you would divide both sides by 7, and get x.