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The main rule is that whatever rule you perform on one side of the equation must also be performed on the other side of the equation. You have to choose the operation in such a way as to isolate the variable you want to solve for.
When isolating a variable, you want to get the variable alone on one side of the equation and then what it equals on the other side. Anything you do to one side of the equation, you must do to the other. e.g.3x+2=8First, you subtract 2 from both sides leaving:3x=6Then you divide both sides by 3, and you are left with: x=2
That is called "solving for a variable". If there is only one variable in the equation, then it is a "solution". For example, 3x + 4y = 13 can be solved for x as 3x = -4y + 13 x = -(4/3)y + 13/3 This is solved for x. Another equation with only one variable: 5z - 6 = 4 5z = 10 z = 2 This is a solution.
The idea is to "isolate" the variable, in this case "x", on one side. In this case, you would start by multiplying both sides of the equation by "x".
There are a few ways to isolate a variable. First, add or subtract anything to get a monomial on one side containing the variable. Then divide by anything that is being multiplied to the variable. Here is an example: xy-4z=2z-4y solving for x xy=(2z+4z)-4y xy=6z-4y x=(6z-4y)/y