Get the variable you wish to solve for on one side. That is, if your equation has the variable of interest on both sides of the equals sign, use algebra to move it to a single side. For example, if you are solving 5x -- 17 = 2x -- 2, you will notice that you have x-variables on both sides. Use subtraction on both sides to move the x-variable to a single side. In this case, subtract 2x from both sides to yield 3x -- 17 = -2.
Write down the operations being applied to the variable of interest. Ask yourself why the variable you wish to solve for is not completely by itself, without any numbers accompanying it on its side of the equation. Write down what is happening to the variable in the order it happens (moving outward from the variable in terms of operations). For example, in 3x -- 17 = -2 you will see that there is a 3 being multiplied by "x." Second, there is a 17 being subtracted from the 3x. Here, you would write down "multiply by 3" and "minus 17."
Reverse the order of what you have written down: "minus 17" and "multiply by 3."
Reverse the operations in what you have written down. Addition becomes subtraction and vice versa. Multiplication becomes division and vice versa. In the example, "minus 17" becomes "plus 17" and "multiply by 3" becomes "divide by 3."
Perform these opposite operations in reverse order. Do this on both sides of the equation. For the example, first add 17, giving 3x = 15. Then divide by 3, giving x = 5, the final answer.
Move all of the variables to one side of the equation, leaving zero on the other side. For the problem 5x -- 17 = 2x -- 2, moving everything over to one side by addition and subtraction yields 0 = 3x -- 15.
Replace the zero in the equation with another variable, such as "y." In the example, we would have the new equation y = 3x -- 15.
Graph this equation as normal.
Find where the graph passes through the x-axis. This point is the solution to the equation. Having graphed the example, you would find that the line for y = 3x -- 15 hits the x-axis at exactly 5, the same answer yielded by algebraic methods.