Algebra can be lumped into the two general categories of "classic" and "modern" algebra. The first pertains to solving equations with an unknown variable or number, and it is within the context of classic algebra that both one- and two-step equations fall. Some basic axioms to follow when solving these equations include using letters like x and y for unknown numbers, performing the opposite of a function to negate it on one side of an equation, and making sure to do the same thing to both sides of the equation.
As the name indicates, one-step equations are simply algebraic expressions that require only one step to solve. For example, "x+10=12" is a one-step equation. As with any classic algebra problem, the way to solve it is to get x alone on one side of the equal sign. To do so, the person solving the problem must do the opposite function of whatever is keeping x from being alone on one side of the equal sign, and she must do it to both sides of the equation. Thus, she must subtract 10 from both the left side and the right side of the equation. Once she does so, she gets "x=2," which is her answer.
Like one-step equations, two-step equations follow all of the same classic algebra principles. The only difference is that these equations require two steps to solve rather than just one. An example of a two-step equation is "2y+6=12." Now there are two numbers on the left side of the equation with which the solver must contend. In this instance, the student would subtract six from both sides of the equation to get ride of the six on the left, and he would end up with "2y=6." To get the y by itself, he must perform the opposite function and must divide "2y" by "2." He must also make sure to divide the "6" on the other side of the equation by "2," to keep it balanced. In the end, he should come up with "y=3."
For both one- and two-step equations, there is a very simple way that students can check an answer to make sure that it is right. Once the student has her final answer, she should simply plug that answer back into the variable spot in the original equation, and solve it as a simple math problem. For the one-step equation example, of "x+10=12," she would plug in her answer of "x=2" and would get "2+10=12" or "12=12." This is true, which proves that her answer is correct. The same checking process applies to two-step equations, as demonstrated by the second example of "2y+6=12." By plugging in the answer of "y=3," the student should get "2(3)+6=12" or "6+6=12," and finally "12=12." Again, the equation is correct, and so is the answer of "y=3."