Begin with a problem. A typical one-step inequality problem might be 6 > x -- 1. Whenever you solve algebra equations or inequalities, you must try to simplify the problem as much as possible. In other words, you must put all numbers on one side of the equation to leave the unknown by itself on the other side. In this example, the unknown is "x."
Learn the rules of addition for inequalities. The goal of this problem is to get the "x" on the right side of the inequality by itself. To do this, you must eliminate the "-- 1." Whenever a number is being subtracted, as in this case, in an inequality, you must add that number to both sides to eliminate it from one side.
Add the number. In this example, you must add a "1" to both sides of the inequality. When you do this, the left side of the inequality equals 7, which is found by adding the 6 plus the 1. The right side of the inequality says "x -- 1." When you add a 1 to this side, it cancels out the "-- 1," leaving just the x. The answer to this inequality therefore is: 7 > x. This is read, "x is less than 7."
Learn the rules of subtraction. The rules for subtraction are similar, but instead of adding the number, the number is subtracted. For example, with the inequality x + 2 > 5; you must eliminate the 2 from the left side of the inequality. This is done by subtracting the 2 from both sides. With the rules of addition and subtraction, whatever action is performed on one side, the same action must be performed on the other side.
Subtract the number. For this example, subtract 2 from both sides, leaving the inequality x > 3. This is read, "x is greater than 3."