Solving linear inequalities is very similar to solving linear equations. You must isolate the variable on one side of the inequality by using the inverse, or opposite operations. To undo addition, you use subtraction and vice versa. To undo multiplication, you use division and vice versa. The only difference in solving linear inequalities occurs when you multiply or divide by a negative number. When this is the case, you must flip the inequality symbol. This means that less than becomes greater than, greater than becomes less than, etc. Another type of inequality is called a compound inequality. A compound inequality contains two inequalities separated by an “and” or an “or” statement. An “and” statement can also consist of a variable sandwiched in the middle of two inequality symbols. To solve this type of inequality, simply separate it into two inequalities applying the middle terms to each. Then, follow the steps to isolate the variable.
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Last updated: 01/25/2018
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