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Solving Inequalities

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Students learn that when solving an inequality, such as –3x < 12, the goal is the same as when solving an equation: to get the variable by itself on one side. Note that when multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality sign must be switched. For example, to solve –3x < 12, divide both sides by –3, to get x > -4. And when graphing an inequality on a number line, less than or greater than means an open dot, and less than or equal to or greater than or equal to means a closed dot.

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