Compound Inequalities – Practice Problems

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Compound inequalities are AND or OR inequalities. It’s important to understand the difference between AND and OR situations and also to recognize their graphs.

For an AND situation, a less than or less than and equal to situation such as -3 < x < 3, the solution is the intersection of the solution for x > -3 and x < 3. The graph of an AND situation (conjunction) will have one piece shaded. For an OR situation, such as x < -3 or x > 3, the solution is the union of the solution for each inequality.

The graph of an OR situation (disjunction) will be shaded in two pieces. How do you solve compound inequalities? Set up the inequalities as two separate inequalities then use algebraic steps to solve. To solve the inequalities, use opposite operations with reverse PEMDAS to isolate the variable.

Don’t forget about the sign. If multiplying or dividing by a negative number, remember to flip the sign so it points in the opposite direction. Otherwise, maintain the direction of the sign. Remember less than or less than and equal to situations are AND inequalities and greater than or greater than or equal to situations are OR inequalities. To investigate compound inequalities, watch this video.

Use inequalities to solve problems. CCSS.MATH.CONTENT.HSA.CED.A.3

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Exercises in this Practice Problem
Write an inequality to describe the situation.
Simplify the following inequalities.
Decide which number line belongs to which compound inequality.
Solve the inequality.
Explain what the inequality means.
Determine the opposite inequality.