What You Will Learn to Do: Solve Compound Inequalities

Many times, solutions to inequalities lie between two quantities, rather than continuing endlessly in one direction. Your blood pressure reading is one example of this. When you go to the doctor, the nurse takes your blood pressure reading. Blood pressure measures the pressure of blood in the circulatory system and is composed of two numbers: systolic and diastolic. When the nurse takes your blood pressure, the nurse is looking to see what range your blood pressure falls into. For example, systolic (top number) blood pressure that is between 120 and 139 mm Hg is called borderline high blood pressure. This can be described using a compound inequality, [latex]b<139[/latex] and [latex]b>120[/latex].

In this section, we will explore how to solve compound inequalities and represent solutions using standard conventions.

In particular, you will learn how to

• Use interval notation to describe intersections and unions
• Use graphs to describe intersections and unions
• Solve compound inequalities – OR
• Solve compound inequalities – AND
• Express solutions to inequalities containing absolute value
• Identify cases of inequalities containing absolute value that have no solutions