3.6 Solve Applications with Linear Inequalities

Learning Objectives

By the end of this section, you will be able to:

  • Solve applications with linear inequalities

Solve Applications with Linear Inequalities

Many real-life situations require us to solve inequalities. In fact, inequality applications are so common that we often do not even realize we are doing algebra. For example, how many gallons of gas can be put in the car for $20? Is the rent on an apartment affordable? Is there enough time before class to go get lunch, eat it, and return? How much money should each family member’s holiday gift cost without going over budget?

The method we will use to solve applications with linear inequalities is very much like the one we used when we solved applications with equations. We will read the problem and make sure all the words are understood. Next, we will identify what we are looking for and assign a variable to represent it. We will restate the problem in one sentence to make it easy to translate into an inequality. Then, we will solve the inequality.

Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.No Alt Text

ⓑ What does this checklist tell you about your mastery of this section? What steps will you take to improve?