Lesson 3: 5-3 Solving Multi-Step Inequalities

How is solving an inequality similar to solving an equation?

How is solving an inequality unlike solving an equation?

What does the graph of the solutions look like for a true, false, and conditional inequality?

A.REI.3 Solve linear equations and inequalities in one variable including equations with coefficients represented by letters.

A.CED.1 Create inequalities in one variable and use them to solve problems.

SAT questions related to inequalities: 5-4-13,7-4-5,4-4-19,8-3-6,1-4-28,5-3-7,6-3-14;

Multi-step inequalities can be solved using the Properties of Inequality and undoing each operation by working backward. If the inequality simplifies to a statement that is never true, the solution is the empty set, Ø. If the solution results in a statement that is always true, the solution is the set of all real numbers.

Adriana has a budget of $115 for taxes. The tax service she uses charges $25 to activate an account and $0.08 per receipt to file taxes. How many receipts can Adriana file and stay within her budget? Use the inequality 25 + 0.08f = 115.

Students may incorrectly assume that the solution of all inequalities in which the variable has been eliminated is the empty set. Remind students that they must simplify the inequality to determine whether it is a true statement. If the inequality is true, the solution set is the set of all real numbers. Only when the inequality is untrue is the solution the empty set.

If you have students who are interested in science, then point out that there are many natural settings, such as those in Exercise 41, that can be connected to linear inequalities. Have students write observations about possible connections in their notebooks and then share their observations with the class.

Extension: Ask students to explain how you can use the graph of y = -2x + 6 to solve the inequality -2x + 6 < 0.

Practice: Exercises 1 - 11

Exercises 60 - 65

Additional Resources

Access textbook through Classlink