Lesson 2: 5-2 Solving inequalitites by Multiplication & Division

What inverse operation will undo multiplication?

When multiplying by a negative number, what happens to the inequality symbol?

What is one way to solve an inequality containing a fraction?

How can you check to see if the solution makes sense?

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;

Some inequalities are solved using the Multiplication and Division Properties of Inequality. When multiplying or dividing each side of an inequality by the same negative number, the direction of the inequality symbol must be reversed.

Mateo walks at a rate of 3/4 mile per hour. He knows that it is at least 9 miles to Onyx Lake. How long will it take Mateo to get there? Write and solve an inequality to find the time.

Point out to students that an inequality is easier to solve using division when the inequality involves whole numbers and easier to solve using multiplication by reciprocals when the inequality involves fractions.

Point out that the rules for the Division Property of Inequalities state that each side of an inequality can be divided by a positive or negative number. In neither case is zero included because division by zero is an undefined operation.

Strategies for mulilingual learners:
Beginning Read the lesson opener or an example aloud one sentence at a time. At the end of each sentence, ask students to say a word or short phrase that describes an important piece of information from the sentence. Model recording the information in preparation for solving the problem. Have students use your model to record information in their notes.

Intermediate Slowly read the lesson opener or an example aloud. After each sentence or two, pause and ask volunteers to identify an important piece of information. Have students write the important idea in their notes.

Advanced Tell students to listen without taking notes while you read aloud. After you have finished, have students write down what they remember from your reading. Have students work in small groups to compare their notes. Then have each group discuss the problem and its solution.

Advanced High Have students practice active listening as you read aloud by taking notes. Then have students work in pairs to summarize the information and solve the problem. Have pairs share with the class.

Practice: Exercises 1 -9

Exercises 48 - 55

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