Lesson 1: 5-1 Solving Inequalities by Addition & Substraction

Why is it important to understand what the symbols in a mathematical sentence represent?

What does a circle on a number line indicate?

How is the solution set of x = p modeled on a number line?

How do you read {x: x = p}?

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

Which inequality symbol models the phrase "at least"?

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;

Some inequalities are solved using the Addition and Subtraction Properties of Inequality. The solution to an inequality can be expressed in set-builder notation or graphed on a number line.

Panya wants to buy season passes to two theme parks. If one season pass costs $54.99 and Panya has $100 to spend on both passes, the second season pass must cost no more than what amount?

Students should always check their solutions but often omit this step in their hurry to finish their assignments. Remind students that checking their solutions is especially important with inequalities because the direction of the inequality sign often is changed when writing solutions in set-builder notation.

If students have trouble understanding some of the phrases used to indicate inequalities, such as at most or no less than, then have them work in pairs or groups to write word problems using the phrases. Have students write inequalities to represent the problem situations.

Extension: Write these three linear inequalities on the board:

y > 3 y + 1 > 4 5 < y + 2

Have students solve each linear inequality and compare the solutions. Ask students to formulate three more linear inequalities that are equivalent to y > 3.

Practice: Exercises 1-11

Exercises 57-62

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