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Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Lesson 3.4 Solving Inequalities using Addition or Subtraction Skill Check Skill Check

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Skill Check 2. 17 23 – 5 3. ½ 1/3 > < > 1. 2 + 3 4 4. 31 – 6 17 + 9< Replace each with > or <.

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Vocabulary Is a mathematical statement formed by placing an inequality symbol between two expressions. Symbols are: <, >, <, > With a variable is the set of all numbers that produce true statements when substituted for the variable. Are inequalities that have the same solution.

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Study Strategy When drawing graphs of inequalities, make sure open circles and closed circles are clear and easily differentiated. Example: 1.All numbers less than 7 2.All numbers greater than 4 3.All numbers less or equal to 1 4.All numbers greater than -4

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Writing and Graphing an Inequality EXAMPLE 1 Cybercafé KIS’s cybercafé charges users a minimum fee of 2000 won for internet access. Write an inequality to represent the access fee f. Then graph the inequality. ANSWER f > 2000 2000 0

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Solving an Inequality Using Subtraction EXAMPLE 2 SOLUTION k + 12 < -4 Solve k + 12 < -4. Graph and Check your solution. -12 + k + 12 < -4 – 12 k < -16 -160

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Solving an Inequality Using Addition EXAMPLE 3 SOLUTION -1 > y - 7 Solve -1 > y - 7. Graph and Check your solution. 7 – 1 > y – 7 + 7 y < 6 60

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Writing and Solving an Equation EXAMPLE 4 Math Test On the first two tests in math class, Diana had scores of 89 and 95 points. The third math test is tomorrow, and Diana’s goal is to have a total score of 279 or higher on the three math tests in order to have an A average for this quarter. What possible scores s can she have on the test tomorrow to attain her goal? Write a verbal model. ANSWER Diana’s possible score that she can have on the test tomorrow to attain her goal is 95 or higher. Diana’s first math score + Diana’s second math score + Diana’s possible scores s > Diana’s goal total score on 3 math tests 89 + 95 + s > 279 -184 + 89 + 95 + s > 279 – 184 s > 95

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Lesson Quiz 1. 17 + a > 20 2. -5 > s – 1 3. A traffic reporter announced that traffic will be delayed at least 15 minutes. Write an inequality to represent this. a > 3 s < -4 t > 15 Min Solve the Inequality. Graph your solution. 4. Challenge Which one of these compound inequalities has a graph that is not an empty number line? A. x > 3 and x > 5 -40 30 A. x > 3 and x > 5 B. y 1 C. z > -5 and z < -6

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Closure 1.) Give an example of an inequality that can be solved using the addition property of inequality, and another that can be solved using the subtraction property of inequality. a – 1 > 3 solve by addition b + 1 < 3 solve by subtraction

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Closure 2.) Celine has cats, geese, and snakes as pets. Her animals have a total of 22 legs. If she has more cats than geese and more geese than snakes, how many of each animal does she have? 4 cats, 3 geese, and two snakes 4 x = cats2 y = geesecats > geese x is the number of cats y is the number of geese x > y 4 x + 2 y = 22 Solve by guess, Check, and revise, or by graphing. y = -2 x + 11 y < x

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Lesson 3.4 Homework: pp.143-144 Exs. (12, 14, 16, 30, 32, 34, 36, 38, 40, 42, 43, 49, 50) Challenge/Bonus 44

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