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

Skill Check – 5 3. ½ 1/3 > < > – < Replace each with > or <.

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.

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

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 >

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

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

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 s > s > 279 – 184 s > 95

Lesson Quiz a > > 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 > A. x > 3 and x > 5 B. y 1 C. z > -5 and z < -6

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

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

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