Chapter 5: Linear Inequalities

Transcription

1 Lesson 5-1: Solving Inequalities by Addition and Subtraction An is a statement that contains <, >,, or. notation is a way of writing a solution set. Example 1: Solve each inequality. Check your solution. Graph your solution on a number line. A. c 12 > 65 B. 6 + x 10 Page1

2 Example 2: Solve each inequality. Graph your solution on a number line. A. x + 23 < 14 B. 4 y + 11 Example 3: Solve each inequality. A. 12n 4 13n B. 3p 6 4p Example 4: Tanya wants to buy season passes to two theme parks. If one season pass costs $54.99 and Tanya has $100 to spend on both passes, the second season pass must cost no more than what amount? Page2

3 Lesson 5-2: Solving Inequalities by Multiplication and Division Page3

4 Example 1: Mateo is walking at a rate of 3 miles per hour. He knows that it is at least 9 miles to Onyx Lake. 4 How long will it take Mateo to get there? Write and solve an inequality to find the length of time. Example 2: Solve each inequality. A. 3 d 6 B. 1 x < Example 3: Solve each inequality. Then graph on a number line. A. 12k 60 B. 8q < 136 Page4

5 Lesson 5-3: Solving Multi-Step Inequalities Example 1: Adriana has a budget of $115 for faxes. The fax service she uses charges $25 to activate an account and $0.08 per page to send faxes. How many pages can Adriana fax and stay within her budget? Example 2: Solve 13 11d 79. Example 3: Define a variable, write an inequality, and solve the problem. A. Four times a number plus twelve is less than the number minus three. B. 6 times a number is greater than 4 times the number minus 2. Page5

6 Example 4: Solve 6c + 3(2 c) 2c + 1. Example 5: Solve each inequality. A. 7(s + 4) + 11s 8s 2(2s + 1) B. 2(4r + 3) (r 2) Page6

7 Lesson 5-4: Solving Compound Inequalities Two or more inequalities connected by the words and or or is called a inequality. There are two types of compound inequalities: Example 1: Solve 7 < z Graph the solution set. Example 2: A ski resort has several types of hotel rooms and several types of cabins. The hotel rooms cost at most $89 per night and the cabins cost at least $109 per night. Write and graph a compound inequality that describes the amount that a guest would pay per night at the resort. Page7

8 Example 3: Solve 4k 7 25 or 12 9k 30. Graph the solution set. Example 4: Write a compound inequality for each graph. A. B. C. D. Page8

9 Lesson 5-5: Inequalities Involving Absolute Value Recall: When solving absolute value equations or inequalities, there are cases to consider. For <, the solution is the intersection of the two cases ( and ). For >, the solution is the union of the two cases ( or ). Example 1: Solve each inequality and graph the solution set. A. s 3 12 B. x + 6 < 8 Example 2: The average annual rainfall in California for the last 100 years is 23 inches. However, the annual rainfall can differ by 10 inches from the 100 year average. What is the range of annual rainfall for California? Example 3: Solve each inequality and graph the solution set. A. 3y 3 > 9 B. 2x Page9

10 Lesson 5-6: Graphing Inequalities in Two Variables To graph a linear inequality, you have to show all possible solutions for that inequality. The equation defines the, which divides the coordinate plane into two different. Graphing Linear Inequalities Step 1: Solve for y. Step 2: Graph the boundary (the equation). Use a solid line for or. This is called a half-plane. Use a dotted line for < or >. This is called an half-plane. Step 3: Use a test point (x, y) to determine which half-plane should be shaded. Step 4: Shade the half-plane that contains the solution. Example 1: Graph 2y 4x > 6. Example 2: Graph x + 4y 2. y y x x Page10

11 Example 4: Ranjan writes and edits short articles for a local newspaper. It takes him about an hour to write an article and about a half-hour to edit an article. If Ranjan works up to 8 hours a day, how many articles can he write and edit in one day? y x Page11