Chapter 5 Inequalities

Transcription

1 Chapter 5 Inequalities 5.1 Solve inequalities using addition and subtraction 1. Write and graph an inequality. 2. Solve inequalities using addition and subtraction. Review- Symbols to KNOW < LESS THAN > GREATER THAN LESS THAN OR EQUAL TO GREATER THAN OR EQUAL TO Write an algebraic expression for the following inequalities: 1. the sum of a number and 4 is less than the product of 2 and a number is greater than the quotient of 30 divided by a number is at most is no greater than the sum of a number and 8 When graphing inequalities, make sure the variable is on the left. Graph the following: closed circle 1. x < 2 2. x 1 Solve by Adding Solve and graph the following inequalities > a k 4 open circle 3. 3 < x 4. x 0 7. y 6 > g 4 1

2 Solve by Subtracting Solve and graph the following inequalities. 9. x + 4 < n 2 Check for Understanding Solve and graph the following inequalities. 9. x 4 < n < b c < b c + 1 Closing Activity Joni and Jessica both solved the problem below. Who is correct? 5.2 Solve inequalities using multiplication and division 1 > a + 2 Joni's answer: a > 1 Jessica's answer: 1 < a 1. Solve inequalities using multiplication and division. The are both correct! Solve by Multiplying by a positive number Solve and graph the following inequalities. 5. g 2 1 CFU k c 2 2 Solve by Multiplying by a negative number When you multiply or divide BOTH sides of an inequality by a NEGATIVE value, you must FLIP the inequality sign!! Solve and graph the following inequalities. 7. h > p 3 1 2

3 Solve by Dividing by a positive number Solve and graph the following inequalities. 9. 4y > < 4b Solve by Dividing by a negative number When you multiply or divide BOTH sides of an inequality by a NEGATIVE value, you must FLIP the inequality sign!! Solve and graph the following inequalities h > m 28 CFU 3p < 6 CFU r > 9 Solve. Check for Understanding Check for Understanding 2x > 10 4x<32 What is special about multiplying or dividing by a negative? 2<m 5 t < 9 6 Laurie and Zach are solving 9b<18. Laurie -9b < 18-9b > b > -2 Closing Activity Who is correct? Zach -9b < 18-9b < b < Solve Multi step inequalities 1. Solve multi step inequalities. Solve and graph. Motivating the Lesson x p < m < x

4 Solving Multi step Inequalities 1. 7b + 19 < 16 Check for Understanding (CFU) 2. 9C + 32 > d 79 2d + 1 < x Write an inequality and then solve. Four times a number plus twelve is less than a number minus 3. What if there are grouping symbols? OH NO!!!!! PANIC! PANIC! PANIC! What would you do? Distribute What happens if the variable disappears? There are three possible outcomes: one solution many solutions no solutions 4

5 5.4 Solve Compound Inequalities 1. Write and graph compound inequalities. 2. Solve inequalities with and and or. A compound inequality consists of two separate inequalities joined by and and or. 5

6 Translate the verbal phrase into an inequality. Then graph the inequality In a certain restricted air space, airplanes must fly below 10,000 feet or above 15,000 feet. Write and graph a compound inequality that models this situation. 6

7 The high temperature on a certain day was 98 F and the low was 78 F. Write a compound inequality that models the range in temperatures. On a road in the city of Rochester, the maximum speed is 65 miles per hour and the minimum speed is 30 miles per hour. Write a compound inequality that models this situation. Junior tickets to an event are available to teenagers below age eighteen at reduced rates. Write an inequality that models this situation. The highest temperature in the US for each month are shown in the table. Write a compound inequality the represent the range of record high temperatures. Steps: 1. Separate into inequalities. 2. Solve each. 7

8 5.5 Solve Absolute Value Equations 1. Solve absolute value equations. Who is closer? ABSOLUTE VALUE Who is closer? Steps: 1. Rewrite the absolute value equation as two equations, one where it equals the same number and the other where it equals the number s opposite. 2. Solve each separately. 8

9 5.5 Solve Absolute Value Equations 1. Solve absolute value equations. 3. x 2 = 4 Problems with more than absolute value First, rewrite the equation in the form ax + b = c. Next, solve the absolute value equation. 9

10 Equations with no solutions *If an absolute value equals a negative number, there is no solution. Ex. 2x 3 = 9 Solve. 2x = 20 2 x = 12 Extension Graph Absolute Value Functions 1. Graph absolute value functions. Graph of Parent Function for Absolute Value Functions f(x) = x x y 1. Make a table of values. 2. Plot points. 10

11 Graph each function. Compare the graph with the graph of f(x) = x. a. g(x) = x 2 Graph each function. Compare the graph with the graph of f(x) = x. b. g(x) = x 1 Graph each function. Compare the graph with the graph of f(x) = x. c. g(x) = 4 x 5.6 Solve Absolute Value Inequalities 1. Solve absolute value inequalities. Review Solve x = 2. 11

12 Solving Absolute Value Inequalities 1. The inequality ax + b < c is equivalent to the compound inequality c < ax + b < c. 2. The inequality ax + b > c is equivalent to the compound inequality ax + b < c or ax + b > c. Given ax + b < c ax + b > c Equal to c < ax + b < c ax + b < c or ax + b > c 12

13 5.7 Graph Linear Inequalities in Two Variables 1. Graph linear inequalities in two variables. Graphing Inequalities If it is < or >, dotted line. If it is < or >, solid line. Greater than is above or to the right. Less than is below or to the left. 13

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