Chapter 6 Solving and Graphing Linear Inequalities 6.1 Solving Inequalities in One Variable: The graph of a linear inequality in one variable is the line of of the inequality on the real number The four types of simple inequalities are listed below. Graph their solution on the line. You must use zero, and the relevant numbers on the graph. x 3 x -2 x 4 x-5 There is only one rule that you have to know to solve linear inequalities. Do you know it? SOLVING LINEAR INEQUALITIES: Don t forget the graph of the solution. p + 5 3 2y - 5 < 7 5 - x > 4
Solve: 2x - 4 4x - 1 -x + 6 > -(2x + 4) 3x + 5 < -7x - 9 Write the inequality for all real numbers greater than or equal to 7. Explain why you must reverse the direction of the inequality symbol when multiplying by a negative. Homework: Do graphs through problem # 40. 17) -x - 8 > -17 20) x -10-6 23) -4x - 2 10 26) 17 4x + 11 29) x + 3 2(x-4) 32) -x + 6 > -(2x +4)
47) x + 2 = 8 53) Find an equation of the line that contains the point (2, -4) and has a slope of 3/2. 6.2 Problem Solving Using Inequalities: Suzanne and Jorah both run in a 2 kilometer race. Suzanne finished ahead of Jorah and Jorah s time for the race was 8 minutes. Write an inequality that describes Suzanne s average speed for the race. LET X = INEQUALITY SOLUTION From 1970 to 1990, the average annual per person consumption of whole milk in the United States dropped from 103 quarts to 43 quarts. The average annual consumption of low-fat milk rose from 25 quarts to 60 quarts. For which years did the consumption of low-fat milk by Americans exceed the consumption of whole milk? Let x = 0 in 1970. LET X = INEQUALITY SOLUTION Whole = Low-fat =
Starting a Small Business You see an advertisement for instructions on how to tie flies for fly-fishing. The cost of materials for each fly is $0.15. You plan to sell each fly for $0.58, and you want to make a profit of at least $200. How many flies will you need to tie and sell? (The R.T. Fisher and Co. of Illinois charges $13.95 plus $1.05 for shipping and handling to receive the instructions.) LET X = INEQUALITY SOLUTION HOMEWORK: 6) Steel Arch Bridge: The longest steel arch bridge is the new River Gorge Bridge near Fayetteville, West Virginia. It is 1700 feet long. Write an inequality that describes the length in feet of, L, of every other steel bridge arch bridge. 9) An amusement park charges $5 for admission and $0.80 for each ride. Suppose you go to the park with $13. Write an inequality that represents the possible number of rides you can go on. What is your maximum number of rides? 10)You and your friends have a total of $12 to spend on pizza. A large pizza with cheese costs $8 plus $0.40 for each additional pizza, tax included. Usa an inequality to find the number of toppings you can afford.
6.3 Compound Inequalities: The compound inequality of 0 x < 4 is also written as and. The compound inequality x is zero and four. Graph: x < -1 or x > 2 Solve and graph: -2 3x - 8 10 Solve and graph: 3x + 1 < 4 or 2x - 5 > 7 Solve and graph: -2 < -2 - x < 1 Homework: Go to page 308 and do # 1-4 1) 2) 3) 4) Go to page 310 and do # 35 Triangular Inequality Theorem: g. 310 do #46 x = #48 x =
Do 1-20 on the Mid-Chapter SELF-TEST page 312. There will be a quiz on Monday, January 12, 2005 on this material. 6.4 Connections: Absolute Value and Inequalities Which values of X would you say are solutions of x < 2? Since the absolute value of x is the distance between x and the origin, it follows that any number between and is a solution. In other words, the inquality x < 2 is equivalent to the compound inequality < x <. Now construct a graph of the solution. Solve: x -4 < 3 First put the inequality into a compound inequality form. < x -4 < Solve the inequality, then graph the solution. Solve: x+1 2 This absolute value inequality is equivalent to the following compound inequality. - 2 OR 2 Now solve each and graph the solution. Now we will work it backwords. 0 2 8 First write an inequality for the graph. < x <
Find the number that is HALF WAY between 2 and 8. that number from each side of your inequality. Now subtract 2 - < x - < 8 - < x - 5 < Are the numbers on both ends of the inquality opposites of each other? Now do you recognize this form from section 6.3? Write the absolute value inequality. Now go to page 315 and do the COMMUNICATING IN ALGEBRA in your textbook. A) B) Homework: Pg. 316 Watch out for the absolute value signs!!!!!!!!!! 7) x - 1 < 3 8) x - 1/2 3/2 9) x + 1 2 10) x + 2 4 11) x - 5/2 > 3/2 12) x + 2 > 1
6.5 Graphing Linear Inequalities: This should be familiar because we have already done this. So get out your colored pencils and go to work on the assignment. Homework: Put inequalities into slope intercept form first Decide if the line is dashed or solid Graph the line as if it were an equation and not an inequality Do you remember the test point? Use it in the inequality (or any other test point of your choosing) and look to see if it is a true inequality. Shade the half plane that contains the test point if the test point worked. If it didn t work shade the other side of the half plane. 6.6 Exploring Data: Time Lines, Picture Graphs, and Circle Graphs TURN TO PAGE 327. Take any notes on facts you need to remember about graph we discuss. Let s look at the time line on page 329. Let s look at the Saudi Arabia s Oil Production graph. pg. 328 Let s look at the graph at the bottom of pg. 328 Let s look at the circle graph on pag. 329 Let s look at the Communicating in Algebra pg 329