1. Graphing Inequalities 2.8 >,≤, <, ≥

2. Equations vs. Inequalities What is the difference in an equation and an inequality? We will look at a graph of each to see how each graph “explains” this difference. What is the difference in an equation and an inequality? We will look at a graph of each to see how each graph “explains” this difference.

3. Equations vs. Inequalities An equation has only one solution. This solution can be graphed. n + 5 = 8 -5 -5 n = 3 A graph of this solution would look like this. An inequality has a range of values. The solutions (right now) are infinite. A graph of an inequality could look like this. n > 3 An equation has only one solution. This solution can be graphed. n + 5 = 8 -5 -5 n = 3 A graph of this solution would look like this. An inequality has a range of values. The solutions (right now) are infinite. A graph of an inequality could look like this. n > 3 0 1 2 3 4 5

4. What Do the Symbols Mean? < < Baby is smaller than the boy.Boy is bigger than the baby. “less than” “greater than” ≥ ≤ This baby is at least as big as this baby This baby is no bigger than this baby. …..maybe bigger …..maybe smaller. “greater than or equal to” “less than or equal to”

5. Inequalities can have more than one value that makes the statement true. You see inequalities all the time. You just don’t think of them as inequalities! Height requirements? Speed limits? Age limits?

6. What do they mean? You must be 4 ft. tall to ride. Can you be taller than 4 ft? Shorter than 4 ft? h ≥ 4ft Your height (h) must be equal to or greater than 4 ft. You are not to drive over 70 mph. Can you drive less than 70? Can you drive 70 mph? S ≤ 70 mph Your speed must be equal to or less than 70 mph You can vote when you are 18. You can vote when you are older, too. v ≥ 18

7. Reading the Inequality As we graph inequalities, learn to “read” the inequality from the variable. This will help as we graph the values. a< 12 means the arrow will point to values less than 12. So does this……. 12 > a. a > -2 means the arrow will point to values greater than -2. So does this……. -2 < a.

8. Each sign has a special graph. ≥ means greater than or equal to ≤ means less than or equal to > means greater than < means less than Go back in your notes and make each circle next to its appropriate sign. ≥ means greater than or equal to ≤ means less than or equal to > means greater than < means less than Go back in your notes and make each circle next to its appropriate sign. Do you notice anything?????

9. Arrows are used in graphing. Since inequalities show a range of values, an arrow is used with the correct “dot” to show the numbers in that range. Numbers that fit in this range are solutions to the inequality. Using our example of a height range: (not in notes) n ≥ 4 ft. 1 2 3 4 5 6 Since inequalities show a range of values, an arrow is used with the correct “dot” to show the numbers in that range. Numbers that fit in this range are solutions to the inequality. Using our example of a height range: (not in notes) n ≥ 4 ft. 1 2 3 4 5 6

10. Speed Limit Graph? 5060708090 Since you can go = to 70 the equal bar will be included under the inequality sign. Since you have to go less than this, the sign will be a less than or = to. Since you can go = to 70 the equal bar will be included under the inequality sign. Since you have to go less than this, the sign will be a less than or = to. The arrow must point to the numbers that are less than seventy. The solid circle shows us that 70 is part of the answer.

11. Using the Open Circle…. Some of our examples will not use a solid circle. Here is an inequality that would use an open circle: You have to be older than 4 ½ years old to attend school. Your age can’t be 4 ½. It must be more than 4 ½. a 4 3 456

12. Let’s Try Some! It will make more sense when you graph your own. n > -1 y < 3 -6 ≤ g Step 1: Where do you start? Step 2: Open or closed? Step 3: Right or left arrow? 324 01 -7-6-5

13. On Your Own…..p. 102 4 > t z < -2 a ≥ -5 2 ≥ c Step 1: Where do you start? Step 2: Open or closed? Step 3: Right or left arrow? -2-3 345 -5-4-3 123

14. Identifying the Inequality What inequalities are represented by these graphs? 123 2 ≤ n or n ≥ 2 01 0 > n or n < 0 5 ≥ n or n ≤ 5 456 n > 0 n ≤ -1

15. Writing Inequalities to Describe Real World Situations The words at most means no more than… So the amount can be equal to or less than….

16. Writing Inequalities Use this same label on p. 103 to write an inequality for n, the number of milligrams of sodium in this sodium-free food. Words: A serving of sodium-free food has 5mg less than Inequality n < 5

17. In Review……… Graph the solutions of each inequality on a number line. n > -2 w ≥ -5 6 > y -3 -2 -1 -6 -5 -4 5 6 7

18. In Review……… Write the inequality shown on each graph. -4 -3 -2 2 3 4 n ≥ -3 -3≤ n n < 3 3 > n Write an inequality to show this situation: No more than 50 students participated in the survey. n ≤ 50

19. In Review……… Write the inequality shown on each graph. -4 -3 -2 2 3 4 n ≥ -3 -3≤ n n < 3 3 > n Write an inequality to show this situation: No more than 50 students participated in the survey. n ≤ 50

20. The End