1. 2-1 Graphing Inequalities

2. Objectives The students will learn to: Identify solutions of inequalities in one variable Write and graph inequalities in one variable

3. What is an inequality ? An inequality is a statement that two quantities are not equal. The quantities are compared by using the following signs: ≤ A ≤ B A is less than or equal to B. < A < BA < B A is less than B. > A > B A is greater than B. ≥ A ≥ B A is greater than or equal to B. ≠ A ≠ B A is not equal to B.

4. What is a solution to an Inequality? Answer: A solution of an inequality is any value of the variable that makes the inequality true.

5. Identifying Solutions of inequalities Example #1 Describe the solutions of x – 6 ≥ 4 in words x-309.91010.112 X-6-9-63.944.16 x – 6 ≥ 4 –9 ≥ 4–6 ≥ 43.9 ≥ 4 4 ≥ 44.1 ≥ 46 ≥ 4 Soluti on? NoNO Yes

6. Example #1 solution When the value of x is a number less than 10, the value of x – 6 is less than 4. When the value of x is 10, the value of x – 6 is equal to 4. When the value of x is a number greater than 10, the value of x – 6 is greater than 4. Solution:It appears that the solutions of x – 6 ≥ 4 are all real numbers greater than or equal to 10.

7. Example #2 Describe the solutions of 2p > 8 in words. p-303.944.15 2p-607.888.210 2p > 8-6 > 80 > 87.8 > 88 > 88.2 > 810 > 8 Soluti on? NoNO NoYes

8. Example #2 solution When the value of p is a number less than 4, the value of 2p is less than 8. When the value of p is 4, the value of 2p is equal to 8. When the value of p is a number greater than 4, the value of 2p is greater than 8. Solution: It appears that the solutions of 2p > 8 are all real numbers greater than 4.

9. How to graph linear inequalities? How can we graph an inequality like 3 + x < 9 An inequality like 3 + x < 9 has too many solutions to list. You can use a graph on a number line to show all the solutions. Solution:

11. Graph Inequality Graph x > 2 Solution: Draw a non-shaded or open circle at 2 and shade everything on the right of 2. The shaded area in red is your solution. It means that the solution can be any number on the right of 2. Notice that 2 is not shaded because 2 is not included in your solution.

12. Graph inequalities Graph x ≥ 6 Solution: Draw a shaded circle at 6 and then shade everything on the right of 6 Notice that this time, the circle is shaded because x is also equal to 6.

13. Graph inequalities Graph x ≤ -1 Solution: Draw a shaded circle at -1 and then shade everything on the left of -1

14. Graph inequalities 2 2 – 4 ≥ w m ≤ –3

15. Student Guided practice Work on problems 1-10 from worksheet

16. Writing Linear inequalities Write the inequality shown by each graph. Solution: x < 2 Use any variable. The arrow points to the left, so use either < or ≤. The empty circle at 2 means that 2 is not a solution, so use <.

17. Writing linear inequalities Write the inequality shown by each graph.

18. Student guided practice Go over writing linear inequalities worksheet problems 3-10

19. Graphing linear inequalities applications Ray’s dad told him not to turn on the air conditioner unless the temperature is at least 85°F. Define a variable and write an inequality for the temperatures at which Ray can turn on the air conditioner. Graph the solutions. Solution: t  85 75 80859070

20. Application’s example A store’s employees earn at least $8.50 per hour. Define a variable and write an inequality for the amount the employees may earn per hour. Graph the solutions.

21. Homework Do problems 22-31 from page 103

22. Closure Today we saw about graphing and writing linear inequalities Next class we are going to learn how to solve for them

23. Have a great day!!