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# Integrated Math 2 Section 3-6

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Graphing Inequalities on a Number Line

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### Integrated Math 2 Section 3-6

1. 1. SECTION 3-6 Graphing Inequalities on a Number Line
2. 2. ESSENTIAL QUESTIONS How do you determine if a number is a solution of an inequality? How do you graph the solution of an inequality on a number line? Where you’ll see this: Business, government, sports, physics, geography
3. 3. VOCABULARY 1. Inequality: 2. True Inequality: 3. False Inequality: 4. Open Inequality: 5. Solution of the Inequality:
4. 4. VOCABULARY 1. Inequality: A mathematical sentence that has an inequality sign in it 2. True Inequality: 3. False Inequality: 4. Open Inequality: 5. Solution of the Inequality:
5. 5. VOCABULARY 1. Inequality: A mathematical sentence that has an inequality sign in it 2. True Inequality: When the given inequality satisﬁes the conditions 3. False Inequality: 4. Open Inequality: 5. Solution of the Inequality:
6. 6. VOCABULARY 1. Inequality: A mathematical sentence that has an inequality sign in it 2. True Inequality: When the given inequality satisﬁes the conditions 3. False Inequality: When the given inequality does not satisfy the conditions 4. Open Inequality: 5. Solution of the Inequality:
7. 7. VOCABULARY 1. Inequality: A mathematical sentence that has an inequality sign in it 2. True Inequality: When the given inequality satisﬁes the conditions 3. False Inequality: When the given inequality does not satisfy the conditions 4. Open Inequality: When there is a variable in the inequality 5. Solution of the Inequality:
8. 8. VOCABULARY 1. Inequality: A mathematical sentence that has an inequality sign in it 2. True Inequality: When the given inequality satisﬁes the conditions 3. False Inequality: When the given inequality does not satisfy the conditions 4. Open Inequality: When there is a variable in the inequality 5. Solution of the Inequality: Find all values that make the inequality true
9. 9. SYMBOLS
10. 10. SYMBOLS <, >, ≤, ≥, ≠
11. 11. SYMBOLS <, >, ≤, ≥, ≠ At least At most Greater than Less than Maximum Minimum
12. 12. SYMBOLS <, >, ≤, ≥, ≠ At least At most Greater than ≥ Less than Maximum Minimum
13. 13. SYMBOLS <, >, ≤, ≥, ≠ At least At most Greater than ≥ ≤ Less than Maximum Minimum
14. 14. SYMBOLS <, >, ≤, ≥, ≠ At least At most Greater than ≥ ≤ > Less than Maximum Minimum
15. 15. SYMBOLS <, >, ≤, ≥, ≠ At least At most Greater than ≥ ≤ > Less than Maximum Minimum <
16. 16. SYMBOLS <, >, ≤, ≥, ≠ At least At most Greater than ≥ ≤ > Less than Maximum Minimum < ≤
17. 17. SYMBOLS <, >, ≤, ≥, ≠ At least At most Greater than ≥ ≤ > Less than Maximum Minimum < ≤ ≥
18. 18. EXAMPLE 1 Name all of the inequalities chosen from A-F for which 1 is a solution. A. x ≤ 1 B. x < 1 C. − 2 < x < 2 1 1 D. − 2 < x < 1 E. − 2 < x ≤ 1 F. − ≤ x ≤ 2 2
19. 19. EXAMPLE 1 Name all of the inequalities chosen from A-F for which 1 is a solution. A. x ≤ 1 B. x < 1 C. − 2 < x < 2 Yes 1 1 D. − 2 < x < 1 E. − 2 < x ≤ 1 F. − ≤ x ≤ 2 2
20. 20. EXAMPLE 1 Name all of the inequalities chosen from A-F for which 1 is a solution. A. x ≤ 1 B. x < 1 C. − 2 < x < 2 Yes No 1 1 D. − 2 < x < 1 E. − 2 < x ≤ 1 F. − ≤ x ≤ 2 2
21. 21. EXAMPLE 1 Name all of the inequalities chosen from A-F for which 1 is a solution. A. x ≤ 1 B. x < 1 C. − 2 < x < 2 Yes No Yes 1 1 D. − 2 < x < 1 E. − 2 < x ≤ 1 F. − ≤ x ≤ 2 2
22. 22. EXAMPLE 1 Name all of the inequalities chosen from A-F for which 1 is a solution. A. x ≤ 1 B. x < 1 C. − 2 < x < 2 Yes No Yes 1 1 D. − 2 < x < 1 E. − 2 < x ≤ 1 F. − ≤ x ≤ 2 2 No
23. 23. EXAMPLE 1 Name all of the inequalities chosen from A-F for which 1 is a solution. A. x ≤ 1 B. x < 1 C. − 2 < x < 2 Yes No Yes 1 1 D. − 2 < x < 1 E. − 2 < x ≤ 1 F. − ≤ x ≤ 2 2 No Yes
24. 24. EXAMPLE 1 Name all of the inequalities chosen from A-F for which 1 is a solution. A. x ≤ 1 B. x < 1 C. − 2 < x < 2 Yes No Yes 1 1 D. − 2 < x < 1 E. − 2 < x ≤ 1 F. − ≤ x ≤ 2 2 No Yes No
25. 25. EXAMPLE 2 Graph the solution of each inequality on a number line. a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2
26. 26. EXAMPLE 2 Graph the solution of each inequality on a number line. a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2 -4 -3 -2 -1 0 1 2 3 4 5 6
27. 27. EXAMPLE 2 Graph the solution of each inequality on a number line. a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2 -4 -3 -2 -1 0 1 2 3 4 5 6
28. 28. EXAMPLE 2 Graph the solution of each inequality on a number line. a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2 -4 -3 -2 -1 0 1 2 3 4 5 6
29. 29. EXAMPLE 2 Graph the solution of each inequality on a number line. a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2 -4 -3 -2 -1 0 1 2 3 4 5 6
30. 30. EXAMPLE 2 Graph the solution of each inequality on a number line. a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2 -4 -3 -2 -1 0 1 2 3 4 5 6
31. 31. EXAMPLE 2 Graph the solution of each inequality on a number line. a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2 -4 -3 -2 -1 0 1 2 3 4 5 6 -4 -3 -2 -1 0 1 2 3 4 5 6
32. 32. EXAMPLE 2 Graph the solution of each inequality on a number line. a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2 -4 -3 -2 -1 0 1 2 3 4 5 6 -4 -3 -2 -1 0 1 2 3 4 5 6
33. 33. EXAMPLE 2 Graph the solution of each inequality on a number line. a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2 -4 -3 -2 -1 0 1 2 3 4 5 6 -4 -3 -2 -1 0 1 2 3 4 5 6
34. 34. EXAMPLE 2 Graph the solution of each inequality on a number line. a. x < −2 or x ≥ 3 b. x ≥ −3 and x < 2 -4 -3 -2 -1 0 1 2 3 4 5 6 -4 -3 -2 -1 0 1 2 3 4 5 6
35. 35. EXAMPLE 3 By order of the ﬁre commissioner, the capacity of a local theatre is not to exceed 225 people. a. Write an inequality that describes the capacity of the theatre. b. Graph the solution of the inequality on a number line.
36. 36. EXAMPLE 3 By order of the ﬁre commissioner, the capacity of a local theatre is not to exceed 225 people. a. Write an inequality that describes the capacity of the theatre. Let p be the number of people b. Graph the solution of the inequality on a number line.
37. 37. EXAMPLE 3 By order of the ﬁre commissioner, the capacity of a local theatre is not to exceed 225 people. a. Write an inequality that describes the capacity of the theatre. Let p be the number of people 0 ≤ p ≤ 225 b. Graph the solution of the inequality on a number line.
38. 38. EXAMPLE 3 By order of the ﬁre commissioner, the capacity of a local theatre is not to exceed 225 people. a. Write an inequality that describes the capacity of the theatre. Let p be the number of people 0 ≤ p ≤ 225 b. Graph the solution of the inequality on a number line. 0 50 100 150 200 250
39. 39. EXAMPLE 3 By order of the ﬁre commissioner, the capacity of a local theatre is not to exceed 225 people. a. Write an inequality that describes the capacity of the theatre. Let p be the number of people 0 ≤ p ≤ 225 b. Graph the solution of the inequality on a number line. 0 50 100 150 200 250
40. 40. EXAMPLE 3 By order of the ﬁre commissioner, the capacity of a local theatre is not to exceed 225 people. a. Write an inequality that describes the capacity of the theatre. Let p be the number of people 0 ≤ p ≤ 225 b. Graph the solution of the inequality on a number line. 0 50 100 150 200 250
41. 41. EXAMPLE 3 By order of the ﬁre commissioner, the capacity of a local theatre is not to exceed 225 people. a. Write an inequality that describes the capacity of the theatre. Let p be the number of people 0 ≤ p ≤ 225 b. Graph the solution of the inequality on a number line. 0 50 100 150 200 250
42. 42. HOMEWORK
43. 43. HOMEWORK p. 128 #1-43 odd “I may not have gone where I intended to go, but I think I have ended up where I needed to be.” - Douglas Adams