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SECTION 3-6
Graphing Inequalities on a Number Line
ESSENTIAL QUESTIONS

How do you determine if a number is a solution of an
inequality?
How do you graph the solution of an ...
VOCABULARY
1. Inequality:


2. True Inequality:


3. False Inequality:


4. Open Inequality:
5. Solution of the Inequality:
VOCABULARY
1. Inequality: A mathematical sentence that has an inequality
    sign in it
2. True Inequality:


3. False Ine...
VOCABULARY
1. Inequality: A mathematical sentence that has an inequality
    sign in it
2. True Inequality: When the given...
VOCABULARY
1. Inequality: A mathematical sentence that has an inequality
    sign in it
2. True Inequality: When the given...
VOCABULARY
1. Inequality: A mathematical sentence that has an inequality
    sign in it
2. True Inequality: When the given...
VOCABULARY
1. Inequality: A mathematical sentence that has an inequality
    sign in it
2. True Inequality: When the given...
SYMBOLS
SYMBOLS

<, >, ≤, ≥, ≠
SYMBOLS

            <, >, ≤, ≥, ≠
At least      At most       Greater than



Less than      Maximum        Minimum
SYMBOLS

            <, >, ≤, ≥, ≠
At least      At most       Greater than
  ≥
Less than      Maximum        Minimum
SYMBOLS

            <, >, ≤, ≥, ≠
At least      At most       Greater than
  ≥             ≤
Less than      Maximum      ...
SYMBOLS

            <, >, ≤, ≥, ≠
At least      At most       Greater than
  ≥             ≤               >
Less than   ...
SYMBOLS

            <, >, ≤, ≥, ≠
At least      At most       Greater than
  ≥             ≤               >
Less than   ...
SYMBOLS

            <, >, ≤, ≥, ≠
At least      At most       Greater than
  ≥             ≤               >
Less than   ...
SYMBOLS

            <, >, ≤, ≥, ≠
At least      At most       Greater than
  ≥             ≤               >
Less than   ...
EXAMPLE 1
Name all of the inequalities chosen from A-F for which 1
                     is a solution.

   A. x ≤ 1       ...
EXAMPLE 1
Name all of the inequalities chosen from A-F for which 1
                     is a solution.

   A. x ≤ 1       ...
EXAMPLE 1
Name all of the inequalities chosen from A-F for which 1
                     is a solution.

   A. x ≤ 1       ...
EXAMPLE 1
Name all of the inequalities chosen from A-F for which 1
                     is a solution.

   A. x ≤ 1       ...
EXAMPLE 1
Name all of the inequalities chosen from A-F for which 1
                     is a solution.

   A. x ≤ 1       ...
EXAMPLE 1
Name all of the inequalities chosen from A-F for which 1
                     is a solution.

   A. x ≤ 1       ...
EXAMPLE 1
Name all of the inequalities chosen from A-F for which 1
                     is a solution.

   A. x ≤ 1       ...
EXAMPLE 2
Graph the solution of each inequality on a number line.

  a. x < −2 or x ≥ 3             b. x ≥ −3 and x < 2
EXAMPLE 2
Graph the solution of each inequality on a number line.

  a. x < −2 or x ≥ 3             b. x ≥ −3 and x < 2


...
EXAMPLE 2
Graph the solution of each inequality on a number line.

  a. x < −2 or x ≥ 3             b. x ≥ −3 and x < 2


...
EXAMPLE 2
Graph the solution of each inequality on a number line.

  a. x < −2 or x ≥ 3             b. x ≥ −3 and x < 2


...
EXAMPLE 2
Graph the solution of each inequality on a number line.

  a. x < −2 or x ≥ 3             b. x ≥ −3 and x < 2


...
EXAMPLE 2
Graph the solution of each inequality on a number line.

  a. x < −2 or x ≥ 3             b. x ≥ −3 and x < 2


...
EXAMPLE 2
Graph the solution of each inequality on a number line.

  a. x < −2 or x ≥ 3             b. x ≥ −3 and x < 2


...
EXAMPLE 2
Graph the solution of each inequality on a number line.

  a. x < −2 or x ≥ 3             b. x ≥ −3 and x < 2


...
EXAMPLE 2
Graph the solution of each inequality on a number line.

  a. x < −2 or x ≥ 3             b. x ≥ −3 and x < 2


...
EXAMPLE 2
Graph the solution of each inequality on a number line.

  a. x < −2 or x ≥ 3             b. x ≥ −3 and x < 2


...
EXAMPLE 3
By order of the fire commissioner, the capacity of a local
          theatre is not to exceed 225 people.
a. Writ...
EXAMPLE 3
By order of the fire commissioner, the capacity of a local
          theatre is not to exceed 225 people.
a. Writ...
EXAMPLE 3
By order of the fire commissioner, the capacity of a local
          theatre is not to exceed 225 people.
a. Writ...
EXAMPLE 3
By order of the fire commissioner, the capacity of a local
          theatre is not to exceed 225 people.
a. Writ...
EXAMPLE 3
By order of the fire commissioner, the capacity of a local
          theatre is not to exceed 225 people.
a. Writ...
EXAMPLE 3
By order of the fire commissioner, the capacity of a local
          theatre is not to exceed 225 people.
a. Writ...
EXAMPLE 3
By order of the fire commissioner, the capacity of a local
          theatre is not to exceed 225 people.
a. Writ...
HOMEWORK
HOMEWORK


                     p. 128 #1-43 odd




“I may not have gone where I intended to go, but I think I have
     ...
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Integrated Math 2 Section 3-6

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Graphing Inequalities on a Number Line

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Transcript of "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
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