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5.4 Combining Inequalities Objective:   ,[object Object],Frameworks:   10.P.1, 10.P.7
How would you graph a disjunction? x < 2 or x = 2 The graph should contain all the solutions of the two sentences
Graph 11 – 3x ≤ 26
Graph x ≤ -2 and x > 3
Graph x ≤ -2 or x > 3
Graph x > 1 or x < 4
Graph x > 1 and x < 4
Graph x -1 ≥ -3 and 4 < 2x - 2
Graph x -1 ≥ -3 or 4 < 2x - 2
x > -1 and x < 4 can also be written as: -1 < x < 4 This can be read as:     -1 is less than x and x is less than 4     x is greater than -1 and x is less than 4     x is between -1 and 4
Graph -3 < 2x + 5 ≤ 9
Example This year, Jim’s weight fluctuated within a 7-lb. range.  At times, he weighed as little as 125 lb.  At other times, he weighed almost 132 lb.  Write a conjunction that describes the range of values for Jim’s weight. 125 ≤ x and x < 132 125 ≤ x < 132
Turn to page 182 Do 1-20, 35-37

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Graphing Combinations of Inequalities

  • 1.
  • 2. How would you graph a disjunction? x < 2 or x = 2 The graph should contain all the solutions of the two sentences
  • 3. Graph 11 – 3x ≤ 26
  • 4. Graph x ≤ -2 and x > 3
  • 5. Graph x ≤ -2 or x > 3
  • 6. Graph x > 1 or x < 4
  • 7. Graph x > 1 and x < 4
  • 8. Graph x -1 ≥ -3 and 4 < 2x - 2
  • 9. Graph x -1 ≥ -3 or 4 < 2x - 2
  • 10. x > -1 and x < 4 can also be written as: -1 < x < 4 This can be read as: -1 is less than x and x is less than 4 x is greater than -1 and x is less than 4 x is between -1 and 4
  • 11. Graph -3 < 2x + 5 ≤ 9
  • 12. Example This year, Jim’s weight fluctuated within a 7-lb. range. At times, he weighed as little as 125 lb. At other times, he weighed almost 132 lb. Write a conjunction that describes the range of values for Jim’s weight. 125 ≤ x and x < 132 125 ≤ x < 132
  • 13. Turn to page 182 Do 1-20, 35-37