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Lesson 39 Compound and Absolute Value Inequalities

Lesson 39 Compound and Absolute Value Inequalities. NCSCOS 1.01;4.01 Daily Objectives TLW solve compound inequalities. TLW graph the solution sets of compound inequalities . TLW solve absolute value inequalities. What is the difference between and and or ?. A. B. AND means intersection

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Lesson 39 Compound and Absolute Value Inequalities

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  1. Lesson 39 Compound and Absolute Value Inequalities NCSCOS 1.01;4.01 Daily ObjectivesTLW solve compound inequalities. TLW graph the solution sets of compound inequalities. TLW solve absolute value inequalities

  2. What is the difference between and and or? A B AND means intersection -what do the two items have in common? OR means union -if it is in one item, it is in the solution A B

  3. o o ● ● ● o 2 2 2 2 3 3 3 3 4 4 4 4 1) Graph x < 4 and x ≥ 2 a) Graph x < 4 b) Graph x ≥ 2 c) Combine the graphs d) Where do they intersect?

  4. o o ● ● 2 2 2 2 3 3 3 3 4 4 4 4 2) Graph x < 2 or x ≥ 4 a) Graph x < 2 b) Graph x ≥ 4 c) Combine the graphs

  5. o o -3 -2 -1 Answer Now 3) Which inequalities describe the following graph? • y > -3 or y < -1 • y > -3 and y < -1 • y ≤ -3 or y ≥ -1 • y ≥ -3 and y ≤ -1

  6. o o 6 7 8 4) Graph the compound inequality 6 < m < 8 When written this way, it is the same thing as 6 < m AND m < 8 It can be rewritten as m > 6 and m < 8 and graphed as previously shown, however, it is easier to graph everything between 6 and 8!

  7. Answer Now 5) Which is equivalent to-3 < y < 5? • y > -3 or y < 5 • y > -3 and y < 5 • y < -3 or y > 5 • y < -3 and y > 5

  8. Answer Now 6) Which is equivalent to x > -5 and x ≤ 1? • -5 < x ≤ 1 • -5 > x ≥ 1 • -5 > x ≤ 1 • -5 < x ≥ 1

  9. o o o o -6 -6 1 1 -3 -3 4 4 0 7 0 7 7) 2x < -6 and 3x ≥ 12 Solve each inequality for x Graph each inequality Combine the graphs Where do they intersect? They do not! x cannot be greater than or equal to 4 and less than -3 No Solution!!

  10. - 5 0 5 8) Graph 3 < 2m + 1 < 9 Remember, when written like this, it is an AND problem! 3 < 2m + 1 AND 2m + 1 < 9 Solve each inequality. Graph the intersection of 2 < m and m < 3.

  11. - 5 0 5 9) Graph x < 2 or x ≥ 4

  12. 10) Graph x ≥ -1 or x ≤ 3 The whole line is shaded!!

  13. Then graph the solution set. Write as and Case 2 Case 1 Original inequality Add 3 to each side. Simplify. Answer: The solution set is Example 5-3a

  14. Then graph the solution set. Answer: Example 5-3b

  15. Then graph the solution set. Write as or Case 2 Case 1 Original inequality Add 3 to each side. Simplify. Divide each side by 3. Simplify. Example 5-4a

  16. Answer: The solution set is Example 5-4a

  17. Then graph the solution set. Answer: Example 5-4b

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