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COMPOUND INEQUALITIES

COMPOUND INEQUALITIES. Objectives: 1. solve compound inequalities. 2. graph the solution sets of compound inequalities. Designed by Skip Tyler, Varina High School Edited by Kate Stoltzfus, Lower Dauphin MS. What is the difference between and and or ?. A. B. AND means intersection

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COMPOUND INEQUALITIES

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  1. COMPOUND INEQUALITIES Objectives: 1. solve compound inequalities. 2. graph the solution sets of compound inequalities. Designed by Skip Tyler, Varina High School Edited by Kate Stoltzfus, Lower Dauphin MS

  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. New Vocabulary Conjunction vs. Disjunction Uses “and” Uses “or” Written in either form below: x >-3 and x ≤ 4 -3< x ≤ 4 Graph of solution set: Written as: x ≥ 8 or x < 5 Graph of solution set:

  4. 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?

  5. 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

  6. 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

  7. 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!

  8. 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

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

  10. o o o o -6 -6 1 1 -3 -3 4 4 0 0 7 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!! ●

  11. 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 < 5. Solution: 2<m<5 - 5 0 5

  12. - 5 0 5 9) Graph x < 2 or x ≥ 4

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

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