1 / 24

Union, Intersection, and Compound Inequalities

Union, Intersection, and Compound Inequalities. MATH 017 Intermediate Algebra S. Rook. Overview. Section 2.5 in the textbook Intersection of sets Solving compound inequalities involving intersection: Using the word and Having two inequalities Union of sets

gausej
Télécharger la présentation

Union, Intersection, and Compound Inequalities

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Union, Intersection, and Compound Inequalities MATH 017 Intermediate Algebra S. Rook

  2. Overview • Section 2.5 in the textbook • Intersection of sets • Solving compound inequalities involving intersection: • Using the word and • Having two inequalities • Union of sets • Solving compound inequalities involving union

  3. Intersection of Sets

  4. Intersection of Sets • Intersection (∩) [of 2 sets]:the elements common to both sets. • Usually easier to start with the set containing the least number of elements

  5. Intersection of Sets (Example) Ex 1: Given A = {x | x is a whole number}, B = {x | -2 ≤ x < 5}, find A ∩ B

  6. Intersection of Sets (Example) Ex 2: Given A = {x | xis a natural number}, B = {-3, -2, -1, 0, 1, 2, 3}, find A ∩ B

  7. Intersection of Sets (Examples) Ex 3: Given A = {x | x≤ -7}, B = {x | x < -2}, find A ∩ B

  8. Solving Compound Inequalities Using Intersection

  9. Solving Compound Inequalities Using Intersection • Can be found in two formats: • Two linear inequalities separated by the word and • A statement containing two inequality symbols • -4 < x < 7

  10. Compound Inequalities Separated by and • Solve each linear inequality as normal • Graphing is somewhat trickier: • Draw 3 number lines with equal intervals • On the first number line, graph the solution to the first inequality • On the second number line, graph the solution to the second inequality • On the third number line, lay the first two number lines on top of each other • The intersection is the area between the left ( or [ and the right ) or ] • Obtain the interval notation from the intersection

  11. Compound Inequalities Separated by and (Example) Ex 4: Solve, graph, and put into interval notation: 2x – 3 ≤ 11 and 2x < 3x – 4

  12. Compound Inequalities Separated by and (Example) Ex 5: Solve, graph, and put into interval notation: 2(x – 3) – 3x≤ 3(x + 1) and 8x – 2(x – 3) > 24

  13. Compound Inequalities with Two Inequality Symbols • Most common way to see an intersection compound inequality • Somewhat trickier to solve • Goal is to isolate the variable between the 2 inequalities • Perform Algebraic operations on 3 sides instead of 2 • Simple to graph • Once the variable is isolated, the intersection is obtained

  14. Compound Inequalities with Two Inequality Symbols (Example) Ex 6: Solve, graph, and put into interval notation: -9 < 2x – 7 ≤ 7

  15. Compound Inequalities with Two Inequality Symbols (Example) Ex 7: Solve, graph, and put into interval notation:

  16. Union of Sets

  17. Union of Sets • Union (U) [of 2 sets]:the distinct elements from both sets • In other words, dump the elements of both sets together and remove the duplicates

  18. Union of Sets (Example) Ex 8: Given A = {-2, 0, 1, 3, 4} and B = {1, 2, 3, 4, 5}, find A U B

  19. Union of Sets (Example) Ex 9: Given A = {x | x≥ 0} and B = {x | x≥ 5}, find A U B

  20. Solving Compound Inequalities Using Union

  21. Solving Compound Inequalities Using Union • Two inequalities separated by the word or • Solve each linear inequality as normal • Graphing is somewhat trickier: • Draw 3 number lines with equal intervals • On the first number line, graph the solution to the first inequality • On the second number line, graph the solution to the second inequality • On the third number line, lay the first two number lines on top of each other – this represents the union • Remove any parentheses or brackets that have shading to the left and right • Obtain the interval notation from the union

  22. Solving Compound Inequalities Using Union (Example) Ex 10: Solve, graph, and put into interval notation: 6(x – 3) – 5(x – 2) > -4 or 3(1 – x) – 6(2 – x) ≥ 0

  23. Solving Compound Inequalities Using Union (Example) Ex 11: Solve, graph, and put into interval notation:

  24. Summary • After studying these slides, you should know how to do the following: • Find the intersection of [2] sets • Solve compound inequalities involving intersection when: • The keyword and is used • The statement contains two inequalities • Find the union of [2] sets • Solve compound inequalities involving union

More Related