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BELL-WORK

Learn how to solve and graph compound inequalities with examples and step-by-step explanations. Explore the concepts of conjunction and solution sets.

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BELL-WORK

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  1. BELL-WORK Eureka Module 3 Lesson 16 Exercise 1-2 (round to the nearest tenth).

  2. Exam 1.2 Signatures

  3. HW 2.1(b) Due 10/19/18: On website # 2,3,4,7,8,11,25,26,30,31

  4. HW 2.1(a) Solutions 3. (a) x ≈ -0.7 OR x = 2 (b) x = 2, x = 4, x ≈ -0.8 4. Disagree 5. Disagree

  5. HW 2.1(a) Solutions 1. y = 3x – 7 3. y = -¼x + 4 5. y = 3x – 20 2 • Parallel; same slope 9. Perpendicular; opposite reciprocal slopes 11. Parallel; same slope 13. Sometimes 15. Always 17. y = -3x + 22 19. y = ⅓x + 6 21. y = -6x – 5

  6. Exit Ticket Review

  7. Guiding question: What are compound inequalities?

  8. Solving Inequalities Before we discuss compound inequalities, let us review how to solve inequalities. x + 2.5 ≤ 8 x ≤ 5.5 Notice that this inequality only has 1 variable, so we will graph its solution on a number line.

  9. Graphing Inequalities in 1 Variable > and < symbols are represented by an opened circle, ≤ and ≥ symbols are represented by a closed circle. Why?

  10. Solving and Graphing Inequalities Examples: x + 2.5 ≤ 8 x ≤ 5.5

  11. Solving and Graphing Inequalities Examples: 5t > 15 t > 3

  12. Solving and Graphing Inequalities Examples: 5t > 15 t > 3

  13. Solving and Graphing Inequalities Examples: w – 1 < 8 w < 9

  14. Solving and Graphing Inequalities Examples: w – 1 < 8 w < 9

  15. Solving and Graphing Inequalities Examples: 3 ≥ p 4 12 ≥ p p ≤ 12

  16. Solving and Graphing Inequalities Examples: 3 ≥ p 4 12 ≥ p p ≤ 12

  17. Solving and Graphing Inequalities Examples: w < 3 -2 w > -6

  18. Solving and Graphing Inequalities Examples: w < 3 -2 w > -6

  19. Solving and Graphing Inequalities 5 – 2x ≥ 11 -2x ≥11 - 5 -2x ≥ 6 x ≤ -3

  20. Compound Inequalities What does the word compound mean? When two inequalities are joined, a compound inequality is formed. If the inequalities are joined by the word ‘and’ a conjunction is formed. Example: All real numbers that are at least -1 and at most 3. So, x ≥ -1 and x ≤ 3 Which is written as -1 ≤ x ≤ 3, and is graphed as:

  21. Compound Inequalities What does the word compound mean? When two inequalities are joined, a compound inequality is formed. If the inequalities are joined by the word ‘and’ a conjunction is formed. Example: All real number that are at least -1 and at most 3. So, x ≥ -1 and x ≤ 3 Which is written as -1 ≤ x ≤ 3, and is graphed as:

  22. Compound Inequalities What does the word compound mean? When two inequalities are joined, a compound inequality is formed. If the inequalities are joined by the word ‘and’ a conjunction is formed. Example: All real numbers that are at least -1 and at most 3. So, x ≥ -1 and x ≤ 3 Which is written as -1 ≤ x ≤ 3, and is graphed as: Notice there is no gap in the graph, which implies that solutions to a conjunction make both components of the conjunction true.

  23. Compound Inequalities Write a compound inequality for the following: Today’s temperature will be no more than 70 degrees but it will be higher than 55. T ≤ 70 and T > 55 55 < T ≤ 70 Graph the solution.

  24. Solving Conjunctions Solve and graph -4 < r – 5 ≤ -1 If this were just a regular inequality: r – 5 ≤ -1 how would you solve it? What ever is done to one side of a conjunction, must be done to all other sides. -4 < r – 5 ≤ -1 -4 + 5 < r ≤ -1 + 5 1 < r ≤ 4

  25. Solving Conjunctions Solve and graph -4 < r – 5 ≤ -1 -4 < r – 5 ≤ -1 -4 + 5 < r ≤ -1 + 5 1 < r ≤ 4

  26. Who wants to answer the guiding question? What are compound inequalities?

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