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BELL-WORK

Learn to write, solve, and graph compound inequalities. Explore concepts such as conjunctions and disjunctions, identifying solutions. Practice with engaging examples and improve your understanding of inequalities in algebra.

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BELL-WORK

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  1. BELL-WORK *Eureka Module 1 Lesson 15 Exercise 4,f,g **Write a compound inequality for the phrase and then graph the solutions: All real numbers that are greater than or equal to -4 and less than 6. ***Solve and graph 5 > 5 – f > 2

  2. Solving Conjunctions Solve and graph 5 > 5 – f > 2 5 – 5 > -f > 2 – 5 0 > -f > -3 0 < f < 3

  3. Solving Conjunctions Solve and graph 5 > 5 – f > 2 5 – 5 > -f > 2 – 5 0 > -f > -3 0 < f < 3

  4. Solving Conjunctions Solve and graph 5 > 5 – f > 2 5 – 5 > -f > 2 – 5 0 > -f > -3 0 < f < 3 Why do we ‘flip that junt’?

  5. Solving Conjunctions What are the solutions of 20x – 18 < 50 < 36x – 16? Notice that the variable is not in the middle! When that happens, the inequality must be broken into 2 parts: 20x – 18 < 50 and 50 < 36x – 16 x < 17 and x > 11 5 6 11 < x < 17 6 5

  6. Solving Conjunctions What are the solutions of 8 ≤ 2y + 4 ≤ -6(y – 2) + 48 Notice that the variable is not only in the middle! When that happens, the inequality must be broken into 2 parts: 8 ≤ 2y + 4 and 2y + 4 ≤ -6(y – 2) + 48 y ≥ 2 and y ≤ 7 2 ≤ y ≤ 7

  7. Compound Inequalities What is the difference between ‘x is between -5 and -7’ and ‘x is between -5 and -7 inclusive’? To earn a B in your Algebra course, you must achieve an unrounded test average between 84 and 86, inclusive. You score 86, 85, and 80 on the first three tests of the grading period. What possible scores can you earn on the fourth test to earn a B in the course? Suppose you scored 78, 78, and 79 on the first three tests. Is it possible for you to earn a B in the course? Explain.

  8. HW 2.1(c) Due 10/22/18: On website HW 2.1(b) # 1,9,10,12,24,27,29

  9. HW 2.1(b) Solutions 2. 25 ≤ x ≤ 30; GRAPH 3. 7 < x < 13; GRAPH 4. -12 < x < -6; GRAPH 7. 3 < x ≤ 7½ ; GRAPH 8. -23 ≤ x < 1; GRAPH 11. 2 ≤ y ≤ 7; GRAPH 25. -3 ≤ x ≤ 2 26. -2 < x < 1 30. -9 ≤ w ≤ 33 10 10 31. 4.6 < y < 10.6

  10. Lunch With Mrs. Matt

  11. Crunch With Mrs. Matt

  12. Guiding question: What are compound inequalities?

  13. Compound Inequalities What is a compound inequality? Yesterday we learned one type of compound inequality known as a… conjunction. Today we will learn another type of compound inequality.

  14. Compound Inequalities When two inequalities are joined by the word ‘or’ a disjunction is formed. Ex. All real numbers that are less than 0 or greater than 3. So, x < 0 or x > 3

  15. Compound Inequalities When two inequalities are joined by the word ‘or’ a disjunction is formed. Ex. All real numbers that are less than 0 or greater than 3. So, x < 0 or x > 3 Which is graphed as:

  16. Compound Inequalities When two inequalities are joined by the word ‘or’ a disjunction is formed. Ex. All real numbers that are less than 0 or greater than 3. So, x < 0 or x > 3 Notice there is a gap in the graph, which implies that solutions to disjunctions make only one of the components true.

  17. Compound Inequalities Write a compound inequality to represent all real numbers that are less than or equal to 2½ or greater than 6.

  18. Solving Disjunctions Solve and graph 3x + 2 < -7 OR -4x + 5 < 1 When solving disjunctions, simply solve each inequality separately. 3x + 2 < -7 OR -4x + 5 < 1 3x + 2 < -7 OR -4x + 5 < 1 3x < -9 OR -4x < -4 x < -3 OR x > 1

  19. Solving Disjunctions Solve and graph 3x + 2 < -7 OR -4x + 5 < 1 When solving disjunctions, simply solve each inequality separately. 3x + 2 < -7 OR -4x + 5 < 1 3x + 2 < -7 OR -4x + 5 < 1 3x < -9 OR -4x < -4 x < -3 OR x > 1

  20. Solving Disjunctions What are the solutions of -2y + 7< 1 or 4y + 3 ≤ -5? Graph the solutions.

  21. Who wants to answer the Guiding question? What are compound inequalities?

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