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Lesson 6.4 - Solving Compound Inequalities pg. 339

Lesson 6.4 - Solving Compound Inequalities pg. 339. Goals : To solve compound inequalities containing the word AND and graph their solution set. To solve compound inequalities containing the word OR and graph their solution set. Vocabulary.

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Lesson 6.4 - Solving Compound Inequalities pg. 339

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  1. Lesson 6.4 - Solving Compound Inequalities pg. 339 Goals: To solve compound inequalities containing the word ANDand graph their solution set. To solve compound inequalities containing the word ORand graph their solution set.

  2. Vocabulary • Compound inequality: two or more inequalities that are connected by the words AND or OR. • Intersection: the graph of a compound inequality containing AND; the solution is the set of elements commonto both inequalities. • Union: the graph of a compound inequality containing OR; the solution is a solution of either inequality, not necessarily both.

  3. Ex. 1: Graph an Intersection 1. y ≥ 5 and y < 12 Note: Intersection- elements that they have in COMMON.

  4. 2. a ≤ 6 AND a ≥ -2

  5. 7 < z + 2 ≤ 11 6 < w + 3 and w + 3 < 11 Ex. 2: Solve and Graph an Intersection

  6. -8 < x - 4 ≤ -3 r + 8 ≤ 3 and r + 9 ≥ -4

  7. Ex. 3: Graph a Union 1. r > 6 OR r < 6 Note: Union-means shade EVERYTHING

  8. 2. y > 12 OR y < 9

  9. Ex. 4: Solve and Graph a Union 1. 4k – 7 ≤ 25 or 12 – 9k ≥ 30

  10. 2. h – 10 < -21 or h + 3 < 2

  11. 3. 3n + 11 ≤ 13 OR-3n ≥ -12

  12. 3g + 12 ≤ 6 + g ≤ 3g – 18

  13. Ex. 5: Write a compound inequality for each graph. 1. 2. 3.

  14. WITHIN- is meant to be inclusive. Use ≤ or ≥. • BETWEEN- is meant to be exclusive. Use <or >.

  15. Ex. 6: Define a variable, write an inequality, and solve each problem. 1. The sum of 3 times a number and 4 is between – 8 and 10.

  16. 2. Three times a number minus 7 is less than 17 and greater than 5.

  17. 3. One half of a number is greater than 0 and less than or equal to 1.

  18. SUMMARY • Intersection- elements that they have in COMMON. • Union-means shade EVERYTHING • WITHIN- is meant to be inclusive. Use ≤ or ≥. • BETWEEN- is meant to be exclusive. Use < or >. • Reverse the inequality symbol when multiplying or dividing by a negative. • NBA #10, page 342, problems 14-44 even

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