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Name: Date: Period: Topic: Solving & Graphing Compound Inequalities Essential Question: How does a compound inequality differ from a regular inequality? What is the meaning of “and” and “or” in a compound inequality? Warm-Up: Match the following graphs with its’ corresponding inequality: 1. 2. 3. 4. 5. 6. 5>x 5<x x > 10 5≥x 5≤x x < 10 a) - 10 -5 0 5 10 - 10 -5 0 5 10 - 10 -5 0 5 10 - 10 -5 0 5 10 - 10 -5 0 5 10 b) c) d) e) Home-Learning Assignment #1 – Review: Do you remember the difference between and and or on Set Theory? A B 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 Vocabulary: Compound Inequality A compound inequality consist of two inequalities connected by and or or. Guided Example: Graph x < 4 and x ≥ 2 a) Graph x < 4 o 2 3 4 3 4 b) Graph x ≥ 2 ● 2 c) What if I Combine the graphs? d) Where do they intersect? ● 2 3 o 4 Guided Example: Graph x < 2 or x ≥ 4 a) Graph x < 2 o 2 b) Graph x ≥ 4 2 3 3 c) Combine the graphs 4 ● 4 1) Which inequalities describe the following graph? o o 1. 2. 3. 4. -3 -2 y > -3 or y < -1 y > -3 and y < -1 y ≤ -3 or y ≥ -1 y ≥ -3 and y ≤ -1 -1 Lets 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. o 6 7 o 8 2) Which is equivalent to -3 < y < 5? 1. 2. 3. 4. y > -3 or y < 5 y > -3 and y < 5 y < -3 or y > 5 y < -3 and y > 5 1. 2. 3. 4. 3) Which is equivalent to x > -5 and x ≤ 1? -5 < x ≤ 1 -5 > x ≥ 1 -5 > x ≤ 1 -5 < x ≥ 1 All real numbers that are greater than – 2 and less than 6 -2<x<6 All real numbers that are less than 0 or greater than or equal to 5 x < 0 or x ≥ 5 Guided Example: All real numbers that are greater than zero and less than or equal to 4. 0 x4 All real numbers that are less than –1 or greater than 2 x 1or x 2 4) Graph x < 2 or x ≥ 4 5) Graph x ≥ -1 or x ≤ 3 6) All real numbers that are greater than or equal to – 4 and less than 6 7) All real numbers that are less than or equal to 2.5 or greater than 6 8) x is less than 4 and is at least -9 a.)4 x 9 b.) 9 x 4 c.) 9 x 4 d .) 9 x 4 Solving & Graphing and and 3 < 2m – 1 < 9 and HINT: ONLY “AND” PROBLEMS WILL LOOK LIKE THIS. “OR” PROBLEMS MUST SAY “OR” and Answer: 3 < 2m – 1 < 9 +1 +1 +1 -----------------------------4 < 2m < 10 2 2 2 2 < m <5 -5 0 5 3 x 8 17 or 2 x 5 7 Answer: 3 x 8 17 or 2 x 5 7 –8 –8 3x > 9 3 3 x>3 –5 –5 2x ≤ 2 2 2 x≤1 9) 2 3x 8 10 10) 3x 1 4 or 2 x 5 7 11) - 3 < - 1 – 2x ≤ 5 12) 6 x 6 8 13) 14) 13 5 2x 9 -15 ≤ –3x – 21 ≤ 25 Additional Practice: Page 204 - 206 (1 – 8, 14, 36) For those who complete the work before time is over, proceed to work on the following problems: Page 204 - 206 (10, 15, 24, 26, 38, 41, 55) Based on the meaning of ‘and,’ why is this No Solution ? 2x < -6 and 3x ≥ 12 1. Solve each inequality for x 2. Graph each inequality 3. Combine the graphs 4. Where do they intersect? 5. They do not! x cannot be greater than or equal to 4 and less than -3 No Solution!! 2 x 6 2 2 x 3 o -3 3x 12 3 3 x4 0 4 7 -6 1 o ● Wrap-Up: Vocabulary Review Summary Home-Learning Assignment #2: Page 204 – 206 (9, 16, 18, 37, 54)