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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: 1.5 > x a) 2.5 < x 3.x > 10 4.5 ≥ x 5.5 ≤ x 6.x < 10 0 0 0 0 0 5 5 5 - 5 5 5 10 - 10 b) d) e) c)

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Home-Learning Assignment #1 – Review:

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Do you remember the difference between and and or on Set Theory ? 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 A AB B

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Compound Inequality A compound inequality consist of two inequalities connected by and or or. Vocabulary:

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Graphing Compound Inequalities

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Graph x < 4 and x ≥ 2 342 ● a) Graph x < 4 b) Graph x ≥ 2 342 o c) What if I Combine the graphs? ● 342 o d) Where do they intersect? ● 342 o Guided Example:

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Graph x < 2 or x ≥ 4 342 ● a) Graph x < 2 b) Graph x ≥ 4 342 o c) Combine the graphs 342 o 342 ● Guided Example:

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1) Which inequalities describe the following graph? -2-3 o o 1.y > -3 or y < -1 2.y > -3 and y < -1 3.y ≤ -3 or y ≥ -1 4.y ≥ -3 and y ≤ -1

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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. Lets graph the compound inequality 6 < m < 8 786 o o

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2) Which is equivalent to -3 < y < 5? 1.y > -3 or y < 5 2.y > -3 and y < 5 3.y 5 4.y 5

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3) Which is equivalent to x > -5 and x ≤ 1? 1.-5 < x ≤ 1 2.-5 > x ≥ 1 3.-5 > x ≤ 1 4.-5 < x ≥ 1

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Writing Compound Inequalities

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All real numbers that are greater than – 2 and less than 6 All real numbers that are less than 0 or greater than or equal to 5 - 2 < x < 6 x < 0 or x ≥ 5

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All real numbers that are greater than zero and less than or equal to 4. All real numbers that are less than –1 or greater than 2 Guided Example:

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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 4) Graph x < 2 or x ≥ 4 5) Graph x ≥ -1 or x ≤ 3

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8) x is less than 4 and is at least -9

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Solving & Graphing Compound Inequalities

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3 < 2m – 1 < 9 and and and and HINT: ONLY “AND” PROBLEMS WILL LOOK LIKE THIS. “OR” PROBLEMS MUST SAY “OR” Solving & Graphing

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3 < 2m – 1 < 9 05 -5 Answer: + 1 + 1 + 1 ------------------------------ 4 < 2m < 10 2 2 2 2 < m < 5

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Answer: – 8 3x > 9 3 3 x > 3 – 5 – 5 2x ≤ 2 2 2 x ≤ 1

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- 3 < - 1 – 2x ≤ 5 11) 12) 13) -15 ≤ –3x – 21 ≤ 25 14) 10) 9)

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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)

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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!! -30-6 o -30-6 o 471 o ● 471 o ● Based on the meaning of ‘and,’ why is this No Solution ?

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Wrap-Up: Vocabulary Review Summary Home-Learning Assignment #2: Page 204 – 206 (9, 16, 18, 37, 54)

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