Name Date Period Topic Solving Graphing Compound Inequalities
- Slides: 25
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: 5>x 5<x x > 10 5≥x 5≤x x < 10 a) b) c) d) - 10 -5 -5 5 10 5 10 0 5 10 0 e) - 10 -5 1. 2. 3. 4. 5. 6.
Home-Learning Assignment #1 – Review:
Do you remember the difference between and or on Set Theory? 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.
d n u o p m o s C e i g t i n i ual h p q a e r G In
Guided Example: Graph x < 4 and x ≥ 2 a) Graph x < 4 o 2 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
d n u o p m s o e C i t i g l n a i t u ri neq W I
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. All real numbers that are less than – 1 or greater than 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
g n i es h i p t a i l r a G qu & e n g I n i d v n l o S pou m o C
and Solving & Graphing and 3 < 2 m – 1 < 9 and HINT: ONLY “AND” PROBLEMS WILL LOOK LIKE and THIS. “OR” PROBLEMS MUST SAY “OR”
Answer: 3 < 2 m – 1 < 9 +1 +1 +1 ---------------4 < 2 m < 10 2 2 < m <5 -5 0 5
Answer: – 8 3 x > 9 3 3 x>3 – 5 2 x ≤ 2 2 2 x≤ 1
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 ? 2 x < -6 and 3 x ≥ 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!! -6 1 o -3 o ● 4 0 7
Wrap-Up: Vocabulary Review Summary Home-Learning Assignment #2: Page 204 – 206 (9, 16, 18, 37, 54)
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- Reintroducing inequalities
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- Lesson 1-6 solving compound and absolute value inequalities
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- Lesson 3-3 compound inequalities
- 1-6 solving compound inequalities
- Inequalities in one triangle
- 1-6 solving compound and absolute value inequalities
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