Algebra 2 Week #2A Section 2

Highway to Mt. McKinley, Alaska

Week #2A – Section 1 Reflection Question Reflection Question for Today: What is the difference between an equation and an inequality? Sides of an equation are the same (equal). One side of an inequality is biggr than the other side. Solve: 3(2 – x) < 2( 2 – x) – 1 6 – 3x < 4 – 2x – 1 6 – 3x < 3 – 2x 6 < 3 + x 3 3)

Week #2A Section 1 Homework Answers Classwork: Switch sign answersDon’t switch sign answers 2. x > 1/31. x > - ½ 3. x > 24. x > - 7/3 5. x < -5/46. x ≥ - 8/7 14. x ≥ x < -13/2 15. x ≥ x ≤ x ≤ 4/ x ≥ x ≤ ½ 12. x ≤ x ≥ - 13/6 16. x ≤ - 5

Week #2A Section 1 Homework Answers Homework: CAHSEE #1B CAHSEE #2 C 1. x > 142. x > x ≤ ≤ x 5. x > < x 7. x = 17/48. x =

Week #2A – Section 2 GOAL: To review solving compound inequalities. (Preliminary Review) CA ALGEBRA 2 STANDARD 1.0: To be able to solve equations and inequalities involving absolute value. WARMUP QUESTIONS 1.Which of the following values for x satisfy this inequality? x < 0 - 6, - 2, 0, 3, 9 2. Which of the following values for x satisfy this inequality? - 3 x > 0 - 6, - 2, 0, 3, 9 3. Which of the following values for x satisfy this inequality? 2x - 3 ≥ 3 - 6, - 2, 0, 3, 9 Solve. 4.3 < x ½x < - 7

Week #2A – Section 2 GOAL: To review solving compound inequalities. (Preliminary Review) CA ALGEBRA 2 STANDARD 1.0: To be able to solve equations and inequalities involving absolute value. WARMUP QUESTIONS 1.Which of the following values for x satisfy this inequality? x < 0 - 6, - 2, 0, 3, 9 2. Which of the following values for x satisfy this inequality? - 3 x > 0 - 6, - 2, 0, 3, 9 3. Which of the following values for x satisfy this inequality? 2x - 3 ≥ 3 - 6, - 2, 0, 3, 9 Solve. 4.3 < x ½x < - 7

Week #2A – Section 2 GOAL: To review solving compound inequalities. (Preliminary Review) CA ALGEBRA 2 STANDARD 1.0: To be able to solve equations and inequalities involving absolute value. WARMUP QUESTIONS 1.Which of the following values for x satisfy this inequality? x < 0 - 6, - 2, 0, 3, 9 2. Which of the following values for x satisfy this inequality? - 3 x > 0 - 6, - 2, 0, 3, 9 3. Which of the following values for x satisfy this inequality? 2x - 3 ≥ 3 - 6, - 2, 0, 3, 9 Solve. 4.3 < x ½x < - 7

Week #2A – Section 2 GOAL: To review solving compound inequalities. (Preliminary Review) CA ALGEBRA 2 STANDARD 1.0: To be able to solve equations and inequalities involving absolute value. WARMUP QUESTIONS 1.Which of the following values for x satisfy this inequality? x < 0 - 6, - 2, 0, 3, 9 2. Which of the following values for x satisfy this inequality? - 3 x > 0 - 6, - 2, 0, 3, 9 3. Which of the following values for x satisfy this inequality? 2x - 3 ≥ 3 - 6, - 2, 0, 3, 9 Solve. 4.3 < x ½x < - 7

Week #2A – Section 2 GOAL: To review solving compound inequalities. (Preliminary Review) CA ALGEBRA 2 STANDARD 1.0: To be able to solve equations and inequalities involving absolute value. WARMUP QUESTIONS 1.Which of the following values for x satisfy this inequality? x < 0 - 6, - 2, 0, 3, 9 2. Which of the following values for x satisfy this inequality? - 3 x > 0 - 6, - 2, 0, 3, 9 3. Which of the following values for x satisfy this inequality? 2x - 3 ≥ 3 - 6, - 2, 0, 3, 9 Solve. 4.3 < x < x 5.- ½x < - 7

Week #2A – Section 2 GOAL: To review solving compound inequalities. (Preliminary Review) CA ALGEBRA 2 STANDARD 1.0: To be able to solve equations and inequalities involving absolute value. WARMUP QUESTIONS 1.Which of the following values for x satisfy this inequality? x < 0 - 6, - 2, 0, 3, 9 2. Which of the following values for x satisfy this inequality? - 3 x > 0 - 6, - 2, 0, 3, 9 3. Which of the following values for x satisfy this inequality? 2x - 3 ≥ 3 - 6, - 2, 0, 3, 9 Solve. 4.3 < x < x 5.- ½x < x < - 14 x > 14

Week #2A Section #2 Notes Solving Compound Inequalities Vocabulary Compound inequality – an algebraic expression usually between two numbers.

Week #2A Section #2 Notes Solving Compound Inequalities The Questions 1. WHAT is one way to solve a compound inequality? Solve it together. Do the same thing to both ends. EXAMPLE:

Week #2A Section #2 Notes Solving Compound Inequalities The Questions 1. WHAT is one way to solve a compound inequality? Solve it together. Do the same thing to both ends. EXAMPLE: 3 < 3x – 6 < 12

Week #2A Section #2 Notes Solving Compound Inequalities The Questions 1. WHAT is one way to solve a compound inequality? Solve it together. Do the same thing to both ends. EXAMPLE: 3 < 3x – 6 < 12 9 < 3x < 18

Week #2A Section #2 Notes Solving Compound Inequalities The Questions 1. WHAT is one way to solve a compound inequality? Solve it together. Do the same thing to both ends. EXAMPLE: 3 < 3x – 6 < 12 9 < 3x < 18 3 < x < 6 2. WHEN would you use this method?

Week #2A Section #2 Notes Solving Compound Inequalities The Questions 1. WHAT is one way to solve a compound inequality? Solve it together. Do the same thing to both ends. EXAMPLE: 3 < 3x – 6 < 12 9 < 3x < 18 3 < x < 6 2.WHEN would you use this method? Whenever you can.

Week #2A Section #2 Notes Solving Compound Inequalities The Questions 3. WHAT is the other way to solve a compound inequality? Split it up. Solve each inequality on its own. EXAMPLE: 4. WHEN would you use this method?

Week #2A Section #2 Notes Solving Compound Inequalities The Questions 3. WHAT is the other way to solve a compound inequality? Split it up. Solve each inequality on its own. EXAMPLE: 3 < 3x – 6 < WHEN would you use this method?

Week #2A Section #2 Notes Solving Compound Inequalities The Questions 3. WHAT is the other way to solve a compound inequality? Split it up. Solve each inequality on its own. EXAMPLE: 3 < 3x – 6 < 12 3 < 3x – 6 3x – 6 < WHEN would you use this method?

Week #2A Section #2 Notes Solving Compound Inequalities The Questions 3. WHAT is the other way to solve a compound inequality? Split it up. Solve each inequality on its own. EXAMPLE: 3 < 3x – 6 < 12 3 < 3x – 6 3x – 6 < 12 9 < 3x 3x < WHEN would you use this method?

Week #2A Section #2 Notes Solving Compound Inequalities The Questions 3. WHAT is the other way to solve a compound inequality? Split it up. Solve each inequality on its own. EXAMPLE: 3 < 3x – 6 < 12 3 < 3x – 6 3x – 6 < 12 9 < 3x 3x < 18 3 < x x < 6 4. WHEN would you use this method?

Week #2A Section #2 Notes Solving Compound Inequalities The Questions 3. WHAT is the other way to solve a compound inequality? Split it up. Solve each inequality on its own. EXAMPLE: 3 < 3x – 6 < 12 3 < 3x – 6 3x – 6 < 12 9 < 3x 3x < 18 3 < x x < 6 3 < x < 6 4. WHEN would you use this method?

Week #2A Section #2 Notes Solving Compound Inequalities The Questions 3. WHAT is the other way to solve a compound inequality? Split it up. Solve each inequality on its own. EXAMPLE: 3 < 3x – 6 < 12 3 < 3x – 6 3x – 6 < 12 9 < 3x 3x < 18 3 < x x < 6 3 < x < 6 4.WHEN would you use this method? When it can’t be solved together (usually because there are x’s on the outsides).

Week #2A Section #2 Notes Solving Compound Inequalities REAL LIFE ALGEBRA: Speed Limits Believe it or not, you can get a ticket for going too slow on a freeway (unless there is something wrong with your car) as well as too fast. Generally, you should be between 50 mph and 65 mph on a freeway. If that’s the case, what is the shortest and the longest distance you can drive in 4 hours on the freeway? Remember the rule that d = rt.

Think he’s busted?

Week #2A Section #2 Notes Solving Compound Inequalities REAL LIFE ALGEBRA: Speed Limits Believe it or not, you can get a ticket for going too slow on a freeway (unless there is something wrong with your car) as well as too fast. Generally, you should be between 50 mph and 65 mph on a freeway. If that’s the case, what is the shortest and the longest distance you can drive in 4 hours on the freeway? Remember the rule that d = rt. Let d = distance (number of miles) you can drive d = rt and we know t = 4 hours

Week #2A Section #2 Notes Solving Compound Inequalities REAL LIFE ALGEBRA: Speed Limits Believe it or not, you can get a ticket for going too slow on a freeway (unless there is something wrong with your car) as well as too fast. Generally, you should be between 50 mph and 65 mph on a freeway. If that’s the case, what is the shortest and the longest distance you can drive in 4 hours on the freeway? Remember the rule that d = rt. Let d = distance (number of miles) you can drive d = rt and we know t = 4 hours 50(4) ≤ d ≤ 65(4)

Week #2A Section #2 Notes Solving Compound Inequalities REAL LIFE ALGEBRA: Speed Limits Believe it or not, you can get a ticket for going too slow on a freeway (unless there is something wrong with your car) as well as too fast. Generally, you should be between 50 mph and 65 mph on a freeway. If that’s the case, what is the shortest and the longest distance you can drive in 4 hours on the freeway? Remember the rule that d = rt. Let d = distance (number of miles) you can drive d = rt and we know t = 4 hours 50(4) ≤ d ≤ 65(4) 200 ≤ d ≤ 260 You can legally travel in between 200 miles and 260 miles on the freeway in 4 hours.

Week #2A – Section 2 - Ending Quiz 1. Solve 4 < x + 4 < 7 A. 0 x > 3C. x < 3D. 0 < x < 3 2. If the hottest temperature on earth was 136°F and the coldest was - 126°F, which compound inequality represents this? A < x < 136B ≤ x ≤ 136 C > x > 136 D ≥ x ≥ 136