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Algebra 2
Week #2A
Section 2
Highway to Mt. McKinley, Alaska
Week #2A – Section 1Reflection 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 < x (or x > 3)
Week #2A Section 1Homework Answers
• Classwork: Switch sign answers Don’t switch sign answers• 2. x > 1/3 1. x > - ½• 3. x > 2 4. x > - 7/3• 5. x < -5/4 6. x ≥ - 8/7• 14. x ≥ - 2 7. x < -13/2• 15. x ≥ - 12 8. x ≤ - 9• 9. x ≤ 4/15• 10. x ≥ 15• 11. x ≤ ½• 12. x ≤ - 6• 13. x ≥ - 13/6• 16. x ≤ - 5
Week #2A Section 1Homework Answers
• Homework:CAHSEE #1 B
CAHSEE #2 C1. x > 14 2. x > - 53. x ≤ 6 4. 10 ≤ x5. x > - 5 6. - 2 < x7. x = 17/4 8. x = 69. 105 10. 4
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 + 6
• 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 + 6
• 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 + 6
• 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 + 6
• 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 + 6• - 3 < 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 + 6• - 3 < x
• 5. - ½x < - 7• - 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 < 12
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
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
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
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 B. 0 > x > 3 C. x < 3 D. 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. - 126 < x < 136 B. - 126 ≤ x ≤ 136• C. - 126 > x > 136 D. - 126 ≥ x ≥ 136
