Warm – up # 6 1. It takes Cassidy 9 hours to do her math project. It takes Shannon 8 hours to do...

Warm – up # 61. It takes Cassidy 9 hours to do her math project. It takes Shannon 8 hours to do the same project. How long would it take them if they worked together?

AloneRate

Time Together

Part of Job

Completed

Cassidy

Shannon

x

x

Cassidy’s Part + Shannon’s Part = 1 Job Completed

• =𝟏𝟖

𝟏𝟗

𝒙𝟗𝒙𝟖

AloneRate

Time Together

Part of Job

Completed

Cassidy

Shannon

x

x

Cassidy’s Part + Shannon’s Part = 1 Job Completed

• =Work Problem #5

Cont’d

𝟏𝟖

𝟏𝟗

𝒙𝟗𝒙𝟖

𝑥9

+𝑥8

=1(72) (72)(72)

8x + 9x = 7217x = 72

4.24 hours

Homework LogFri

10/9

Lesson 2 – 3

Learning Objective: To solve linear inequalities & write solutions in interval notation

Hw: #207 Pg. 120 #1 - 39 odd - graph all & write answers in interval notation

10/9/15 Lesson 2 – 3 Linear Inequalities Day 1

Advanced Math/Trig

Learning Objective

To solve linear inequalities

To graph solutions to linear inequalities

To write linear inequalities’ solutions in interval notation

Open circle on the number lineDoes NOT include the #

> Greater than

< Less than Closed circle on the number lineINCLUDES the #

Greater than or equal toLess than or equal to

Graphing Inequalities

Use ( ) if open circle Use [ ] if closed circle # on left is smallest x can be # on right is largest x can be 2 x < 5 [2, 5) x > – 4 (–4, ) x 7 (–, 7 ] is always “open” circle

Interval Notation

ALWAYS FLIP THE

INEQUALITY SIGN

WHEN YOU

DIVIDE BY – #

1. – 3(2x – 5) + 1 4 – 6x + 15 + 1 4 – 6x + 16 4 – 16 – 16 – 6x – 12

– 6 – 6 x 2

Solve & Graph Inequalities

FLIP!!!

(– , 2]

2. – 2(3x + 1) > – 6x + 7 – 6x – 2 > – 6x + 7 +2 +2 – 6x > – 6x + 9

+6x +6x 0 > 9

NEVER TRUE! No Solution!


∅

3. 5(2x – 3) – 7x < 3x + 810x – 15 – 7x < 3x + 8 3x – 15 < 3x + 8 –3x –3x

– 15 < 8ALWAYS TRUE! Infinite Solutions


Compound Inequality – join two inequalities with the word and or or

“And” compound inequality – Find all values of the variable that make BOTH inequalities true. Need overlap

“Or” compound inequality – Find all values of the variables that make at least one of the inequalities true

4. 7 < 2x + 1 and 3x 18 –1 –1 & 3 3

6 < 2x & x 6 2 2 3 < x


x > 3 and x ≤ 6 3 < x ≤ 6(3, 6]

5. 7 + x 6 or 8 + x < 3 –7 –7 –8 –8

x – 1 or x < – 5


00

(–)

6. 1 and 2x 8(8) 1(8) 2 2

x 8and x 4Need OVERLAP because

AND x 4


(–

7. x + 8 > 2 or 7x – 5 > 51 –8 –8 + 5 +5

x > – 6 or 7x > 56 7 7x > – 6 or x > 8Either OR Don’t need overlapx > – 6


(–

8. – 8x + 2 > – 22 and 9x – 7 > 47 –2 –2 + 7 +7 –8x > –24 and 9x > 54

–8 –8 9 9x < 3 and x > 6

Not Possible!!No Solution


FLIP!!!

∅

9. –5 + x 5+6x or 7x – 2 8x+1 +5 +5 +2 +2

x 10 + 6x or 7x 8x + 3 –6x –6x –8x –8x

–5x 10 or –x 3–5 –5 –1 –1x – 2 or x – 3


FLIP!!!

(−∞ ,∞)

10. – 77 – 9x + 4 < – 41 – 4 –4 –4 – 81 – 9x < – 45 –9 –9 –9

9 x > 5 5 < x 9


FLIP!!!

(5, 9]

11. 10 – 9x 10 or 3x + 2 26 –10 –10 –2 –2 –9x 0 or 3x 24 –9 –9 3 3

x 0 or x 8


FLIP!!!

()

12. 10+6x > 22 and 5x+3 < 8 –10 –10 –3 –3

6x > 12 & 5x < 5 6 6 5 5

x > 2 and x < 1No Solution


∅

13. 8 + 6x > – 16 or 9x + 1 > 91 –8 –8 –1 –1

6x > – 24 or 9x > 90 6 6 9 9

x > – 4 or x > 10x > – 4


()

14. 3x – 4 > 5 and -3x – 9 < 21 + 4 +4 +9 +9

3x > 9 and –3x < 30 3 3 –3 –3

x > 3 and x > -10x > 3


()

Distance Problem15. It takes a plane as long to fly 400 km against the wind as it does to fly 450 km with the same wind. Find the speed of the plane in still air if the wind speed is 20 km/hr. Rate Time Distance

Against Wind

With Wind

tx + 20

x – 20

t

𝟒𝟎𝟎450

d = r(t)

• =400 = (x – 20)(t) 450 = (x + 20)(t)

Distance Problem #15 Cont’d

400(x + 20) = 450(x – 20)

400x + 8000 = 450x – 9000

17000 = 50x

x = 340 km/hr

Grocery Store16. You went to the grocery store to buy milk and eggs. Suppose that a carton of milk cost $0.93, and a carton of eggs cost $0.99. How many cartons each of milk and egg did you buy if you spent $7.74 and bought 8 items?Amount $/each Total

Milk

Egg

Total 7.74

0.93

8

8 – x

x

0.99

.93x

.99(8 – x)

.93x + .99(8 – x) = 7.74

• =

Grocery Problem #16 cont’d

.93x + .99(8 – x) = 7.74

.93x + 7.92 – .99x = 7.74 –.06x = –.18

x = 3 8 – x = 5

3 cartons of milk5 cartons of eggs

Concert17. Reserved-set cost $18 each, and cheap-seats cost $12.50 each. How many tickets were sold if 3 times as many cheap-seat tickets were sold as reserved seat tickets and tht eotal proceeds were $688,200? Amount $/each Total

Reserved

Cheap

Total 688200

18

3x

x

12.50

18x

12.5(3x)

18x + 12.5(3x) = 688200

• =

Concert Problem #17 cont’d

18x + 12.5(3x) = 68820018x + 37.5x = 688200

55.5x = 688200x = 12,4003x = 37,200

12,400 reserved seats37,200 cheap-seats

Ticket Out the Door

Solve

Write solution in interval notation

Graph your solution.

Homework

#207 Pg. 120 # 1 - 39 odd - graph all

Write answers in interval notation

Warm – up # 6 1. It takes Cassidy 9 hours to do her math project. It takes Shannon 8 hours to do...

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