Bell workBell work

1. Solve. 1. Solve.

A painter can be paid in two ways. A painter can be paid in two ways.

Plan A: $300.00 + $15.00 per hourPlan A: $300.00 + $15.00 per hour

Plan B: $20.00 per hourPlan B: $20.00 per hour

Suppose the job takes Suppose the job takes nn hours for what values of hours for what values of nn

is plan A better for the painter?is plan A better for the painter?

2. Find all sets of three consecutive odd positive 2. Find all sets of three consecutive odd positive integers integers

whose sum is less than 20 but greater than 10. whose sum is less than 20 but greater than 10.

Bell work answers Bell work answers

1.1. n < 60 hours n < 60 hours

2.2. 3,5,7 3,5,7

Pre-AP Algebra 3Pre-AP Algebra 3Chapter 2 Section 5Chapter 2 Section 5

Objective: Students will:Objective: Students will:

1. Solve compound inequalities.1. Solve compound inequalities.

Types of Compound Types of Compound StatementsStatements

1. 1. Conjunctions (Intersections – (Conjunctions (Intersections – (ՈՈ)))) – “and” – “and”

statementsstatements

Example: “It is the weekend Example: “It is the weekend andand I get to rest.” I get to rest.”

Example: Example: x > - 3x > - 3 andand x < 3x < 3

This can be written as This can be written as -3 < x < 3-3 < x < 3

2. 2. Disjunctions (Unions ( Disjunctions (Unions ( Ս ))Ս )) – “or” statements – “or” statements

Example: It is cloudy Example: It is cloudy oror the sky is clear. the sky is clear.

Example: Example: y < - 4 y < - 4 oror y y >> 6 6

Solving Conjunctions Solving Conjunctions (Intersections)(Intersections)

Example 1. Solve. Example 1. Solve.

4 < 3x + 1 < 74 < 3x + 1 < 7

4 < 3x + 14 < 3x + 1 and and 3x + 1 < 73x + 1 < 7

-1-1 -1-1 -1 -1 -1 -1

33 < < 3x3x and and 3x3x < < 66

33 3 3 3 33 3

1 < x1 < x andand x < 2 x < 2

1 < x < 21 < x < 2

Interval notation: (1,2)Interval notation: (1,2)

Graphing the solutionsGraphing the solutions

Example 1:Example 1: 4 < 3x + 14 < 3x + 1 and and 3x + 3x + 1 < 71 < 7

1 < x1 < x andand x < x < 22

1 < x< 21 < x< 2

|---|---|---|---|---|---||---|---|---|---|---|---|

00 1 1 2 2 3 3

Solving Disjunctions Solving Disjunctions (Unions)(Unions)

Example 2. Solve. Example 2. Solve.

5x + 1 < 115x + 1 < 11 or or 2x + 3 2x + 3 >> 9 9 - 1- 1 -1 -1 - 3 - 3 - 3 - 3

5x5x < < 1010 or or 2x2x >> 66 5 5 5 5 2 2 2 2

x < 2x < 2 or or x x >> 3 3Interval notation: (-Interval notation: (-∞,2) U [3, ∞)∞,2) U [3, ∞)

Graphing the solutionsGraphing the solutions

Example 2:Example 2: 5x + 1 < 11 or 5x + 1 < 11 or 2x + 2x + 3 3 >> 9 9

x < 2x < 2 or or x x >> 3 3

--|---|---|---|---|---|---|--|---|---|---|---|---|---| 11 2 3 2 3 4 4

HomeworkHomework

PRE _AP ALGEBRA 3PRE _AP ALGEBRA 3

P. 85 - 86 (2 - 46) evenP. 85 - 86 (2 - 46) even

Grade HomeworkGrade Homeworkp. 69 (2- 28) even&29 p. 69 (2- 28) even&29

# correct/ 22# correct/ 222. 6m;4m 2. 6m;4m 4. 14. 1⅞m ; 3⅛m⅞m ; 3⅛m 6. 86. 8 8. 8.

$500$50010. $800 10. $800 12. 2512. 25°°,100,100°°,55,55°° 14. l = 110m ; w = 45 m 14. l = 110m ; w = 45 m 16. 14, 1616. 14, 1618. $43,00018. $43,000 20. G = $375. ; F= $1875.20. G = $375. ; F= $1875.

22. 25% increase22. 25% increase 24. $36024. $360

26. no solution26. no solution 28. answer may vary, ie. 28. answer may vary, ie. rope = 36 ft rope = 36 ft

29. 84 years29. 84 years

Grade HomeworkGrade Homeworkp. 77 (2- 44) even p. 77 (2- 44) even

# correct/22 # correct/22 2. yes 2. yes 4. 4. 6. a = (F/m)6. a = (F/m) 8. P = (I/rt)8. P = (I/rt)

10. c10. c² = (E/m)² = (E/m) 12. w = 12. w = p-2lp-2l 14. b14. b² = c² - a²² = c² - a² 2 2

16. 16. ππ = (A/r²) = (A/r²) 18. h = (2/11)w + 4018. h = (2/11)w + 40

20. 20. ππ = (3V/4r³) = (3V/4r³) 22. b = 22. b = (2A-ha)(2A-ha) 24. v24. v² = (rF/m)² = (rF/m) h h

26. s = 26. s = (A – r(A – r²)²) 28. $75.0028. $75.00 ππrr

29. Take the Square root and the cube root29. Take the Square root and the cube root 30. V1 = 30. V1 = (T1P2V2)(T1P2V2)

P1T2P1T2

Journal Topic Journal Topic

How are compound inequalities How are compound inequalities applied applied

to our daily activities?to our daily activities?