Warm – up # 6 1. 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.

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Warm – up # 6 1. 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? Alone Rate Time Together Part of Job Completed Cassidy Shannon x x Cassidy’s Part + Shannon’s Part = 1 Job Completed =

Alone Rate Time Together Part of Job Completed Cassidy Shannon x x Cassidy’s Part + Shannon’s Part = 1 Job Completed = Work Problem #5 Cont’d 8x + 9x = 72 17x = hours

Homework Log Fri 10/9 Lesson 2 – 3 Learning Objective: To solve linear inequalities & write solutions in interval notation Hw: #207 Pg. 120 # 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

Graphing Inequalities

Interval Notation

ALWAYS FLIP THE INEQUALITY SIGN WHEN YOU DIVIDE BY – #

Solve & Graph Inequalities FLIP!!!

2. – 2(3x + 1) > – 6x + 7 – 6x – 2 > – 6x – 6x > – 6x x +6x 0 > 9 NEVER TRUE!No Solution! Solve & Graph Inequalities

3. 5(2x – 3) – 7x < 3x x – 15 – 7x < 3x + 8 3x – 15 < 3x + 8 –3x –3x – 15 < 8 ALWAYS TRUE!Infinite Solutions Solve & Graph Inequalities

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

Solve & Graph Inequalities (3, 6]

Solve & Graph Inequalities 0

7. x + 8 > 2 or7x – 5 > 51 –8 – x > – 6or 7x > 56 7 x > – 6 or x > 8 Either OR Don’t need overlap x > – 6 Solve & Graph Inequalities

8. – 8x + 2 > – 22 and 9x – 7 > 47 –2 – –8x > –24and9x > 54 –8 –8 9 9 x 6 Not Possible!! No Solution Solve & Graph Inequalities FLIP!!!

Solve & Graph Inequalities FLIP!!!

Solve & Graph Inequalities FLIP!!! (5, 9]

Solve & Graph Inequalities FLIP!!!

x > 22 and5x+3 < 8 –10 –10 –3 –3 6x > 12 &5x < x > 2 and x < 1 No Solution Solve & Graph Inequalities

x > – 16 or9x + 1 > 91 –8 –8 –1 –1 6x > – 24or9x > x > – 4orx > 10 x > – 4 Solve & Graph Inequalities

14. 3x – 4 > 5 and -3x – 9 < x > 9and–3x < –3 –3 x > 3 andx > -10 x > 3 Solve & Graph Inequalities

Distance Problem 15. 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. RateTimeDistance Against Wind With Wind t x + 20 x – 20 t450 d = r(t) =

Distance Problem #15 Cont’d

Grocery Store 16. 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 $7.74 and bought 8 items? Amount$/eachTotal Milk Egg Total – x x x.99(8 – x).93x +.99(8 – x) = 7.74 =

Grocery Problem #16 cont’d.93x +.99(8 – x) = x –.99x = 7.74 –.06x = –.18 x = 3 8 – x = 5 3 cartons of milk 5 cartons of eggs

Concert 17. 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 $688,200? Amount$/eachTotal Reserved Cheap Total x x x 12.5(3x) 18x (3x) = =

Concert Problem #17 cont’d 18x (3x) = x x = x = x = 12,400 3x = 37,200 12,400 reserved seats 37,200 cheap-seats

Ticket Out the Door

Homework #207 Pg. 120 # odd - graph all Write answers in interval notation