Warm Up1. Solve: 3𝑥 − 9 ≥ 9

2. Solve on a number line: 2𝑥 − 5 2(𝑥 + 3)(𝑥 + 2) < 0

3. Sketch the graph of: 𝑦 ≤ 𝑥3 + 2𝑥2

𝒙 ≤ 𝟎 𝒐𝒓 𝒙 ≥ 𝟔

−𝟑 < 𝒙 < −𝟐

Linear Programming (Aka Linear Optimization)

Practice

CHAPTER 3 REVIEW

Quiz Topics•Solve & Graph Linear Inequality (number line) #1•Solve & Graph Absolute Value Inequality (number line) #2•Solve Polynomial Inequality #3•Graph Linear Inequality (xy grid) #4 & #5a•Graph Quadratic Inequality (xy grid) #6b•System of Equations #6•Linear Programming #8

Homework: Chapter Test

Page 115 #1-8

Solve and graph each inequality

on a number line.

1 2

1. (a) 3 8 4 9 7 (b) 3

24 12 9 7 4 12 3 6

24 9 5 12 6

15 5

6

3 4

xx x x

x x x x

x

x x

x

3x

0 1 2 3 4 5 6 7 88 7 6 5 4 3 2 1

0 1 2 3 4 5 6 7 88 7 6 5 4 3 2 1

Solve and graph each inequality

on a number line.

2. (a) 3 5 (b) 6 4

5 3 5 6 4 6 4

2 8 10 2

x

x x or

x

x x or x

x

2 3 8 10 6 2

Solve and graph each inequality

on a number line.

80

(c) 3 4 4

3 4 4 3 4 4

3 0 3 8

43 4

3

4 4

3 3

3

x

x or x

x or x

x x

x

or

x

8

3

4

3 0

Solve and graph each inequality

on a number line.

(d) 7 5 2

2 7 5 2

9 5 5

91

5

9

15

x

x

x

x

x

0 1 2 3 4 5 6 7 88 7 6 5 4 3 2 1

Solve each inequality.

2

(a) 2 1 4 3 0x x x

0 1 2 3 4 5 6 7 88 7 6 5 4 3 2 1

4x 1

2x

Solve each inequality.

2(b) 4 5 6 0

4 3 2 0

x x

x x

0 1 2 3 4 5 6 7 88 7 6 5 4 3 2 1

32

4x

Solve each inequality.

3 2

3 2

2

(c) 2

2 0

2 1 0

2 1 1 0

x x x

x x x

x x x

x x x

0 1 2 3 4 5 6 7 88 7 6 5 4 3 2 1

1x 1

02

x

Solve each inequality.

2

6 1(d) 0

3

x x

x

0 1 2 3 4 5 6 7 88 7 6 5 4 3 2 1

1 6, 3x x

4. Describe the set of points that satisfy the

inequality 2 5.y

Writing

x

1

1

5. Graph each inequality in the coordinate plane.

(a) 2 3 3

3 3 2

2

3

y x

y x

y x

1

1

Unit 3 Pretest Presentation

5. Graph each inequality in the coordinate plane.

(b) 3x

1

1

3 3x

6. Graph the solution set of each system.

(a) 0

3 4 2

4 3 2

3 1

4 2

x

x y

y x

y x

1

1

2

6. Graph the solution set of each system.

(b) 2

6

2

1 12

y x x

y x

y x x

bx y

a

1

1

7. Give a set of inequalities that defines the

shaded region.

2

1 3

1

1 1 1,4 4 1

2 2

9

2 2

x

m y

y

y x

x

500 350P x y

# of trucksx # of carsy

0

0

x

y

6 3 150x y

4 4 120x y

8. Cars and trucks are made in a factory that is divided into two shops.

Shop 1 performs the basic assembly operation, working 6 person-days

on each truck and only 3 person-days on each car. Shop 2 performs

finishing operations, working 4 person-days on each car or truck that

it produces. Shop 1 has 150 person-days per week available, while

Shop 2 has 120 person-days per week. The manufacturer makes a

profit of $500 on each truck and $350 on each car. How many of

each should be produced each week to maximize profit.

0

Feasible

Region

6 3 150 2 50x y y x

5

4 4 120 30x y y x

20,10

5

Problem

0

Feasible

Region

6 3 150 2 50x y y x

5

4 4 120 30x y y x

20,10

5

The Corner Point Principle

A maximum or minimum value of a linear

expression , if it exists, will

occur at a corner point of the feasible

region.

P Ax By

* Applies only to convex polygonal regions

Which corner point maximizes profit?????

0,30

25,0

500 350P x y