Equations Lesson 6.10 Linear Inequalities.notebook
Linear Inequalites Equations and Inequalities
• Students will solve an inequality.
• Students will write an inequality from real­world problem situation.
TEKs
8.8 ­ The student applies mathematical process standards to use one­variable equations or inequalities in problem situations. answer
8.8A ­ Write one­variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants 8.8B ­ write a corresponding real­world problem when given a one­variable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants 8.8C ­ model and solve one­variable equations with variables on both sides of the equal sign that represent mathematical and real­world problems using rational number coefficients and constants Title Page
Warm­Up
Practice Answers
1. y < ­4
1. x
0 1 2 3 4 5 6
3. y < 8
4. y > ­8
5. ­11 < x or x > ­11
Test for x = ­12: ­29 < ­30; False Test for x = ­10: ­25 < ­24; True
y
20,000 19,100 18,200 17,300 16,400 15,500 14,600
What is an owl's favorite type of math?
Math Humor
Owl­gebra Debt
2. y > ­23
Maintain Your Skills
1
2
3
4
5
6
Months
c. y = 20,000 – 900x
d. No, he sll owes $2000 aer 20 months
2. A
6. y > ­5/2 or ­2 1/2
Test for y = ­2: ­7 > ­8; True Test for y = ­3: ­12 > ­11; False
7.
8.
9.
10.
2x ­ 5 < 3x + 7; x > ­12
3x + 6 > 4.5x + 3; 2 > x
2x – 5 > x – 2; x > 3
3x + 7 > 2x ­ 4; x > ­11
Practice Answers
Math Humor
Cut and tape Labsheet in your journal.
A. 1. From the graph, find where the two companies would be the same.
What is the cost?____________________ Number of days? ________________________
Launch
click here for video
2. For what number of days will Super Locks cost less than Fail Safe? _______________________
3. For what number of days will Fail Safe cost less than Super Locks? ________________________
B.
1. For each company write an equation for the cost c for d days of security services.
Fail Safe: __________________________
Super Locks: _____________________________
2. Find the number of days when the two companies cost the same. (Hint: set equations equal to one another and solve; then substitute d into equation to find cost)
3. Write an inequality to describe when each of the companies will cost less. (Hint: same as above with inequality symbol)
Fail Safe: __________________________
Pull
What is the cost? _______________________Number of days? _________________________
Super Locks: _____________________________
4. Find the number of days when each company costs less.
(Hint: solve the above inequalities for d)
Fail Safe: __________________________
Super Locks: _____________________________
Super Locks
Fail Safe
$17.95
per day
$3,975
Installation
Launch
$6
Daily
$995
Installation
Labsheet
1
Equations Lesson 6.10 Linear Inequalities.notebook
Live in Wonderland...
Find a Friend
or Neverland?
Find a friend and tell them what the
inequality symbols are.
Find A Friend
_____
Would You Rather?
2. How to • write two linear inequalities
compare two inequalities? • look for key phrases for inequality symbols
Linear Inequalities
Date
1. What is a y > mx + b y < mx + b
linear • m is the slope / rate of inequality?
change
• b is the y­intercept
• less than or equal to
• no more than
• at most
<
• less than
• is fewer than
Notes
≤
• greater than or equal to
• no less than
• at least
≥
• greater than
• more than
• exceeds
>
Notes
Example
3. What • x ­ intercept: where the line crosses the x­axis; y = 0
are the x­ and y­
• y ­ intercept: where the line intercepts?
crosses the y­axis; x = 0
Plant A is 5 centimeters tall and growing at the rate of 3 centimeters a month. Plant B is 4 centimeters tall and growing at the rate of 5 centimeters a month. When will Plant B exceed the height of Plant A?
pull
y = 5 + 3m
y = 4 + 5m
pull
Plant B
Plant A
answer
Notes
4 + 5m > 4 + 2m >
Example
2
Equations Lesson 6.10 Linear Inequalities.notebook
Closing Questions
Practice
Linear Inequality
Worksheet
How many solutions does an inequality have? many How to write a linear equation? y = mx + b
Practice
Closing Questions
3
Attachments
IIS Investigation 3.1.webm
Security Companies ﴾linear inequalities﴿.mp4