Linear Inequalities in One Variable

1
Linear Inequalities in One Variable

• - We will graph subsets of real numbers on a
  number line.
• - We will solve linear inequalities.
• - We will solve applied problems using linear
  inequalities.

2
Problem to consider

• Using a new postal service you can mail a flyer
  to a residence for .145. You have a maximum
  budget of 800 for printing and postage.
  Printing fee is 300. Let x be the number of
  flyers you mail. How can we represent all
  possible values for x?

3
Graphing subsets of real numbers on a number line
We will graph subsets of real numbers on a number
line

•  

a
b
a
b
a
b
a
b
a
b
4
Graph the following subsets

•  

0
2
1
3
-3
-1
-4
-2
4
0
2
1
3
-3
-1
-4
-2
4
0
2
1
3
-3
-1
-4
-2
4
0
2
1
3
-3
-1
-4
-2
4
0
2
1
3
-3
-1
-4
-2
4
5
Let us Reconsider the earlier problem
This time we will solve the inequality

• Using a new postal service you can mail a flyer
  to a residence for .145. You have a maximum
  budget of 800 for printing and postage.
  Printing fee is 300. Let x be the number of
  flyers you mail. How can we represent all
  possible values for x?

6
Solving Linear Inequalities

• The procedure for solving linear inequalities is
  the same as linear equations with one important
  exception!!!!
• When multiplying or dividing both sides of the
  inequality by a negative number, reverse the
  direction of the inequality symbol.

 
 
7
Solve and graph linear inequalities
We will solve linear inequalities

•  

0
2
1
3
-3
-1
-4
-2
4
0
2
1
3
-3
-1
-4
-2
4
0
2
1
3
-3
-1
-4
-2
4
0
2
1
3
-3
-1
-4
-2
4
0
2
1
3
-3
-1
-4
-2
4
8
Solving a Linear Inequality

•  

9
Solving a Three Part Inequality

•  

0
2
1
3
-3
-1
-4
-2
4
10
An Application using inequalities
We will solve applied problems using linear
inequalities.

• You have a class which only grades 4 tests. You
  have grades of 87, 76 and 83 with one test left
  to take. What must you score on the test to get
  a B (83 87 average)?