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Linear Inequalities in One Variable

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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 ... – PowerPoint PPT presentation

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Title: 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)?
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