Math 1513 Sec 1.6
1
Section
1.6
Solving Linear Inequalities
An inequality is a statement similar to an equation except that
the = sign is replaced by one of 4 inequality signs
, , ,
.
The rules and techniques for solving inequalities are almost the
same as those for solving equations except for the following:
Anytime you multiply or divide both sides of an inequality
by a negative number, you must reverse the direction of the
inequality sign.
Example 1:
Solve
2
5 4 6
x
x
9
4
4
4
9
9
4
4
2
5 4 6
5 4 6
2
9 4
x
x
x
x
x
x
x
or x
Example 2:
Solve
2
5 4 6
x
x
9
4
4
4
9
4
2
5 4 6
2
6
4 5
4
9
x
x
x
x
x
x
x
Notice that in the next to the last step we divided both sides
by 4.
This required us to reverse the > to <.
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2
Let’s look at this problem graphically.
Example 3:
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 Fall '08
 staff
 Algebra, Inequalities, Negative and nonnegative numbers, Solution Set, Solving Linear Inequalities, 1513 Sec

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