# Solving Inequalities In order to solve inequality problems you

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```					                                   Solving Inequalities

In order to solve inequality problems you must be familiar with these Inequality
Properties:

Property               Statement                    Example
If a < b and b < c ,
Transitive Property then a < c.               If 3 < 7 and 7 < 9, then 3 < 9
If a < b and c < d , then If 2 < 5 and 6 < 8, then 2 + 6 < 5
Add Inequalities    a + c < b +d              +8
If 3 < 4 and k = 5 then, 3 + 5 < 4
Add / Subtract a       If a < b then                + 5 or
Constant                                            3-5<4-5
Multiply by a          If a < b and k > 0, then If 2 < 4 and k = 9, then (2)(9) <
Positive Constant      ak < bk                  (4)(9)
If a < b and k > 0, then
Divide by a Positive                                If 4 < 6 and k = 2, then 4 / 2 < 6 /
Constant                                            2
Multiply by a          If a < b and k < 0, then If 2 < 7 and k = - 3, then (2)(- 3) >
Negative Constant      ak > bk                  (7)( -3)
If a < b and k < 0, then
Divide by a Negative                                If 4 < 8 and k = - 2, then 4 / -2 > 8
Constant                                            / -2

If 0 < a < b, or a < b <
Reciprocal Property
I                   0, then

Reciprocal Property
II                  If a < 0 < b, then

Solve each of the following inequalities. Specify your solution set using set and interval
notation.

example 1: Solve

( add -3 to both sides )

( add -2x to both sides )

( divide 5 to both sides )
Solution Set:

Example 2:

( add -2 to each member )

( divide each member by -5 )

Solution Set:

remember open dots for greater than or less than signs        , but closed dots for greater
than or equal to , or less than or equal to signs .

Example 3:

( factor )

Indicate zeros ( with 0 ) and complete the sign analysis ( with - or + ) of each factor and

of the overall expression

sign of

sign of

sign of

The solution must have positive x values since          , Therefore the solution set is:
Example 4:

( use reciprocal property I ,
remember to change the signs)

( multiply both members by 2 )

( subtract 4 to both members ; remember
a common denominator for sub fractions)

The solution set is :

Last update: February 16, 2005

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