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5.4 Polynomial and Rational Inequalities

In this section, we will study the following topics:

Solving polynomial inequalities

Solving rational inequalities

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Examples Of Polynomial And Rational Inequalities

3 4 0x x

Polynomial Inequalities Rational Inequalities

4 29x x

( 5)( 3)( 6) 0x x x

50

2

x

x

32x

x

3

• If the inequality symbol is ≤ or ≥, include the solutions of f(x)=0 in the solution set.

• We will use interval notation to indicate the solution to these inequalities.

NOTE:

continued

Thus, the solution set is ____________________________________.

Graph of solution set:

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The Related Graph

4 2( ) 4f x x x

Solve the inequality , and graph the solution set. 3 24 12 0x x x

continued

Thus, the solution set is ____________________________________.

Graph of solution set:

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The Related Graph

3 2( ) 4 12f x x x x

and at which f is undefined.

continued

Thus, the solution set is ____________________________________.

Graph of solution set:

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3 20

1

x x

x

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The Related Graph

2

3 2( )

1

x xf x

x

Write the expression on left as a single fraction.

and at which f is undefined.

continued

Thus, the solution set is ____________________________________.

Graph of solution set:

19

The Related Graph

1( )

2

xf x

x

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End of Section 5.4