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December 1, 2017
3.7 - Solving Polynomial and Rational
Inequalities
For more complicated inequalities, it is often useful to use a sign diagram.
Steps for solving polynomial and rational inequalities:
1. Identify any real undefined values.
2. Rewrite inequality so one side is 0.
3. Find the real zeroes of the inequality from step 2.
4. Create a sign diagram using the zeroes and undefined values. Be sure to label
points with open or closed circles
Remember only zeroes can be closed circles, and only if the inequality is
allowed to be equal to zero. Holes and Vertical Asymptotes must be open
circles.
5. Test each interval with the inequality from step 2 (or use of multiplicity rules) to
determine which intervals provide solutions to the inequality.
December 1, 2017
Example 1: Solve the inequality. Write your answers in inequality and interval notation.
December 1, 2017
December 1, 2017
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