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Module 2                                                                                                                             38

   d.  Graph P(t).

Polynomial and Rational Inequalities

Solve the following polynomial inequalities by first writing them in general form, factoring (if needed) to identify boundary points, drawing a number line with boundary points labeled, and testing each interval.  Express the solution in interval notation.

1.  x2 > 7x

2.  12x2 < 37x + 10

3.  (x + 2)(x – 5)(x + 7) ≤ 0

Solve the following rational inequalities by first writing them as a single simplified rational expression on one side and zero on the other side of the inequalities. Identify the boundary points by labeling them on a number line and then testing the intervals.  Express the solution in interval notation.

4.  

5.  

6.  

Applications

7.  The profit from selling x pieces of handmade jewelry can be modeled by the

    equation P(x) = –x2 + 130x – 3000.  What is the range of profitable orders (P(x) > 0)?

8.  The difference between the value of a piece of equipment and what is owed on it is

    modeled by the expression  d(x) = , where x is the number of years since

    the equipment was purchased.  When does the amount owed exceed the value of

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