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