Other inequalities

Example 1

We find zeros of corresponding equation

Table of signs

The graph of x is a rising line that passes through the origin. It is negative before zero and positive after zero. The quadratic factor is an upward-opening parabola and negative when it is between its zeros. The last line contains the product, that is, the signs of our third degree polynomial. The answer to the inequality is

Rational equations and inequalities are covered in more detail in Course 6. Let’s look at a simple example.

The zero point of the numerator x-7 is 7 and the graph is a rising line. The graph of the denominator 2x-4 is also rising line and a zero point is 2. From the signs of the numerator and denominator we can find the signs of the quotient. The solution to the inequality is