In Example 5, change the exponent on (x − 2) from 2 to 3, then solve the resulting inequality, and graph the solution.

Data from Example 5

Solve the inequality

Since this function is a fraction, the critical values are the values of x that make either the numerator or denominator equal to zero. Thus, the critical values are −3, 2, and 4, and we have the following table:

Thus, the solution is x 4. The graph of the function is shown in Fig. 17.23(a), and the graph of the solution is shown in Fig. 17.23(b).

(x - 2)(x + 3) 4- x < 0.