Question

Correctly order the steps involved in finding the solution to a polynomial or rational inequality.

A) Identify critical points, Test intervals, Determine signs, Solve inequalities
B) Solve inequalities, Identify critical points, Test intervals, Determine signs
C) Test intervals, Solve inequalities, Identify critical points, Determine signs
D) Determine signs, Test intervals, Solve inequalities, Identify critical points

Answer 1

To correctly order the steps involved in finding the solution to a polynomial or rational inequality, you need to identify the unknowns, test intervals, determine signs, and solve the inequalities.

Step-by-step explanation:

1. Identify exactly what needs to be determined in the problem (identify the unknowns). In this case, the unknowns would be the values of x that satisfy the polynomial or rational inequality.
2. Test intervals: Divide the x-axis into intervals using the critical points obtained from step 1. Then, choose a test point from each interval and substitute it into the inequality. Determine whether the inequality is true or false for each test point.
3. Determine signs: Look at the values obtained from step 2 to determine the signs of the inequality. For example, if the test point is positive, it means the inequality is true in that interval. If it's negative, it means the inequality is false.
4. Solve inequalities: Combine the intervals where the inequality is true to obtain the solution set for the polynomial or rational inequality.