A rational inequality is an inequality with one or more rational expressions involving variables in the numerator and denominator.
To solve a rational inequality, you need to follow these steps:
1. Simplify both sides of the inequality if possible.
2. Find the critical values by setting the denominator equal to zero and solving for the variable.
3. Use the critical values to create intervals on a number line.
4. Test a value in each interval to determine if it satisfies the original inequality.
5. Write the final solution using interval notation.
Yes, the methods for solving rational equations can also be used to solve rational inequalities. However, when multiplying or dividing both sides of the inequality by a negative number, the direction of the inequality sign must be flipped.
Some common mistakes when solving rational inequalities include:
- Forgetting to flip the inequality sign when multiplying or dividing by a negative number.
- Not simplifying the rational expressions before solving.
- Forgetting to include the solution to the critical values in the final answer.
Yes, you can graph a rational inequality to help you solve it. The solution to a rational inequality is represented by the shaded region on the graph. However, it is still important to follow the steps for solving algebraically to ensure accuracy.
