**Rational Inequalities**

We adapt the preceding method when an inequality involves rational expressions.

We call these **rational inequalities.**

** **

**To solve a rational inequality:**

**a. **Change the inequality symbol to an equals sign and solve the

related equation.

**b. **Find the numbers for which any rational expression in the

inequality is not defined.

**c. **Use the numbers found in steps (a) and (b) to divide the number

line into intervals.

**d. **Substitute a number from each interval into the inequality. If the

number is a solution, then the interval to which it belongs is part

of the solution set.

**e. **Select the intervals for which the inequality is satisfied and write

set-builder or interval notation for the solution set.