1. Solving Rational Equations and Inequalities
Lesson Presentation
Holt McDougal Algebra 2
Holt Algebra 2

2. A rational inequality is an inequality that contains one or more rational expressions. One way to solve rational inequalities is by using graphs and tables.

3. You can also solve rational inequalities algebraically.

4. Example 6: Solving Rational Inequalities Algebraically
Solve ≤ 0 algebraically. x
x – 8
Step 1 Set the numerator and denominator = 0
x – 8
= 0 and x = 0
Solve for x.
X = 8
8 and 0 are your critical values.

5. Example 6 Continued
Solve ≤ 0 algebraically. x
x – 8
Step 2 Set up a number line and test the critical values.

6. Example 6: Solving Rational Inequalities Algebraically
Solve ≤ 0 algebraically. x
x – 8

7. Check It Out! Example 6a
Solve > 0 algebraically.
x+4
x – 2
Step 1 Set the numerator and denominator = 0
x – 2= 0 x+4 = 0
Solve for x.
x = 2
x = –4
2 and -4 are your critical values.

8. Check It Out! Example 6a Continued
Solve > 0 algebraically.
X+4
x – 2
Step 2 Set up a number line and test the critical values.

9. Check It Out! Example 6a Continued
Solve > 0 algebraically.
X+4
x – 2

10. Check It Out! Example 6b
Solve < 6 algebraically.
X-7
x + 3
**This problem is different, because we are not comparing it to 0. We must first subtract the 6 and combine the fractions on the left hand side of the equation. Remember this will require getting common denominators.
-5x -25
x + 3
< 0

11. Check It Out! Example 6b Continued
Solve < 0 algebraically.
-5x-25
x + 3
Step 1 Now, set the numerator and denominator = 0
x + 3 = 0
-5x -25 = 0
Solve for x.
x = –3
x = –5

12. Check It Out! Example 6b Continued
Solve < 0 algebraically.
-5x-25
x + 3
Step 2 Set up a number line and test the critical values.

13. Check It Out! Example 6b Continued
Solve < 0 algebraically.
-5x-25
x + 3