Solving rational inequalities

Rational Inequalities

1. SOLVING RATIONAL INEQUALITIES www.slideshare.net/reycastro1 General Mathematics

2. RATIONAL INEQUALITIES LEARNING OUTCOMES: Able to solve rational inequalities and solve problems involving rational inequalities.

3. INTERVAL AND SET NOTATION An inequality may have infinitely many solutions. The set of all solutions can be expressed using set notation or interval notation.

4. INTERVAL AND SET NOTATION

5. INTERVAL AND SET NOTATION Ex. If -2 < x < 2 Interval: (-2, 2) Set Notation: { x|-2 < x < 2 }

6. INTERVAL AND SET NOTATION Ex. If Interval: [0, 3] Set Notation: { x| }  

7. INTERVAL AND SET NOTATION Ex. If and Interval: ________ and __________ Set Notation: ______ and __________ Graph:  

8. INTERVAL AND SET NOTATION Ex. If 2 Interval: (-2, ) Set Notation: { x| -2 }  

9. INTERVAL AND SET NOTATION Ex. If Interval: [ , ) Set Notation: { x| }  

10. INTERVAL AND SET NOTATION Ex. If Interval: ______________ Set Notation: _______________

11. INTERVAL AND SET NOTATION Ex. If x < -1 Interval: ______________ Set Notation: _______________ Graph:

12. PROCEDURE FOR SOLVING RATIONAL INEQUALITIES To solve rational inequalities Rewrite the inequality as a single fraction on one side of the inequality symbol and 0 on the other side. Determine over what intervals the fraction takes on positive and negative values.

13. SOLVING RATIONAL INEQUALITIES Example 1: Solve the inequality  

14. SOLVING RATIONAL INEQUALITIES Example 1: Solve the inequality The solution set is The interval notation:  

15. SOLVING RATIONAL INEQUALITIES Example 2: Solve the inequality  

16. SOLVING RATIONAL INEQUALITIES Example 3: A box with a square base is to have a volume of 8 cubic meters. Let x be the length of the side of the square base and h be the height of the box. What are the possible measurements of a side of the square base if the height should be longer than a side of the square base?

17. SOLVING RATIONAL INEQUALITIES Example 4: A dressmaker ordered several meters of red cloth from a vendor only but 4 meters of red cloth in stock. The vendor bought the remaining lengths of red cloth from a wholesaler for P1120. He then sold those lengths of red cloth to the dressmaker along with the original 4 meters of cloth for a total of P1600. if the vendor’s price per meter is at least P10 more than the wholesaler’s price per meter, what possible lengths of cloth did the vendor purchase from the wholesaler?

18. Try this! Find the solutions of the following. (a) (b) (c) You have a 6 liters of a pineapple juice blend that is 50% pineapple juice. How many liters of pure pineapple juice needs to be added to make a juice blend that is 75% pineapple juice? Hint: If x is the amount of pure pineapple juice to be added, the percentage can be written as  

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