Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Successfully reported this slideshow.

Like this presentation? Why not share!

4,507 views

Published on

Published in:
Education

No Downloads

Total views

4,507

On SlideShare

0

From Embeds

0

Number of Embeds

2

Shares

0

Downloads

58

Comments

0

Likes

3

No embeds

No notes for slide

- 1. InequalitiesQuadratic, Fractional andIrrational Inequalities
- 2. To solve more complicated inequalities, use the following procedure: • Make the RHS zero by shifting all terms to the LHS. • Fully factorise the LHS to get critical values. • Draw sign diagram for the LHS. • Determine the values required from the sign diagram.
- 3. Quadratic Inequalities Find the range of x formaking RHS zerofully factorise LHSfind the critical valuesdraw sign diagram -2determine thevalues
- 4. Find the range of values of x of thefollowing inequalities
- 5. Fractional Inequalities Find the range of x formaking RHS zeroSimplify the equationfind the critical valuesdraw sign diagram -3 4determine thevalues
- 6. Find the range of values of x of the following inequalities
- 7. Irrational Inequalities Find the range of x forSquare both sidesmaking RHS zeroMeeting therequirementdraw sign diagramFind commonsolution
- 8. Find the range of values of x of the following inequalities
- 9. Absolute Value Inequalities x 0Properties : x a a x a x a x a OR x a 2 x x
- 10. Example 1 Find the range of x forUse property 1 3 x 2 3 3 2 x 3 2 Solution 1 x 5 Example 2 Find the range of x for 3x 6 3 Use property 2 3x 6 3 OR 3 x 6 3 3x 3 OR 3 x 9 Solution x 1 or x 3
- 11. Example 3Find the range of x for x 2 1 2x 2 2Square both sides (x 2) (1 2 x)Simplify x 2 4x 4 1 4x 4x 2 2 3x 3 0 2 3( x 1) 0 ( 3)Factorize ( x 1) ( x 1) 0Find critical values x 1, x 1Draw sign diagram + - + -1 1 Solution x 1 OR x 1
- 12. Example 4Find the range of x for x 1 3 x 2 2Square both sides (x 1) (3 x) 2 2Simplify x 2x 1 9 6x x 2x 6x 9 1 4x 8 (4) Solution x 2Meeting the requirement 3 x 0 x 3 x 3 Draw sign diagram 2 3 2 x 3
- 13. Find the range of values of x of the following inequalities1. 3 x 6 9 5. x 3 x 5 x 1 OR x 5 x 1 6. 2 x 1 x 22. 2 x 3 1 1 2 x 1 x OR x 3 3 23. 3 x 1 6 7. x 20 16 x 1 OR x 3 6 x 2 OR 2 x 6 24. x 3 x 2 8. x 3x 14 4 1 x 2 x 3 OR 2 x 5 OR x 6 2

No public clipboards found for this slide

Be the first to comment