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InequalitiesQuadratic, Fractional         andIrrational Inequalities
To solve more complicated inequalities,     use the following procedure:  •   Make the RHS zero by shifting all terms to t...
Quadratic Inequalities    Find the range of x formaking RHS zerofully factorise LHSfind the critical valuesdraw sign diagr...
Find the range of values of x of thefollowing inequalities
Fractional Inequalities    Find the range of x formaking RHS zeroSimplify the equationfind the critical valuesdraw sign di...
Find the range of values of x of the       following inequalities
Irrational Inequalities  Find the range of x forSquare both sidesmaking RHS zeroMeeting therequirementdraw sign diagramFin...
Find the range of values of x of the       following inequalities
Absolute Value Inequalities   x       0Properties :  x    a               a    x   a  x    a           x       a OR x   a ...
Example 1  Find the range of x forUse property 1          3        x       2           3                        3    2    ...
Example 3Find the range of x for                 x            2           1    2x                                         ...
Example 4Find the range of x for                   x       1        3    x                                      2         ...
Find the range of values of x of the        following inequalities1. 3 x     6       9               5. x        3        ...
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Inequalities quadratic, fractional & irrational form

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Inequalities quadratic, fractional & irrational form

  1. 1. InequalitiesQuadratic, Fractional andIrrational Inequalities
  2. 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. 3. Quadratic Inequalities Find the range of x formaking RHS zerofully factorise LHSfind the critical valuesdraw sign diagram -2determine thevalues
  4. 4. Find the range of values of x of thefollowing inequalities
  5. 5. Fractional Inequalities Find the range of x formaking RHS zeroSimplify the equationfind the critical valuesdraw sign diagram -3 4determine thevalues
  6. 6. Find the range of values of x of the following inequalities
  7. 7. Irrational Inequalities Find the range of x forSquare both sidesmaking RHS zeroMeeting therequirementdraw sign diagramFind commonsolution
  8. 8. Find the range of values of x of the following inequalities
  9. 9. Absolute Value Inequalities x 0Properties : x a a x a x a x a OR x a 2 x x
  10. 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. 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. 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. 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

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