Solve the inequality (x-2)(x-3) >0

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Please find below the solution to the asked query :

x-2 x-3 >0First we will find out the intervalsx-3=0 , x-2=0x=3 , 2So , intervals are-,2 , 2,3 , 3,Now in inteval -,2Put x=0x-2x-3=0-20-3=6>0So , this interval will be a solution .Now in inteval 2,3Put x=2.5x-2x-3=2.5-22.5-3=-0.25<0So , this interval will not be a solution .Now in inteval 3,Put x=4x-2x-3=4-24-3=2>0So , this interval will be a solution .Hence , x -,23, .
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  • 2
For (x-2)(x-3) to be greater than 0 either both terms should be negative or both should be positive.
Case 1 - Both are positive,
So x-2>0 and x-3 >0  
  x>2 and x>3   i.e x>3  ------------------1
Case 2-Both are negative
So x-2<0 and x-3<0
   x<2 and x<3  i.e x<2   ---------------------2
Solution of inequality from 1 and 2 is ( - infinity,2) U (3,infinity)
  • 2
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