Solve Present answers using interval notation x 2x 1 10Solu

Solve. Present answers using interval notation. x (2x- 1) > 10

Solution

x(2x-1)>10

or, 2x²-x-10>0

or, 2x²-5x+4x-10>0

or, x(2x-5)+2(2x-5)>0

or, (2x-5)(x+2)>0

hence 2 cases may happen

1) (2x-5)<0 and (x+2)<0

hence x<5/2   and x<-2

combining we get x<-2..............(i)

2) (2x-5)>0 and (x+2)>0

or, x>5/2   and x>-2

combining we get x>5/2............(ii)

hence the solution is x<-2 and x>5/2    [answer]