. If x (x + 3) (x + 5) (x + 8 ) < 250, how many integer values can x take?

1,-1,0,,-2,-3,-4,-5,-6,-7,-8,-9. 11 values!!

Hi
We have x(x+3)(x+5)(x+8)<250
We have x(x+8)(x+3)(x+5)<250
(x^2+8x)(x^2+8x+15)<250
Take x^2+8x=t
t(t+15)<250
t^2+15t-250<0
(t+25)(t-10)<0
so t will range from -24 to 9
Now x^2+8x=t
x^2+8x-t=0 ,
Now 8 can be 1+7 , 6+2 ,5+3, 4+4 ,0+8 and -9+1
We get 11 integral values

11 ?

3

1?