Solve `3x+8 gt2`, when
(i) x is an integer.
(ii) x is a real number.

Solve 5x-3 lt 7 , when (i) x is an integer. (ii) x is a real number.

Solve 5x-3 lt 3x+1 when (i) x is an integer (ii) x is a real number.

Solve 30 x lt 200 when (i) x is a natural number. (ii) x is an integer.

Solve -12x gt 30 , when (i) x is a natural number. (ii) x is an integer.

Solve 24x lt 100 , when (i) x is a natural number, (ii) x is an integer.

Prove that : If n is a positive integer and x is any nonzero real number, then prove that C_(0)+C_(1)(x)/(2)+C_(2).(x^(2))/(3)+C_(3).(x^(3))/(4)+….+C_(n).(x^(n))/(n+1)=((1+x)^(n+1)-1)/((n+1)x)

tan x gt x when x lies in

Solve x^(2)-7x+6 gt 0 .

We know that any real number x can be expressed as followig x=[x]+{x} , where [x] is an integer and 0 le {x} lt 1 . We define [x] as the greatest integer less than or equal to x or integer part of x and [x] as the fractional part of x. Suppose for any real number x, we write x=(x)-(x) , where (x) is integer and 0 le (x) lt 1 . We define (x) as the least integer greater than (or) equal to x. For example (3.26) =4(-14.4)= - 14(5)=5 elearly, if x in I then (x)=[x] . If x !in I , then (x)=[x]+1 we can also define that x in ( n , in +1) rArr (x)=n+1 , where n in I The domain of defination of the function f(x)=(1)/(sqrt(x-(x))) is