Find all integers `x` for which `(5x-1)<(x+1)^2<(7x-3)dot`

Find all values of x for which |{:(2,-1,4),(3,0,5),(4,1,6):}|=|{:(x,4),(5,x):}| .

Find the set of all s for which (2x)/(2x^(2)+5x+2) gt (1)/(x+10

Find all values of x for which |2x+3| ge 5.

Find the set of all x foir which (2x)/((2x^2+5x+2))>1/((x+1))dot

Find an integer x such that (i) x+1=0 (ii) x+5=0

Find the integral values of a for which (a+2)x^2+2(a+1)x+a=0 will have both roots integers

For all integers x > 1, = 2x + (2x - 1) + (2x -2) + …..+ 2 + 1 . What is the value of cdot ?

Verify Mean Value Theorem, if f(x)=x^3-5x^2-3x in the interval [a, b], where a = 1 and b = 3 . Find all c in (1, 3) for which f^(prime)(c)=0 .

Find the smallest value of x for which 5 - 2x lt 5 (1)/(2) - (5)/(3)x , where is an integer.

If f(x)={{:(,5 tan^(-1)alpha-3x^(2),0 lt x lt 1),(,5x-3,x ge 1):} then find the least integer value of alpha for which f(x) has minima at x=1.