Question

For how many integral values of x, is (x-5)/(x+7) > 4

Answer 1

Soln:

Given, (x - 5)/(x + 7) > 4

or, (x - 5)/(x + 7) - 4 > 0

or, (x - 5 - 4(x + 7) ) / (x + 7) > 0

or, (-3x - 12) / (x + 7) > 0

or, -3(x + 4) / (x + 7) > 0

Multiply by -1/3 both side

or, (x + 4) / (x + 7) < 0

or, {x - (-4)} / {x - (-7)} < 0

or, -7 < x < -4

integral values of x are : - 6, - 5

So, Number of integral value of x = 2