Q. Number of integral values of $x$ the inequality $\log _{10}\left(\frac{2 x-2007}{x+1}\right) \leq 0$ holds true, is
Continuity and Differentiability
Solution:
$ 0<\frac{2 x-2007}{x+1} \leq 1 $
$0< 2 x-2007 \leq x+1 $
$0< x \leq 2008 \ldots(1) $
$\text { also } 2 x-2007>0 $
$ x>1003.5 \text { or } x \geq 1004$ ....(2)
$\text { from (1) and (2) }$
