Question

Number of integral values of $x$ the inequality ${\log }_{10}\left(\frac{2x-2007}{x+1}\right)\le 0$ holds true, is

• A. 1004
• B. 1005
• C. 2007
• D. 2008

Answer 1

Answer: (B)

$0<\frac{2x-2007}{x+1}\le 1$
$0<2x-2007\le x+1$
$0<x\le 2008\dots (1)$
$\text{ also }2x-2007>0$
$x>1003.5\text{ or }x\ge 1004$ ....(2)
$\text{ from (1) and (2) }$