Question

Solve the following inequalities: $\frac{|x+2|-x}{x}<2$

• A. $(1,\infty )$
• B. $(-\infty ,-1)$
• C. $(-\infty ,-0)$
• D. None of these

Answer 1

Answer: (A)

$(1,\infty )$

$\frac{|x+2|-x}{x}<2$
$\Rightarrow |x+2|-x<2x$
$\Rightarrow x+2-x<2x$
$\Rightarrow 2x>2$
$\Rightarrow x>1$
$\therefore x=(1,\infty )$