Question

The solution set of $\left|\frac{2}{x-6}\right|\ge 1,x\ne 6$ is

• A. $[4,6)\cup (6,8]$
• B. $(-\infty ,4)$
• C. $6,8)$
• D. $6,\infty )$

Answer 1

The correct option is A $[4,6)\cup (6,8]$

$\left|\frac{2}{x-6}\right|\ge 1$
$2\ge |x-6|$
$-2\le x-6\le 2$
$-2+6\le x\le 2+6$
$x\le x\le 8$
$\therefore$ Solution is $[4,6)\cup (6,8]$
$\therefore$ (1) is correct