Question

The solution set of the in equation $|x-1|\ge |x-3|$, is

• A. $[-\alpha ,2]$
• B. $[2,\alpha ]$
• C. $[1,3]$
• D. none of these

Answer 1

The correct option is B $[2,\alpha ]$

Given : $|x-1|\ge |x-3|$

case I : $x\ge 3,|x-1|\ge |x-3|$

$\Rightarrow x-1\ge x-3$

$2\ge 0$ (true)

case II : $x<3,x\ge 1|x-1|\ge |x-3|$

$\Rightarrow x-1\ge 3-x$

$2x\ge 4$

$x\ge 2$

$\Rightarrow x\in [2,3]$

case III : $x<1,|x-1|\ge |x-3|$

$1-x\ge 3-x$

$0\ge 2$ (false)

combining I,II,III

$x\in [2,\infty ]$ $\therefore$ option B is correct.