# Write the solution set of the equation

Question:

Write the solution set of the equation |2 − x| = x − 2.

Solution:

We have,

$|2-x|=x-2$

Now 2 cases arise.

CASE 1 : When $2-x \geq 0$, then $|2-x|=2-x$

$\Rightarrow|2-x|=x-2$

$\Rightarrow 2-x=x-2$

$\Rightarrow 2 x=4$

$\Rightarrow x=2$

So, this condition is satisfied when $x=2$.

CASE 2 : When $2-x<0$ (i. e. when $x>2$ ), then $|2-x|=-(2-x)$

$\Rightarrow|2-x|=x-2$

$\Rightarrow-(2-x)=x-2$

$\Rightarrow-2+x=x-2$

$\Rightarrow-2=-2$

So, this condition is satisfied when $\mathrm{x}>2$

Hence, from the given two cases, the solution set of the given equation is $[2, \infty)$