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 $[2, \infty)$
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