Question

If $|x-2|<3$, then number of integers in the range of $x$ is

Answer 1

Let $x-2=y$

Given, $\left|y\right|<3$
$=>\left|y\right|-3<0$
Now, when $y>0$ , we have $\left|y\right|=y$
So, $y-3<0$
$=>y<3$

$=>x-2<3$

$=>x<5$ -- (1)
And when $y<0$ , we have $\left|y\right|=-y$
So, $-y-3<0$
$y>-3$

$=>x-2>-3$

$=>x>-1$ -- (2)
From $\left(1\right),\left(2\right);x\in (-1,5)$