Question

Solve: $|2x-5|<1$

• A. $x\in (4,5)$
• B. $x\in (3,5)$
• C. $x\in (2,3)$
• D. $x\in (1,2.5)$

Answer 1

The correct option is C $x\in (2,3)$

Let $2x-5=y$

Given, $\left|y\right|<1$
$=>\left|y\right|-1<0$
Now, when $y>0$ , we have $\left|y\right|=y$
So, $y-1<0$
$=>y<1$

$=>2x-5<1$

$=>x<\frac{6}{2}=3$ -- (1)

And when $y<0$ , we have $\left|y\right|=-y$

So, $-y-1<0$

$y>-1$

$=>2x-5>-1$

$=>x>2$ -- (2)
From $\left(1\right),\left(2\right);x\in (2,3)$