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Question

Solve: $$\left | 2x-5 \right |< 1$$


A
x(4,5)
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B
x(3,5)
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C
x(2,3)
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D
x(1,2.5)
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Solution

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, $$ y - 1 < 0 $$
$$ => y < 1$$ 

$$ => 2x - 5 < 1 $$

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

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

So, $$ -y-1 < 0 $$ 

$$ y > -1 $$

$$ => 2x -5 > -1 $$

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


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