Question

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

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

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 $$(1), (2) ; x \in (2, 3)$$Maths

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