Question

The inequality
$|2x - 3| < 1$
Is valid when x lies in interval _________?​

Answer 1

Heya!!!

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( 2x - 3 ) < 1 OR - ( 2x - 3 ) < 1

=>

2x < 4 OR 2x > 2

=>

x < 2 OR x > 1

So, x lies between ( 1 2 )

x € ( 1 2 )

Answer 2

| 2x - 3 | < 1

For, ( 2x - 3 ) < 1

2x - 3 + 3 < 1 + 3

2x < 4

2x/2 < 4/2

x < 2

For [ - ( 2x - 3 )] < 1

-2x +3 < 1

-2x + 3 - 3 < 1 - 3

-2x < - 2

-2x / (- 2 ) < ( - 2) / ( - 2)

x < 1

So, x is defined when x lies in interval ( x < 2) and ( x < 1 ).