how to solve modulus (2x - 1/x - 1)>2?

if the given inequality is: .............(1)

if

therefore for given in equality two cases will arise:

case I :

............(2)

case II:

first plot the number 3/4 and 1 on the number line. and find solution by wavy curve method.

thus ............(3)

so from (2) and (3),

hope this helps you.

cheers!!

  • 17

hi friend, kindly take all of elements in left hand side

2x-1/x-1 - 2>0

2X-1 - 2X+2/x-1 >0

1/x-1>0

Now friend in this step treat x-1 as denominator

x-1>0

so, x belongs to (1,infinity)

  • -6

We have,

(2x - 1) / (x - 1) 2

⇒ [2x (x + 1) - 1 (x + 1)] / (x2 - 1) 2

⇒ (2x2 + 2x - x - 1) 2 (x2 - 1)

⇒ 2x2 + x - 1 2x2 - 2

⇒ x - 1

∴ Solution set = [ x ∈ R; x - 1 ] = ( - 1 ,)

  • -8

We have,

(2x - 1) / (x - 1) 2

⇒ [2x (x + 1) - 1 (x + 1)] / (x2- 1) 2

⇒ (2x2+ 2x - x - 1) 2 (x2- 1)

⇒ 2x2+ x - 1 2x2- 2

⇒ x - 1

∴ Solution set = [ x ∈ R; x - 1 ] = ( - 1 ,)

  • -8
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