COMEDK Exam 2015 Solved Paper

Given, inequality is
‌‌

6x

4x−1

<‌

1

2

⇒‌

12x

4x−1

<1
‌⇒‌‌‌

12x

4x−1

−1<0⇒‌

8x+1

4x−1

<0 . . . (i)
For above inequality Eq. (i), we have two cases either
Case I 8x+1>0,4x−1<0
Case II 8x+1<0,4x−1>0
From Case (I), we get x>‌

−1

8

,x<‌

1

4

∴‌‌x∈(−‌

1

8

,‌

1

4

) . . . (ii)
From Case (II), x<‌

−1

8

,x>‌

1

4

, both of which can not be true.
∴Eq. (ii) represent the solution set of given inequality.