Question

Solve:
1/2x-3 > 1, x not= 2/3, x represents R

Answer 1

Question:

Solve for "x" in the given inequation :

1/(2x-3) > 1 , x ≠ 2/3 , x € R.

Answer:

x € (3/2 , 2)

Solution:

We have;

=> 1/(2x-3) > 1

=> 1/(2x-3) - 1 > 0

=> {1 - (2x-3)}/(2x-3) > 0

=> (1-2x+3)/(2x-3) > 0

=> (4-2x)/(2x-3) > 0

=> 2(2-x)/(2x-3) > 0

=> (2-x)/(2x-3) > 0

=> -(x-2)/(2x-3) > 0

=> (x-2)/(2x-3) < 0

Now,

Two cases arises;

Case(1):

When (x-2) > 0 and (2x-3) < 0

=> x > 2 and 2x < 3

=> x > 2 and x < 3/2

{This case is not possible, as there exist no real number which is greater than 2 and smaller than 3/2 simultaneously.}

OR

Case (2):

When (x-2) < 0 and (2x-3) > 0

=> x < 2 and 2x > 3

=> x < 2 and x > 3/2

=> x € (3/2 , 2)

The solution set for the given inequation will be given as the union of case(1) and case(2).

Hence,

The solution set for the given inequation is : x € (3/2 , 2) .