Question 59826
1/4x-2=1/2x-3

first add 3 to both sides of the equation
1/4x-2 + 3 =1/2x-3 + 3

you get 
1/4x +  1 = 1/2x

now subtract 1/4x to both sides of the equation
1/4x - 1/4x + 1 = 1/2x - 1/4x
or
1 = 1/2x - 1/4x

but we know that
1/2x = 2/4x

substitute in previous equqtion and you have
1 = 2/4x -1/4x
or
1 = 1/4x

multiply both sides times 4 and

4 = x

so 
x=4