Question

Solve algebraically:
4/2x-3 < 1/x+4

Answer 1

Again, watch those needed brackets, assuming you meant:
4/(2x-3) < 1/(x+4)

I see critical values at x = 3/2 and x = -4

try a value x between -4 and 3/2, say x = 0
is 4/(0-3) < 1/(0+4)
is -4/3 < 1/4, YES, so -4 < x < 3/2

try a value x < -4 , say x = -5
is 4/(-10-3) < 1/-1 ?
is -4/13 < -1 ?? , NO

try a value x>3/2, say x = 2
is 4/(8-3) < 1/(2+4) ?
is 4/5 < 1/6 , NO

-4 < x < 3/2

or , look at the graphs of
y = 4/(2x-3) and y = 1/(x+4)
where is the first curve below the second curve?
http://www.wolframalpha.com/input/?i=plot+y+%3D+4%2F(2x-3)+,+y+%3D+1%2F(x%2B4)

Wolfram shows the blue curve below the pink curve between -4 and 1.5