Algebra Help...Super Simple!!?

Question

can any one solve

x+2/2x-3>1

i just started functions and i cant remember how to do it,..if any one can solve it and show me the steps then that'll be great!!

Thank You

Answer 1

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

x +2 > 2x-3

5 > x

therefore, x<5

Answer 2

u need to becareful with inequalities because if the denominator can be a negative term then u'll have multiple answers.

times both sides by the square of the denominator to avoid having negatives.

(x+2)/(2x-3) * (2x-3)^2 > (2x-3)^2

move terms and factorise in terms of (2x-3)

(x+2)(2x-3) - (2x-3)^2>0

(2x-3)(x+2-(2x-3))>0

(2x-3)(-x+5)>0

u have intercepts at x = 5 and 1

then check for numbers <1, between 1 and 5 and >5 to determine which section the question is asking for

Answer 3

x+2 2x-3>1
3x-1>1
+1 +1
3x>2

x>2/3

Answer 4

if it's super simple why can't you solve it???