|(x-3)/(x+5)|< 2

Question

i've asked so many ppl, but they all give me different answers :(

Well if the expression is less than two, and the abs function is positive, then the ratio is between 0 and 2. Lets look inside the abs function, it can be negative, because the abs will make it positive.
If that is so, then...
-2 < (x-3)/(x+5)<2 multiply the expression by x+5
-2 (x+5)< (x-3) <2(x+5)
-2x -10 < x-3 < 2x +10
-10 < x-3+ 2x < 4x +10
Now, examining this part -10 < x-3+ 2x
or -7 <3x
or x > -7/3
x>-2.33333 Examining the other part.. x-3+ 2x < 4x +10
-3 < 3x +10
-13 < 3x
x > -13/3 x>- 4.3333 but both of these must occur, so x> -2.333..
Now to check it. Let x=-2, 4, and -5(it should not check on this one. Let me know if you have difficulty.