Need some help understanding inequalities

ok so i missed a few classes and i have a test comming up soo and i need some help understanding inequalities.

the example im trying to do is:

If |x-2|< 2, show that |(x^2+3x+1)/(x+1)| < 7

form what i could understand from a textbook was something like:

-2<x-2<2
0 < x < 4

and from there on i do a restriction for the x+1 so it cant be divided by 0 right and after that i just kinda get lost... i think i have to find when the top one becomes 0 too but its not exact and i would have to use -b+-sqrt() equation thing soo any help on this one really helps

 

so if that is that and i have a restriction on the lower value i can multiply with out reversing the sign right?? soo
x^2 + 3x + 1 = 7(x+1)
X^2 - 4x -6 = 0

and then use -b formula thing
a = 1, b = -4, c = -6

(4+-sqrt(4^2 - 4(1)(-6)))/2
(4+- sqrt (40))/2
??? for some reason it sound like im doing something wrong

 

wait ... where did that

[tex]2\pm\sqrt{10}[/tex]

edit: i found i see where you got it but still... im lost..
the original range for x was ]0,4[...
and one more thing im seeing here that there is a table in which you put this values to see if they are positive or negative once evaluated...... so maybe i could use that???