Graph on the number line :
-|x| - 2 > -5; D = [ integers ]

OK so for starters you need to get the absolute value alone with out any thing on its side

so...

-|x| - 2 > -5

add a 2 to both sides

-|x| > -3

multiply through with a -1 (dont forget that the > switches to a < when you multiply or divided with a negative, vice versa)

|x| < 3
so x is either equal to a negative or a positive so you have two equations to set up past this point.

x < 3

or

x > -3

3 and -3 are your critical values you need to to put those on a number line and test a point in each region.

so pick a point between -3 and 3
lets say 0 and put it in the original equation
-|0| -2 > -5
-2 > -5 True

and a number between -infinity and -3
say -4 plug that into your original equation
-|-4| -2 > -5
-4 -2 > -5
-6 > -5 False

and a number between 3 and infinity
say 4 and plug that into you equation
-|4| -2 > -5
-4 -2 > -5
-6 > -5 False

so that being said you know that x can be any value between -3 and 3 but is not: x<-3 or x>3 so -3<x<3 would be your answer and graph it however you were taught.

Sorry if I confused you more..