Solve absolute value inequality, use interval notations.

Question

|4+2x|-3>

I know the answer is x>2 or x<-6
But I'm unsure how to solve it.

Thanks

Answer 1

since |x| = x if x >= 0, and -x if x<0, either

(4+2x) - 3 > 5 or
-(4+2x) - 3 > 5

so either
4+2x-3 > 5
2x+1 > 5
2x > 4
x > 2

or

-4-2x-3 > 5
-2x - 7 > 5
-2x > 12
x < -6