Help me solve this.

Test Preparation
1

If, |x+3|<3 and |2y+1|<2
then |x+y|< ??

2

The given inequalities are equivalent to

-3 < x+3 < 3 <–> -6 < x < 0
-2 < 2y+1 < 2 <–> -3/2 < y < 1/2

Then max(|x+y|) is achieved by setting x = -6 and y = -3/2, so we achieve an upper bound of -15/2 (not exactly, since x, y are strictly larger than -6, -3/2. More formally we say that sup(|x+y|) = 15/2).