Nonlinear Inequalities and unions?

if you can help me with this, well, i'd be very happy.

x(2x + 7) ≥ 0

first off, i understand most of the problem, i just don't know how to tell when an inequality has a union, if i need to use or in the answer, etc

my intervals:

-∞, -7/2

-7/2, 0

0, ∞

sign of x -, -, +

sign of 2x+7 -, +, +

sign of x(2x+7) +, -, +

in the back of the book it shows {x|x ≤ -7/2 or 0 ≤ x}

Interval: ( -∞, -7/2] U [0, ∞)

how the heck am i supposed to know when to use a union?

i have an alternative problem that i can solve on my own to show what i mean...a problem without a union...:

(x+2) (x-3) < 0

answer = {x|-2 < x < 3}. Interval: (-2, 3)

so the real question is, why does one problem have a union, and the other one does not???