Inequality simpmodulus

I want to determine everything $ z in mathbb C $ for which
begin {equation} tag {1} label {1}
left | frac {2 + z} {2-z} right | le 1.
end {equation}

In fact, I already know that eqref {1} is equivalent to $ Re (z) le0 $ (where $ Re (z) $ denotes the real part of $ z $.) However, I do not know how to get to this result and I do not know how to get results for more general inequalities, such as $ dots le c $ by some constant instead of $ 1 $.