Outside, with a Fraction

|x + 1|/2 >= 1: the bars are divided by 2, so multiply both sides by 2 first, |x + 1| >= 2. A "greater than": two cases.

x + 1 >= 2

x >= 1

or

x + 1 <= -2

x <= -3

The solution is x <= -3 or x >= 1.

Isolate, split, solve each case, keep the "or". The fraction outside the bars is the only extra layer, and it comes off first like any other.