Outside, with a Fraction

Take |x + 1|/2 >= 1. The absolute value is divided by 2, so multiply both sides by 2 first to get |x + 1| >= 2. The sign is "greater than or equal to", so there are two cases.

x + 1 >= 2

x >= 1

or

x + 1 <= -2

x <= -3

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

Get the bars alone, split into two cases, solve each case, and keep the word "or" between them. A fraction outside the bars is one more step to do. Remove it first, before the split, by multiplying both sides.