Subtract, Then Flip

5 - 2x >= 1: subtract 5 from both sides (no flip), which leaves -2x >= -4. Now the coefficient is -2, so dividing by it flips the sign:

x <= 2

Two steps, one of them negative, one flip. Check with 0: 5 - 0 = 5, and 5 is at least 1.

The flip happens at the step where you divide by the negative coefficient, not before. Subtracting 5 is an ordinary subtraction and leaves the sign alone. Keep the two ideas separate: "what am I undoing?" and "is this a negative multiply or divide?"