Remark
You have to be awfully careful with this inequality. If can cause you all kinds of grief.
The easiest way to do this is to begin by dividing by - 1. What that does is turn the inequality
from (-x/2) < - 1 to
x /2 > 1
The rule is when you divide by a negative, that turns the < sign to > or the other way around ie > to <. You could actually show that happening.
Start with your given
-(x / 2) < - 1 Add 1 to both sides.
-(x / 2) + 1 < - 1 + 1 The 1 and - 1 cancel on the right.
-(x/2) + 1 < 0 Add x/2 to both sides
-(x/2) + x/2 + 1 < x/2 Add the like terms on the left.
1 < x/2 Which is exactly what we predicted would happen
Multiply by 2
2*1 < (x/2) * 2
2 < x