Solve for x. −x/2< −1 enter the solution to the inequality in the box.

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