-2x - 5 >= -7
The goal here is to get the variable x on one side of the inequality and all the rest on the other side.
The first thing we can do is add 5 to both sides which gives us
-2x >= -2
The next thing we can do is divide both sides by 2 which give us
-x >= -1
Now here is the tricky part, we multiply by -1, and yes we must change the direction of the inequality. The answer is:
x <= 1
Consider the following inequality
-3 <= 4 This equation is true but if you multiply by -1
3 <= -4 This equation is not true
3 >= -4 This one is correct
When multiplying by -1 we must change the direction of the inequality for the equation to remain true.