# Thread: Solving inequalities??

1. ## Solving inequalities??

This is another one I am having trouble with:

-2x - 5 >= -7

Do I have to change the direction of the inequality?

2. ## To Solve an Inequality

-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.

Math Guru

3. yes. the rule is always when dividing (or multiplying????) by a negative, the inequality must be switched right?

4. ## Multiplying or Dividing

Yes that is correct. The inequality is switched when multplying or dividing by a negative number.

Math Guru