## What If I deal with It, however "x" Is on The Right?

No matter, simply swap sides, however **reverse the sign** so it still "points at" the exactly value!

Note: "x" **can** it is in on the right, yet people usually favor to watch it top top the left hand side.

You are watching: If you multiply an inequality by a negative number

## Multiplying or dividing by a Value

Another point we execute is multiply or division both political parties by a value (just as in Algebra - Multiplying).

But we need to be a bit an ext careful (as you will certainly see).

** positive Values**

**Everything is good if we want to multiply or divide by a optimistic number**:

### Example: 3y When us multiply or division by a an adverse number ** we must reverse** the inequality. ** **

**Why?**

**Why?**

Well, just look at the number line!

For example, from 3 to 7 is **an increase**, ** yet from −3 come −7 is a decrease. **

See just how the inequality authorize reverses (from ) ?

## Multiplying or splitting by Variables

Here is an additional (tricky!) example:

### Example: bx 3

But we don"t know if b is hopeful or negative, so **we can"t prize this one**!

To help you understand, imagine instead of **b** with **1 or −1** in the example of **bx if b is 1, then the answer is x yet if b is −1, then we are fixing −x 3 **

**The answer might be x 3 and we can"t choose since we don"t know b.**

See more: How To Circumscribe A Circle Around A Triangle S &Mdash; Krista King Math

**So:**

**Do not** shot dividing by a variable to settle an inequality (unless you know the variable is always positive, or always negative).

## A enlarge Example

### Example: *x−3***2** *x−3***2** **×2** *6−2x***3** > x > −3

And that is the solution!

But to it is in neat it is much better to have the smaller number ~ above the left, larger on the right. So let united state swap them over (and make certain the inequalities allude correctly):

−3 x 6

## Summary

Many basic inequalities can be solved by adding, subtracting, multiplying or separating both sides till you are left v the change on its own. But these points will adjust direction the the inequality: multiplying or dividing both sides by a**negative**number Swapping left and also right hand political parties Don"t multiply or division by a

**variable**(unless you know it is always positive or always negative)