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
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When us multiply or division by a an adverse number we must reverse the inequality.

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.

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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−32 x−32 ×2 6−2x3 > 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)