What If I resolve It, yet "x" Is top top The Right?

No matter, just swap sides, yet reverse the sign so the still "points at" the correct value!


Note: "x" can be on the right, yet people usually favor to see it on the left hand side.

You are watching: When does the inequality sign flip

Multiplying or splitting by a Value

Another thing we do is main point or divide both sides by a worth (just together in Algebra - Multiplying).

But we should be a bit much more careful (as you will certainly see).

confident Values

Everything is good if we desire to multiply or divide by a hopeful number:


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

Why?

Well, just look in ~ the number line!

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

*

See exactly how the inequality sign reverses (from ) ?


Multiplying or splitting by Variables

Here is one more (tricky!) example:


Example: bx 3

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


To aid you understand, imagine replacing b with 1 or −1 in the instance of bx if b is 1, climate the price is x however if b is −1, then us are resolving −x 3

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

See more: What Language Is Windows Written In, Question: What Language Is Windows 10 Written In

So:

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


A bigger Example


Example: x−32 x−32 ×2 6−2x3 > x > −3

And the is the solution!

But to be neat the is far better to have actually the smaller number top top the left, larger on the right. Therefore let us swap them end (and make certain the inequalities suggest correctly):

−3 x 6


Summary

Many straightforward inequalities can be addressed by adding, subtracting, multiplying or separating both sides till you space left v the variable on that own. However these things will readjust direction that the inequality: multiplying or splitting both sides by a negative number Swapping left and right hand sides Don"t main point or division by a variable (unless you know it is always positive or constantly negative)