What If I settle It, yet "x" Is top top The Right?
No matter, just swap sides, but reverse the sign so it still "points at" the correct value!
Note: "x" can be on the right, yet people usually favor to watch it ~ above the left hand side.
You are watching: If you multiply by a negative in an inequality does the sign change
Multiplying or separating by a Value
Another thing we carry out is multiply or divide both sides by a value (just together in Algebra - Multiplying).
But we have to be a bit more careful (as you will certainly see).
Everything is well if we desire to multiply or division by a hopeful number:
When we multiply or division by a negative number we must reverse the inequality.
Well, just look in ~ the number line!
For example, indigenous 3 come 7 is an increase, however from −3 to −7 is a decrease.
See how the inequality sign reverses (from ) ?
Multiplying or separating by Variables
Here is another (tricky!) example:
Example: bx 3
But us don"t understand if b is hopeful or negative, therefore we can"t prize this one!
To help you understand, imagine replacing b through 1 or −1 in the example of bx if b is 1, climate the prize is x however if b is −1, then us are solving −x 3
The answer could be x 3 and we can"t choose due to the fact that we don"t understand b.
See more: What Is The Difference Between Clams And Oysters And Clams (With Table)
Do not shot dividing by a variable to deal with an inequality (unless you know the variable is constantly positive, or constantly negative).
A bigger Example
Example: x−32 x−32 ×2 6−2x3 > x > −3
And that is the solution!
But to be neat the is better to have actually the smaller sized number ~ above the left, larger on the right. So let united state swap them end (and make sure the inequalities allude correctly):
−3 x 6