What If I resolve It, yet "x" Is on The Right?
No matter, just swap sides, yet reverse the sign so it still "points at" the correct value!
Note: "x" can be on the right, but people usually like to watch it on the left hand side.
You are watching: When do you change the inequality sign
Multiplying or splitting by a Value
Another thing we perform is main point or divide both sides by a worth (just together in Algebra - Multiplying).
But we must be a bit more careful (as you will see).
Everything is fine if we want to main point or divide by a hopeful number:
When we multiply or division by a an unfavorable number we must reverse the inequality.
Well, just look at the number line!
For example, indigenous 3 to 7 is an increase, but from −3 to −7 is a decrease.
See how the inequality sign reverses (from ) ?
Multiplying or dividing by Variables
Here is another (tricky!) example:
Example: bx 3
But us don"t recognize if b is confident or negative, therefore we can"t prize this one!
To aid you understand, imagine replacing b with 1 or −1 in the example of bx if b is 1, then the prize is x but if b is −1, then us are resolving −x 3
The answer can be x 3 and also we can"t choose due to the fact that we don"t understand b.
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Do not shot dividing through a variable to deal with an inequality (unless you recognize the variable is constantly positive, or constantly negative).
A larger Example
Example: x−32 x−32 ×2 6−2x3 > x > −3
And the is the solution!
But to be neat the is better to have actually the smaller sized number ~ above the left, larger on the right. For this reason let us swap them over (and make sure the inequalities suggest correctly):
−3 x 6