Solve Inequality Math

Introduction of solve inequality math:
In mathematics, an inequality is a statement about the relative size or order of two objects or about whether they are the same or not (See also equality).

The notation a < b means that a is less than b.

The notation a > b means that a is greater than b.

The notation a ≠ b means that a is not equal to b, but does not say that one is greater than the other one.

Source: Wikipedia


Properties of solve inequality math:


Trichotomy property for solve inequality math:

For any real number, a and b, exactly one of the following statements is true:

pq

The trichotomy property indicates that exactly one of the following statements is true about any two real numbers. Either

The first is less than the second
The first is equal to the second, or
The first is greater than the second one.


Transitive property for solve inequality math:

If p,q and s are real numbers with p
If p,q and s are real numbers with a>b and b>c, then a>c.

The first part of the transitive property indicates that:

If a first number is less than a second number and the second is less than a third, then the first number is less than the third.

The second part is similar, with the word “is greater than” substituted for “is less than”.

Addition property for solve inequality math:

Any real number can be added to (or subtracted from) mutually sides of an inequality to produce another inequality with the same direction.

To solve the addition property, we add 6 to both sides of the inequality 2<6 br="" get="" to="">
6+2<6 br="">
8<12 br="">
We note that the < sign is unmovable (has the similar direction).

Subtracting 6 from both sides of 36<46 br="" change="" direction="" does="" either.="" inequality="" not="" of="" the="">
36-6<46-6 br="">
30<40 br="">
Multiplication property for solve inequality math:

If both sides of an inequality are multiple (or divided) by a positive number, another inequality results wilt the same direction as the original inequality.

To solve the multiplication property, we multiply both sides of the inequality -3<6 3="" br="" by="" get="" to="">
3(3)<3 br="">
9<18 br="">
The < symbol is unaffected.

Dividing property for solve inequality math:

Dividing both sides by 4 does not change the direction of the inequality either.

`-8/4`<`12/4`

-2<3 p="">
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Example for solve inequality math:


To solve the inequality -12≤6a+3<7 br="">
Solution:

This inequality means that 6x+3 is between -12 and 7. We can solve it by isolating a between the inequality symbols.

-12≤6a+3<7 br="">
-15≤6a<4 br="">
-15≤6a<4 br="">
The solution set is {a|-15≤6a<4 br="" in="" interval="" notation="" or="">