Math Inequality

Introduction of math inequality:

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

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Properties of math inequality:


Trichotomy property for math inequality:

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 statement is true about any two real number. 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 math inequality:

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 math inequality:

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

To illustrate the addition property, we add 5 to both sides of the inequality 3<12 br="" get="" to="">
5+5<25 br="">
10<25 br="">
10<35 br="">
We note that the < sign is unmovable (has the same direction).

Subtracting 5 from both sides of 10<25 br="" change="" direction="" does="" either.="" inequality="" not="" of="" the="">
10-5<25-5 br="">
5<20 br="">
Multiplication property for math inequality:

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 illustrate the multiplication property, we multiply both sides of the inequality -4<8 2="" br="" by="" get="" to="">
2(-4)<2 br="">
-8<16 br="">
The < symbol is unaffected.

Dividing property for math inequality:

Dividing both sides by 2 does not change the direction of the inequality either.

`-2/2` <`6/2`

-1<2 br="">
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Example for math inequality:


Solve the inequality -5=5x+10<14 br="">
Solution:

This inequality means that 5x+10 is between -5 and 14. We can solve it by isolating x between the inequality symbols.

-5=5x+10<14 br="">
-15=5x<4 br="">
-15=5x<4 br="">
The solution set is {x|-15=5x<4 br="" in="" interval="" notation="" or="">