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A inequality is a mathematical expression which is characterized by signs of inequality, being an algebraic expression as a result gives us a whole in which the independent variable can take any value that set in compliance with this inequality, this set is known as interval

In mathematics a inequality is an expression referring to the size or relative order of two objects (see also equation). The notation a \u0026lt;b means to is less than b and notation a> b means to is greater than b . These relationships are known by the name of strict inequalities , contrasting with a ≤ b ( to is less than or equal to b) and a ≥ b ( to is greater than or equal to b ).

comparative If the sign of the inequality is the same for any value taken by variables that is defined, then discuss an inequality "absolute" or "unconditional" ( see entity). If, however, is the same except for certain values \u200b\u200bof the variables, but is reversed or destroyed if they are changed, will be an inequality "conditional." The comparison sign of an inequality does not change if both members are added or subtracted the same number, or if they are multiplied or divided by a positive number, however, is reversed if both members are multiplied or divided by a number negative .

notation a>> b means to "is much greater than" b . The significance of this can vary referring to a difference between the two indefinitely. Used in equations in which a much higher value will cause the resolution of the equation throw a light a certain result.

PROPERTIES

The inequalities are governed by the following properties:

Trichotomy

The trichotomy property dictates that:

For any two real numbers , to and b , only meet one of the following statements:
- $\, a < b$
$\, a = b$
- $\, a > b$

Symmetry

Relationships in inequalities can be reversed, meaning that that:

For two real numbers to and b :
- If $\, a > b$ then $\, b < a$
- If $\, a < b$ then $\, b > a$

Transitive

For any real numbers, to , b and c :
- If $\, a > b$ $\, b > c$ and then $\, a > c$
- If $\, a < b$ $\, b < c$ and then $\, a < c$
- If $\, a > b$ $\, b = c$ and then $\, a > c$

Addition and subtraction

related properties of addition and susttracción

For any real numbers, to , b and c :
- If $\, a > b$ , then and $\, a + c > b + c$ $\, a - c > b - c$
- $\, a < b$ If, then $\, a + c < b + c$ and $\, a - c < b - c$

Multiplication and division

properties for multiplication and division

For any real numbers, to , b and c :
- If $\, c$ is positive and then $\, a > b$ $\, a \times c > b \times c$ and $\, \frac{a}{c} > \frac{b}{c}$
- If $\, c$ is positive and then $\, a < b$ $\, a \times c < b \times c$ and $\, \frac{a}{c} < \frac{b}{c}$
- If $\, c$ is negative and then $\, a > b$ $\, a \times c < b \times c$ and $\, \frac{a}{c} < \frac{b}{c}$
- If $\, c$ is negative and $\, a < b$ $\, a \times c > b \times c$ and then $\, \frac{a}{c} > \frac{b}{c}$

Note:

If both terms of an inequality are multiplied or divided by the same negative expression, the symbol of inequality turns.

inequalities TYPES

INECUACIÓN	TYPE
2x-3> x-5	1 st degree, 1 incóg.
x-3 ≥ y	1 st degree, 2 incóg
x ² -5x ≤ 4	2 º grade; incóg 1.
xy-3> 0	Grade 2, 2 unknowns.

inequalities SECOND LEVEL

Resolved as a quadratic equation and study the signs that we get to solutions.

x 2 - 5x + 6> 0

The solutions of the equation x 2 - 5x + 6 = 0 are x = 3 x = 2. Therefore 2 x - 5x + 6 = (x - 2) (x - 3).

We have to study signs when x takes values \u200b\u200bfrom - ¥ to 2, from 2 to 3 and from 3 to ¥.

x - 2 is negative for values \u200b\u200bbetween - ¥ and 2.

x - 2 is positive for values \u200b\u200bbetween 2 and 3.

x - 2 is positive for values \u200b\u200bbetween 3 and ¥.

x - 3 is negative for values \u200b\u200bbetween - ¥ and 2.

x - 3 is negative for values \u200b\u200bbetween 2 and 3.

x - 3 is positive for values \u200b\u200bbetween 3 and ¥.

Therefore, multiplying the signs in the same intervals:

x 2-5x + 6 is positive for values \u200b\u200bbetween - ¥ and 2.

x 2 - 5x + 6 is negative for values \u200b\u200bbetween 2 and 3.

x 2 - 5x + 6 is positive for values \u200b\u200bbetween 3 and ¥.

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Thursday, December 3, 2009