(2) transitive a >b, b>c =>a>c.

(3) The same additivity a>b = & gta+c & gt；; b+c

(4) Multiplication (pay attention to symbols) a>b and c>0 = & gtac & gt

A>b and c < 0 = > AC < BC

(5)a & gt； B>0, n is an integer greater than 1 = >; The n power of a > the n power of b

A>b>0, n is an integer greater than 1 = >; A open n power > b open n power

(6) reciprocal a>b and AB>0 =>1/A <; 1/b？

A>b and ab < 0 = >1/a > 1/b

(7) a > can be added in the same direction; b，c & gtd = & gta+c & gt； b+d

(8) Forward multiplication in the same direction a>b>0, c>d>0 = & gtac & gt (abbreviation of base detonating)

Extended data:

Basic inequality is an inequality that is mainly used to find the maximum value of some functions and prove it. It means that the arithmetic mean of two positive real numbers is greater than or equal to their geometric mean.

Algebraic expression inequality:

Both sides of the algebraic expression inequality are algebraic expressions (that is, the unknown is not on the denominator).

One-dimensional linear inequality: an unknown (that is, one dimension) and the degree of the unknown is 1 (that is, once). For example 3-X >0

Similarly, binary linear inequality: an inequality that contains two unknowns (namely binary) and the number of unknowns is 1 (namely once).

The basic skill of scaling method is: when proving inequality, according to the structural characteristics of inequality to be proved, enlarge or shrink one side of inequality appropriately, and then prove inequality by using the transitivity of inequality.

"Scaling method" is also a very important method to prove inequality. It is skillful, flexible and widely used.

The common skills of scaling method are:

(1) Discard some positive terms (or negative terms).

(2) Change some items in the sum or product.

(3) Enlarge (or reduce) the numerator (or denominator) of the fraction, and so on.

Reciprocity of sum product

Maximum sum definite product

while

At a certain moment, and at that moment, the product sum of equal signs is the smallest.

When determined, take the equal sign again.

Solve the maximum value

Example: Find the minimum value of.

Solution: Starting from the basic inequality,

while

Immediate equal sign

A: At that time, it was the lowest.

References:

Baidu encyclopedia-inequality