1, Algebraic Method: For some simple inequalities, we can directly solve them by algebraic operation. Such as inequality x+2 >; 3.x > can be obtained directly by algebraic operations such as shifting terms and merging similar terms. 1, so the solution set of this inequality is x | x >；; 1。

2. Mirror image method: Some inequalities with real variables can be solved by drawing the mirror image of the function. Such as the inequality x 2+y 2 >; 1 can be regarded as the part of the image where the function f (x) = x 2+y 2 is above the x axis. By drawing the image of the function, we can observe that when X takes any real number, the function values are all greater than 1, so the solution set of this inequality is all real numbers.

3. Logical method: Some logical inequalities can be solved by logical reasoning. Such as the inequality x2-4x+4 >; 0 can be regarded as the part of the image where the function f (x) = x 2-4x+4 is above the x axis. By observing the image of the function, we can find that the image of the function is always above the X axis, so the solution set of the inequality is all real numbers.

4. Trigonometric method: Some trigonometric inequalities can be solved by using the properties of trigonometric functions. Such as inequality sin (x) >; 0, which can be regarded as the image part of the function f(x)=sin(x) above the y-axis. By observing the image of the function, we can find that the image of the function has parts above the Y axis and near the origin, so the solution set of this inequality is x2kπ.

Characteristics of inequality:

1, extensiveness: inequality is widely used in mathematics, which can describe the monotonicity of functions, compare sizes, solve practical problems and so on. Therefore, inequality is a very basic and important mathematical tool.

2. Relativity: the solution set of inequality is relative to a specific inequality, and different inequalities have different solution sets. Therefore, when solving the inequality solution set, it is necessary to analyze and calculate specific problems.

3. transitivity: inequality is transitive, that is, if A >；; B, b>c, then a> C. This property is very useful in solving some complex inequality problems and can simplify the calculation process.

4. Boundedness: The solution set of inequality is bounded, that is, every value in the solution set has an upper bound and a lower bound. This property is very useful in solving some practical problems, for example, in optimization problems, the optimal solution can be obtained by limiting the range of variables.