First, the image method.
Take the unknowns in inequality as variables, draw an image of its plane rectangular coordinate system, and then specify which part of the image satisfies the inequality condition according to the symbol of inequality. For example, for the linear inequality ax+b >；; 0, draw an image with y=ax+b, and mark the upper part of it as an area satisfying the inequality, which is the inequality ax+b >；; Solution set for 0.
Second, algebraic method.
Through algebraic deformation of inequality, we can find its solution set. For example, for the linear inequality ax+b >；; 0, which can be converted into X>-B/A. For quadratic inequality AX 2+BX+C >; 0, we can first find its roots x 1 and x2, then divide the real number axis into three segments, and judge the positive and negative of each segment, thus obtaining the solution set of inequality.
It should be noted that the following principles should be followed when solving inequalities:
1, you cannot multiply or divide a negative number on both sides of the inequality at the same time, otherwise the direction of the inequality needs to be reversed.
2. You can't add or subtract formulas with unknowns on both sides of the inequality unless the formulas are greater than or less than zero in all cases.
3. When solving absolute inequality, we need to discuss the absolute value of inequality separately.
4. When there are many unknowns in the inequality, some unknowns can be eliminated by elimination and addition and subtraction, and the inequality can be transformed into a form containing only one unknown, and then solved according to the above methods.
To sum up, there are two common methods to solve inequalities: mirror method and algebraic method, and the appropriate solution needs to be selected according to the specific inequality types. When solving, we need to follow certain principles and laws to avoid wrong results.
In addition to the above methods, some complex inequalities can also be solved by the following methods:
1, collocation method: turn the inequality into a complete square, and then discuss the sign of the root.
2. Parameter method: By introducing a parameter, the inequality is transformed into quadratic inequality or hyperbolic inequality about this parameter.
3. Function method: turn inequality into a non-negative problem of function, and then discuss it according to the nature of function.
4. piecewise function method: divide the function in inequality into several parts and discuss it according to the domain and monotonicity of each function segment.
It should be noted that although the above methods can solve some complex inequalities, they need to be used flexibly in practical application in combination with specific problems.