To find the solution set of inequalities, we can first express the solution set of each inequality on the number axis and observe the common parts. Then remove brackets, move terms, merge similar terms, and make the coefficient temporary. Note whether to divide by a positive number or a negative number.
All solutions of an inequality with unknowns constitute the solution set of this inequality, that is, all solutions satisfying this inequality constitute the solution set.
A set of solutions whose elements are equations or inequalities is called a solution set. For example, the solution set of x 2- 1 ≥ 0 is X={x|x≤- 1, x ≥1}; The solution set of x 2- 1 ≤ 0 is x = {x|-1≤ x ≤1}; The solution set of x 2-3x-4 = 0 is X={- 1, 4}.
The set a consisting of all elements x with the property P(x) is marked as A={x|P(x)} or {x: p (x)}. Where P{x} represents the characteristic attribute of the elements in the set. The so-called characteristic property of set elements means that every element of a set has a property, and none of the elements that do not belong to this set have this property.
All solutions of an inequality with unknowns constitute the solution set of this inequality, that is, all solutions satisfying this inequality constitute the solution set. Inequality is a formula that connects two analytical formulas with an inequality symbol.
The solution set determined by inequality is as follows: if it is greater than two values, it is greater than the larger one. If it is less than two values, it is less than the smaller value (the same as the smaller value). Greater than big, less than small, no solution (big and small are not desirable).
Differences and connections between solutions and solution sets of inequalities;
1, the solution of inequality means that the unknown quantity satisfies one value of this inequality, and the solution set of inequality means that the unknown quantity satisfies all values of this inequality. The solution of inequality is one of the solution sets of inequality, the relationship between inclusion and inclusion, and the relationship between part and whole.
2. The solution set of inequality must meet two conditions: first, all the numbers in the solution set are solutions of inequality; Second, the number outside the solution set is not the solution of inequality. This is also similar to the sufficiency and necessity of conditions.
3. When we are doing a topic with complicated options, if we can't clear our minds, we can find some examples and try them in the options. This method is also a special value method in mathematics, which belongs to incomplete proof and is of great significance to solving problems and innovating associations.
4. Mathematical methods and ideas.
For the case of more letters in the example, it needs to be divided into two levels: principal component and parameter, and then it is done in two steps. Firstly, an equation or inequality with parameters is established according to the principal component, and then it is clear to solve it according to the parameters. At the same time, principal components and parameters are relative and can be treated from different angles. Method of substitution is an important mathematical method to solve parameter problems.