One-dimensional linear inequality refers to a linear term and a constant term with unknown quantity, and the inequality separator is "",which can represent an inequality with interval solution set.
1, the basic concept of inequality
One-dimensional linear inequality refers to an inequality that only contains a single unknown quantity, including linear terms and constant terms of unknown elements. For the linear inequality of one variable, we can use the inequality sign ""to indicate that the solution set is a continuous interval, and all real numbers above or below the interval can be used as the solutions of this inequality.
2. Solution method
When solving one-dimensional linear inequality, it is usually necessary to transform the unknown shift term into the general form "ax+b >；; 0 "or" ax+b "
3. Preventive measures
When solving one-dimensional linear inequalities, we need to pay attention to the following points:
(1) Pay attention to the positive and negative coefficients when the deformation is absolute;
(2) When converting inequalities into standard forms, pay attention to the situation that the denominator is zero;
(3) When the variable is omitted from the analytical formula, it should be declared in the process of solving.
4. General steps
(1) denominator: According to the properties 2 and 3 of inequality, multiply both sides of inequality by the least common multiple of each denominator at the same time to get a small equation with integral coefficient.
(2) Remove brackets: According to the law of brackets, when there is a negative sign outside brackets, special attention should be paid to removing brackets and negative signs and changing the symbols of items in brackets.
(3) Shifting terms: According to the basic properties of inequality 1, generally, the terms containing unknowns are moved to the left of inequality, and the constant terms are moved to the right of inequality.
(4) Merge similar items.
(5) Turn the coefficient of the unknown into 1: According to the basic properties of inequality 2 or 3, pay special attention to that when the coefficient is turned into 1, the coefficient is negative, and don't change the direction without an equal sign.
(6) Sometimes it is necessary to express the solution set of inequality on the number axis.
5. Conclusion
The solution of one-dimensional linear inequality is relatively simple, but some small details need attention. When solving, it is necessary to choose the appropriate solution and method according to the actual situation, and at the same time, it is necessary to pay special attention to the special properties of inequality, such as absolute value. Inequality equation is a very important chapter in high school mathematics and plays a very important role in solving various mathematical problems.