One-dimensional linear equation is the initial content of the equation and the basis of junior high school mathematics. When learning, we should list the equations according to the quantitative relationship in specific problems, and make it clear that the basic idea of solving the equations is transformation, and the basis of transformation is the basic properties of the equations. In order to solve the linear equation correctly, we must master the general steps of solving the linear equation and master it flexibly according to the characteristics of the topic.
The complete solution of knowledge:
1, a linear equation with one variable.
Equation (1): An equation with an unknown number is called an equation.
(2) One-dimensional linear equation: An equation with only one unknown number (element) and an unknown degree of 1 is called a one-dimensional linear equation.
2, to judge an equation is a linear equation, need to pay attention to the following three points:
(1) A linear equation with one variable is an equation with only one unknown number.
(2) The exponent of the unknown quantity of the linear equation with one variable is 1, and the coefficient of the unknown quantity is not 0.
(3) If there is a fractional form in the equation, the denominator of the fraction cannot contain unknowns.
3, the solution of the equation and the solution of the equation.
Solution of the equation: the value of the unknown quantity that can make the left and right sides of the equation equal is called the solution of the equation, and the solution of the equation containing only one unknown quantity can also be called the root of the equation.
Solving equations: The process of solving equations is called solving equations.
Basic properties of the equation:
Property 1: Add (or subtract) the same number (or formula) on both sides of the equation, and the results are still equal.
Expressed by the formula: if a=b, then a c = b c
Property 2: Multiplied by the same number on both sides of the equation, or divided by the same number that is not 0, the result is still equal.
Expressed by the formula: if a=b, ac=bc, if a=b(c≠0), A/C = B/C.
note:
(1) When using the properties of equation 1 to deform the equation, both sides must be added and subtracted at the same time, and one side cannot be omitted without deformation.
(2) When transforming the equation with the property 2 of the equation, it should be noted that both sides cannot be divisible by 0, because 0 cannot be used as a divisor.
(3) The equation is also transitive, that is, if a = b and b = c, then a = c；; Interchangeability, that is, if a=b, then b = a.
There are two main points to grasp when using the properties of the equation: first, the two sides of the equation refer to the whole and the terms on both sides; Second, the changes on both sides are the same, that is, the changes on both sides are the same. Note that no matter which property of the equation is applied, both sides of the equation will have the same change, otherwise the equation will not hold. The nature of equality is the basis of equality deformation, equation deformation and equation solution.