Finish independently (do your homework yourself)

Any mistakes must be corrected (mistakes should be corrected in time)

Usually serious

The exam is easy (needless to say, you know)

The teacher answered why we use equations to solve problems like this:

Equation can transform reverse thinking into positive thinking, which is beneficial to the understanding of the problem. There is a paper written by my classmates and me. Let me show you. I hope it helps.

One-dimensional linear equation

One-dimensional linear equations are widely used in our lives. One-dimensional linear equation refers to an equation with only one unknown number 1. Through the calculation of one-dimensional linear equation, students' operation and reasoning ability can be improved. And correctly identify the linear equation of one variable, which is helpful to identify other integral equations. Therefore, we should first clarify the concepts of "number of elements" and "degree" in the whole equation. The unknowns in the equation are called elements, and the number of elements in the equation refers to the number of unknowns in the equation. An equation has several different unknowns, which is called multivariate equation. The degree of the equation refers to the highest degree of the term with unknown number in the equation. The degree of an equation is called the degree equation.

(1) contains only one unknown number.

(2) The number of unknowns is 1.

(3) The unknown coefficient is not 0. = 3x+2y2 is a quadratic equation in form, but after simplification, the highest number of unknowns is 1, which only contains one unknown, so it is actually a linear equation with one variable. Therefore, only after the integral equation is simplified to the simplest form can it be correctly judged as a polynomial equation.

(4) The denominator of the whole equation is unknown, that is, both sides of the equation are algebraic expressions. Unlike judging how many elements an integral equation has, judging whether it is an integral equation cannot be simplified first. For example, the equation X+= 2+ is not an integral equation because its denominator contains the unknown X. It should be noted that if the above equation is simplified to x=2, then the judgment is wrong. When it comes to the number of equations, it refers to the integral equation, that is, both sides of the equation are algebraic expressions. One-dimensional linear equation is the equation with the least number of elements and the lowest degree in the whole equation.

We express the one-dimensional linear equation as a general form.

ax=b (a≠0)，

Where x represents an unknown number and a and b are known numbers in letters. For the unknown X, the letter A is the coefficient of X, which is called the letter coefficient, and the letter B is a constant term.

If the coefficients in a unitary linear equation are expressed by letters, then this equation is called a unitary letter coefficient equation.

Quadratic equation.

In equations with letter coefficients, we generally use a, b and c to represent known numbers, and x, y and z to represent unknown numbers.

The solution of linear equation with letter coefficient is the same as that of linear equation with number coefficient. According to this solution

The steps of one-dimensional linear equation are finally transformed into the form of ax=b(a≠0). It should be noted here that when multiplying or dividing two sides of the equation with a formula containing letters, the value of this formula cannot be equal to zero. For example, (m-2) x = 3, it must be when m-2 ≠ 0, that is, when m-2 ≠ 0 2.

By understanding the linear equation of one variable, we can know its important role in mathematical calculation. One-dimensional linear equations can not only be applied to algebra and geometry, but also solve some problems in life. The application of linear equation of one variable can help us to solve many problems more concisely and clearly. For example, we need to use a linear equation when calculating the distance between two places and the speed of two cars.