Analysis: This question examines the linear equation of one variable. According to the meaning of the question, let Xiao Ming answer wrong question X and answer correctly (12-x), and let Li Li answer wrong question X and answer correctly (10-x). According to the known conditions, find out the equivalence relation and list the equations to solve.
The problem solving process is as follows:
Solution:
Xiao Ming: Suppose Xiao Ming answers question X incorrectly, which is derived from the meaning of the question.
10×( 10-x)-4x=72
100- 10x-4x=72
Transposition 10x+4x = 100-72
14x=28
x=2
Lili: Suppose Lili answers question X wrong.
10×( 12-x)-4x=50
120- 10x-4x=50
Transposition 10x+4x = 120-50
14x=70
x=5
Xiaoming got two wrong questions and Li Li got five wrong questions.
The method of finding the root of linear equation with one variable;
conventional process
There are five steps to solve a linear equation with one variable, namely, denominating, removing brackets, shifting terms, merging similar terms, and the transformation coefficient is 1. All steps are carried out according to the properties of algebraic expressions and equations.
In one-dimensional linear equations, the denominator removal step is usually multiplied by the least common multiple of each denominator. If the denominator is a fraction, it can be replaced by the other part of the item multiplied by the reciprocal of the fraction on the denominator.
If there is an irrational number on the denominator, it is necessary to make the denominator rational first.
One-dimensional linear equation can solve most engineering problems, travel problems, distribution problems, profit and loss problem, integral table problems, telephone billing problems and digital problems. If only arithmetic is used, some problems may be extremely complicated and difficult to understand. The establishment of linear equation model will be able to find the equivalence relationship from practical problems and abstract it into a mathematical problem that can be solved by linear equations.
For example, it may not be possible to start with algebraic expressions for the Diophantine problem, but finding "age" as an equivalent relationship through a linear equation will simplify the problem.