Analysis: This question examines the problem that chickens and rabbits are in the same cage, which can be solved by a one-dimensional equation. According to the meaning of the question, suppose that she made X wrong questions, and the right answer was10-X. According to the equivalence relation, the score of the right answer was equal+the score deducted from the wrong question was 52, and then the equation was listed for solution.

The problem solving process is as follows:

Solution: suppose she did the wrong X.

( 10-x)× 10+(-2x)=52

100- 10x-2x=52

100- 12x=52

Transposition 12x= 100-52

12x=48

x=4

She made four mistakes.

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.