Method:

Unknown number of examination questions (direct setting and indirect setting); Find the equivalence relation and make equations; Solve the equation; Check that the solution of the equation should meet the actual requirements; Answer, answer.

Skills:

The key to solving practical problems is to examine the questions. When examining questions, we should grasp the key words that express the relationship between quantity and quantity, and correctly find out the equation of equivalent relationship.

Common methods for finding equivalence relations

1, according to the basic formula (trip problem, sales problem)

Such as: speed × time = distance; Work efficiency × working time = total workload; Price = list price × discount; Profit-selling price-purchase price-purchase price × profit rate, etc.

2. (Engineering problem) The sum of each component is equal to the total.

For example, many people finish a job, and the sum of all people's workload is equal to the total amount of work.

3. (Sum and Difference Doubling Problem) Grasp the "key words" in the problem and find the equivalence relation.

For example, the key words of multiplication with difference are sum, difference, "greater than (less than)", "greater than several times" and "less than several times" and so on.

4. Grasp the problem of "expressing the same quantity in different ways" and find the equivalence relationship.

Extended data:

One-dimensional linear equation refers to an equation with only one unknown number, the highest order of which is 1, and both sides are algebraic expressions. A linear equation with one variable has only one root. 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.

One-dimensional linear equations were first seen in ancient Egypt around 1600 BC. Mathematician Hua La Zi Mi put forward the idea of "merging terms" and "shifting terms" in his book "Eliminating Yuan and Reducing Yuan". In16th century, after the mathematician David founded symbolic algebra, he put forward the propositions of shifting terms and division of the same equation. 1859, mathematician Li officially translated this kind of equations into linear equations.

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. 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.