On the question of simple equations, what is a simple equation?

Definition: The equation ax ( b=c (a,b,c is constant) is called a simple equation. 2.

The basic way to solve a simple equation is to add (or subtract) the same appropriate number on both sides of the equation at the same time; Multiply (or divide) both sides of the equation by the same appropriate number at the same time. Finally, the solution to the problem is found.

The key to judging whether it is "appropriate" to add (or subtract) and multiply (or divide) the same number on both sides of the equation is to see whether the first step of the operation can make only one side of the equation contain only the number with unknowns, and the second step can make only one side of the equation only have unknowns, that is, the result. The key is to select appropriate unknowns on the basis of figuring out the meaning and interrelationship of various quantities in the problem statement, and then express the sentences related to the quantity with algebraic formula, and finally use the equality relationship in the problem to list the equation and solve it.

Laying water diversion channels, all with 8 meters of pipes, super long four meters, all with 5 meters, then more than 3 meters, and than with 8 meters of water pipes more than 10, if mixed, with 21 just finished, then mixed use, how many of the two kinds of water pipes are used?

Column equations. X pipes are required to set up an 8-meter pipe. An 8-meter tube is required for mixing.

then there is 5=x+10

8x-1=5x+50

If x=17 is obtained, the total length of this section of the canal is 8x-4=132 meters.

Then another equation can be listed as:

8y+5(21-y)=132, resulting in y=9

This example lists two equations, you understand well.

1. Fill in the blank 1 The ( ) that makes the left and right sides of the equation equal ( ) is called the solution of the equation 2 The difference between the subtraction ( ) the subtraction, the divisor (

3 The process of finding ( ) is called solving an equation

4 Xiao Ming buys 5 fountain pens, each for yuan; Buy 4 pencils, each of which costs a total of ( ) yuan

2. Judgment 1 The formula containing unknowns is called an equation (2, both are equations (

The solution of 3 is 3 (

4 An equation is not necessarily an equation, an equation must be an equation (

3. Option 1 In the equation below, ( is the equation

The solution of 2 equation = is ( ).

3 is the solution of the following equation ( ).

4. Solve equations

5. Use the equation to represent the following quantitative relations, and find that the solution of the equation 1 is equal to 3 times.

2 7 divided equals.

The difference of 3 minus is.

Two. 1. Solve equations

2. Column equations and solve them

4 times of 1 minus 8, the difference is 10, find ?

2 6 times the product of a number plus 4 times, and is, find this number?

3. Calculate 1 When is equal to what number, the value of 4 6 is equal to 18?

2 When is equal to what number, the value of 4 6 is greater than 18?

Fourth, food for thought

If 3 8 16, then 4 3 (

It must be when you can't solve it with ordinary methods. Set the amount in its question to x. For example: What is the average monthly profit? Let's assume an average monthly profit of $x. There are also quantities on both sides of the equation to be equal.

Set the argument to x

Generally, it is the unit price and the like, look at the example questions, and you can find the rules from the example questions.

Set the unknowns in the question as letters, e.g. a, b, x, y, z, etc.

The equation ax (b) c (a, b, c is constant) is called the simple equation.

An equation is an equation that contains unknowns. It is an equation that expresses the equality relationship between two mathematical formulas (such as two numbers, functions, quantities, and operations), and the value of the unknown number that makes the equation hold is called the "solution" or the "root". The process of finding the solution of an equation is called "solving an equation."

The relationship between equations and equations.

An equation must be an equation, but an equation is not necessarily an equation.

Example: a+b=13 conforms to the equation with unknowns. This is an equation and an equation.

1+1=2，100×100=10000。These two equations conform to the equation, but there are no unknowns, so neither is the equation.

In the definition, the equation must be an equation, but the equation can have others, such as 1+1=2, 100 100=10000 as mentioned above, all of which are equations, and obviously the range of equations is a little larger.

Simple equations are the learning content of the fifth grade mathematics unit of the People's Education Edition, and the main contents that students need to master are: using letters to represent numbers, solving simple equations, and solving problems with column equations.

Through the study of the content of this unit, students will understand and master the method of using letters to represent numbers, understand the concept of equations, solve simple equations, and be able to solve some simple practical problems with equations.

Since the content of equations is not only a simple understanding of primary school, but also a key learning content in junior high school, Tongfan students should study the content of this unit carefully from now on, not only to have a solid grasp of the content of this unit, but also to lay a solid foundation for the study of equations in the future.

Solve simple equations:

1.The meaning of the equation, the equation containing the unknown is the equation, and the two conditions have unknowns and must have an equal sign.

2.All equations are equations, but equations don't have to be equations.

3.Property 1 of equality: If the same number is added or subtracted from both sides of the equation, the left and right sides are still equal.

4.Equation property 2: Multiply the same number on both sides of the equation, or divide by the same number that is not 0, and the left and right sides are still equal. The solution of an equation is the value of the unknown number that is found, and solving an equation refers to the process of finding the solution of an equation.

5.The method of testing: make the left side of the equation = the right side of the equation.

6.To solve the equation, add and subtract, subtract the numbers.

Subtract plus subtract, subtract who adds whom. Multiply and eliminate, divide by the number. Divide by multiplication and elimination, divide by who multiplies by whom.

These four formulas are all for the left side of the equation, and you should use these formulas flexibly to solve the equation. If the equation has parentheses, you must first eliminate the numbers outside the parentheses, and then eliminate the numbers inside.

7.Practical problems and equations: flexibly use the six-step process, the first step is to review the problem + solve the problem, the second step is to find the relation, the third step is to list the equation according to the relation, the fourth step is to solve the equation, the fifth step is to test whether the answer is correct, and the sixth step is to answer.

In the six steps, the examination of the question and the finding of the relationship are the most important, and the question must be reviewed and found to find the correct relationship. When finding two quantities, we should set the smaller quantity as x, and then obtain the other quantity represented by x through the quantity relation.

8.Encounter problems must be used flexibly Speed multiplied by time = total distance.

The simple equation solves the problem as follows:

Example 1: 3x+9=27.

Before learning equations, we were learning how to add, subtract, multiply, divide, and how to calculate the four mixed operations, that is, to give the numbers and the operation to find the result. But the equation is just the opposite, the equation is one part of the equation that gives the result and the equation, and finds the other part.

Therefore, the order of solving the equation is exactly the opposite of the order of operation, and the order of operation must be clarified before solving the equation, and the subsequent process of solving the equation will be a matter of course.

Going back to the equation above, on the left side of the equation is a mixture of multiplication and addition, and the order of operation is: multiplication (multiplication by 3) first, then addition (plus 9). So the order of solving the equation is exactly the opposite, first make 9 disappear and then 3 disappear.

How can I make 9 disappear?

Let's first look at what operations are applied on 9?

9", so both sides of the equation should be "-9" at the same time, so that 9 disappears.

3x+9-9=27-9。

3x=18。

The next task is to make 3 disappear, and 3x is 3 x, so both sides of the equation should be "3" at the same time, so that 3x becomes x.

3x÷3=18÷3。

x=6。Putting the whole process together, the complete process is as follows:

3x+9=27。

Solution: 3x+9-9=27-9.

3x=18。

3x÷3=18÷3。

x=6。How do you know if x=6 is the solution to an equation?

This requires a test, i.e., substituting x=6 into the equation to see if both sides of the equation are equal. The process of inspection is as follows:

Test: Left side of equation = 3x+9.

The right side of the equation.

So, x=6 is the solution of equation 3x+9=27.

Set x chickens and 11-x rabbits.

2x+4(11-x)=42

2x+44-4x=42

2x=2x=111-x=10

A: There is 1 chicken and 10 rabbits.

Solve the chicken x, then the rabbit (11-x), according to the meaning of the title:

2x+4(11-x)=42

x=111-1=10

A: 1 chicken, 10 rabbits. (Anhua Lao Jiu).

Suppose x chickens, then rabbits (11-x).

2x+4(11-x)=42

x=111-1=10

1 chicken and 10 rabbits.

Solution: Set the unit price of the flashlight x yuan.

Analysis: 4 flashlights for a total of 4x yuan.

Equivalence relationship: the total price of 4 flashlights - 7 = emergency light ** 4x - 7 = 49

4x=49+7

4x=56x=56÷4

x=14 A: The unit price of the flashlight is 14 yuan.

Solution: Set the unit price of the flashlight x yuan.

4x-7=49

4x=56x=14

Answer: The unit price of the flashlight is 14 yuan.

Definition. The equation ax (b) c (a, b, c is constant) is called the simple equation.

Basic approach. Add or subtract the same appropriate number on both sides of the equation at the same time; Multiply or divide both sides of the equation at the same time (0 divides.

Part 8 The Ninth Part of the Simple Equation.

outside) the same appropriate number. Finally, the solution to the problem is found.