How to solve equations and how to move equations

The principle of shifting terms in equations is "If one term in the equation is moved from one side of the equal sign to the other, then the positive and negative properties of the term (plus or minus signs.

and then change" [i.e. from positive to negative or from negative to positive].

It's very abstract to say that, I'll give you an example and you'll get the idea:

Equation 2x-5=-3x+10

If you move -3x to the right of the equal sign to the left of the equal sign, then -3x will become +3x; Similarly, if you move -5 from the left to the right, then -5 will become +5

The original equation is shifted to obtain 2x+3x=10+5

5x=15x=3

However, why does the equation change its sign when the term is shifted?

In fact, the change of sign in the process of equation shift is not a theorem, but the experience that people summarize in the process of calculation.

Let's take 2x-5=-3x+10 as an example.

Solve equations. The whole process is actually the original definition of the equation that has been being applied, like this:

2x-5=-3x+10

2x-5)+5=(-3x+10)+5

2x=-3x+15

2x+3x=-3x+3x+15

5x=15x=3

See? In fact, this is the most scientific explanation for solving the equation shift term - that is, "both sides of the equation are adding numbers" (this is a bit popular, but it is definitely inaccurate, and it is only applicable to the scope of your current knowledge), but later people found that the calculation is faster according to the way of shifting terms, so based on these processes, the law of shifting terms was studied.

It's as simple as moving a term on one side of the equation to the other, which is called a shift.

For example. 3x+80=50After moving the item, we get 3x=50-80

After 80 is moved, it changes from a positive sign to a negative sign.

Summary. Hello dear, glad to answer for you; A: 1

When moving items, write the original items that do not move first, and then write the transferred items. 2.The basis for shifting terms is to add (or subtract) the same algebraic formula to both sides of the equation according to the fundamental properties of the equation.

3.The purpose of shifting the term is to obtain a one-dimensional equation of the shape ax=b. 4.

Items on the same side of the equal sign are swapped with each other, and the symbols of those terms do not change.

Hello dear, glad to answer for you; A: 1When moving items, write the original items that do not move on the left and right sides, and then write the items that are moved to the loose fiber.

2.The basis for shifting terms is to add (or subtract) the same first algebraic formula to both sides of the equation according to the fundamental properties of the equation. 3.

The purpose of shifting the term is to obtain a one-dimensional equation of the shape ax=b. 4.The terms on the same side of the equal sign are reversed, and the symbols of these terms do not change.

Hello dear, glad to answer for you; A: 1When moving items, write the original items that do not move on the left and right sides, and then write the items that are moved to the loose fiber.

2.The basis for shifting terms is to add (or subtract) the same first algebraic formula to both sides of the equation according to the fundamental properties of the equation. 3.

The purpose of shifting the term is to obtain a one-dimensional equation of the shape ax=b. 4.The terms on the same side of the equal sign are reversed, and the symbols of these terms do not change.

One-sixth x + 8 = three-quarter x-6

How do you calculate it? Hello dear, it's a pleasure to answer for your friend's call; Answer: x- (1/6 + 3/8) = 1x of 4 - 13/24 = 1x of 4 = 1/4 + 13x of 24 = 19/24

1) "Shift the item and change the number to miss the item, and the known unknown interval is equal sign".

When moving an term in the equation to the other side of the equal sign, pay attention to the change sign.

Don't omit a term in the process of moving terms, there are six terms on both sides of the equation after removing the parentheses, and there should be six terms after moving terms.

In general, move the items containing unknowns to the left of the equal sign and the items without unknowns to the right of the equal sign.

2) "The unknown is known to be separated, and the separation method is to shift, the addition and subtraction of the shift item should be changed, and the multiplication and division should be reversed." ”

A shift step in a one-dimensional equation.

1.Merge items of the same kind.

In the same way as in the addition and subtraction of integers, the process of merging the terms containing unknowns and the common terms on the same side of the equal sign into one term is called merging similar terms. The purpose of merging similar terms is to deform a form close to x=a, and further find the solution of the unary equation.

2.Transposition. Concept: Moving an term on one side of the equation to the other side is called a shift.

Basis: The basis for the shift is the nature of equation 1.

Objective: Usually move the terms containing unknowns to the left of the equal sign, and the terms without the sensitivities of the unknowns to the right of the equal sign, so that the equation is closer to the form of x=a.

3.The coefficient is reduced to 1

Concept: The process of converting an equation of the form ax=b(a≠0) into the form of x=b a, that is, finding the solution of the equation x=b a, is called the coefficient to 1.

Basis: Using the property of equation 2, the left and right sides of the equation are multiplied by the reciprocal of the unknown coefficient.

4.Remove the brackets.

In the process of solving an equation, the process of removing the parentheses contained in the equation is called deparentheses.

5.Go to the denominator.

Denominator removal method: Each item of a one-dimensional equation is multiplied by the least common multiple of all denominators, and the denominator in the equation becomes 1 according to the property of equation 2.

The basis for removing the denominator is the property of equation 2, i.e., multiplying the least common multiple of all denominators on both sides of the equation to make the coefficients of the equation an integer.

15000+x-x×8%/4≥4500

Multiply the good slag on both sides by 4 at the same time, and get:

60000+4x-x×8%≥18000

Add 60,000 on both sides at the same time, Texas stares: Friends quietly.

4x-x×8%≥78000

That is: both sides are divided at the same time to get:

x (yuan).

<> involves blind and shifting terms, general points, percentage calculations, and a few steps to remove the denominator from the source and return to the state.

15000+x-x×8%/4≥4500

Add 15,000 to both sides of the inequality spring at the same time:

Don't wait to guess the two sides of the eggplant style at the same time to divide: Zhaoyu.

x approx. etc.).

The inequality in the problem can be written as: —15000 + x —(8% 4) x 4500 Solution: First the constant term is moved to the right stool and the edge and simplified.

x—(8 100 1 Sakura-collapse 4) x 15000+4500x—(1 50) x 19500

1—1/50)x≥19500

49/50)x≥19500

x≥19500×50/49

Ridge coarse round x 975000 49.

The principle of shifting terms in the equation is "if you move one term in the equation from one side of the equal sign to the other side, then the positive and negative (plus and negative signs) of this item will also change" [the girder mill is from positive to negative or from negative to positive] This is very slag potato elephant, I will give you an example and you will understand: square roller bucket range 2x-5=-3x+10 If you move the -3x on the right side of the equal sign.

If you start with the relationship between the unknown and the unknown, that is, you can also use it, and the easier mistake in this point is not knowing how many numbers x represents, in fact, such a representation is telling you that it is 1x, then the latter is easier to understand, and now the previous problem is solved, and it will be later. This is a simple multiplication and division problem, but there is a mistake that can be forgotten when dividing by 16. In fact, we can see it as dividing 64 by Hanshan 100, so when dividing by 16, we must use 16 times 100 divided by 64, which is the literal expression of this question.

And the representation of the number is, ( x=(16 100) 64=25, which is the way of mathematicsIn fact, we found that the solution of such a mathematical problem is relatively easy, and there is basically no technical content in a simple mathematical calculation problem in time. There are many problems in solving equations like this in the exam papers, especially in the corresponding grades. This kind of equation solving problem is really to move the unknown to one side and our disparate value to the other, so that we can solve the unknown value we want.

But this knowledge point involves the problem of the shift of our learning.

If you move the direction, the plus or minus signs need to be changed, which is also the most common mistake that many people make when doing such a problem, that is, forgetting to move the direction and causing calculation errors. Shift refers to the left and right direction, for example, when the value is on the left, then when it is moved to the right, we need to change its symbol, from exactly to minus. This is a question that must be paid more attention to.

If you want to solve such equations and be able to get them right, then you need to practice more in your spare time.

A shift is an extension of the nature of the equation.

The rule of shifting terms is to cross the "bridge" change, the so-called bridge, which means that when an term is moved to the other side of the equation along with the sign in front of it (+ or -), it is necessary to change the sign in front of it (+change-,-change +).

What you write is not standard, it should be.

x/100=

After moving the item, it is x 100-x=

After merging the same terms, it is -99 100x=

The coefficient is x=

Don't mind if you don't simplify)

And the copy-and-paste one upstairs, don't believe him...

According to the basic properties of the equation 1, that is, if a=b, then a+c=b+c [definition of shift]: adding (or subtracting) the same number or the same integer on both sides of the equation is equivalent to moving some terms in the equation from one side of the equation to the other after changing the sign, and such a deformation is called shifting.

Example question]: Example 1 determines whether the following shift is correct, if not, how to correct it?

1) From. 7+x=13

Get x=13+7

2) From. 5x=4x+8

This gives 5x4x=8

3) From 3x-

2=x+1.

3x+x=2+1；

4) From. 8x=7x

2 gives 8x-7x=2

Analysis: The key to judging whether the move item is correct depends on whether the symbol after the move item has changed, and we must keep in mind the "shift change sign". Note: There are no moving items, and the symbol should not be changed; In addition, the terms on the same side of the equal sign are reversed from each other, and the symbols of these terms do not change.

Solution: (1) No, the 7 on the left side of the equal sign should be moved to the right side of the equal sign, and the symbol should be changed. The correct should be: x=13-7

2) Right. 3) Not true. The 2 on the left end of the equal sign was moved to the right of the equal sign and changed the symbol, but the x to the right of the equal sign was moved to the left of the equal sign without changing the sign The correct one should be:

3x-x=1+2

4) It is correct that the 7x on the right side of the equal sign is moved to the left of the equal sign and becomes -7x, but the 2 on the right side of the equal sign is still not shifted to the right of the equal sign, and the strain sign should be correct:

8x-7x=-2

The equation shift is based on the fact that when both sides of the equation are added or subtracted by a number at the same time, the two sides of the equation remain equal.

The two sides of the equal sign are equal, and the shift should be changed. Multiply and divide by, add and subtract.

Regardless of how the item is moved, it must: Left = Right.

When the item is moved, the calculation sign is reversed.

The terms on the left and right sides of the equal sign are equal.