A few questions about integer equations, what is an integer equation

then x-1=6a, x=6a+1

2x-(x-a) 3=0 then 6x=x-a, x=-a 5 The two equations are solved together, then 6a+1=-a 5

30a+5=-a, so a=-5 31

2.ax 6-2=0, then x 6=2 a

So x= (2 a) open to the sixth power.

Then (n-1)x=m-n

Discussion: When n=1, if m=n=1, then x can take any value; (Because the equation is equal to 0).

When n=1, if m≠n, there is no solution; (Left side of the equation = 0, right side is not equal to 0) when n≠1, x = (m-n) (n-1).

4.(k+1)(k-1)x-2(k+1)(k+2)=0k+1)(k-1)x=2(k+1)(k+2)discussion: When k=1, there is no solution.

Because the left side of the equation is always equal to 0, and the right side = 12) when k = -1, x can take any value. (Because the equation is equal to 0 left and right) when k≠ 1, x=2(k+2) (k-1).

1。The solution of the first equation is x=6a+1; The second solution is x=-a 5. The two solutions are equal, then 6a+1=-a 5, so a=-5 31.

x = 6th root number (2 a). The 6th root sign is to write a 6 in the upper left corner of the root number.

3。Solution: The original equation is reduced to (n-1)x=m-n.

When n-1=0 and m-n=0, m=n=1, m=n=1. In this case, x takes any value.

Condition When n-1=0 and m-n≠0, i.e., n=1, m≠1; At this point, there is no solution to the equation.

Condition When n-1=0 and m-n≠0, i.e., n=1, m≠1; In this case, x=m-n (n-1).

4。It's actually about the same as 3.

Solution: When k+1=0, i.e., k=-1, x is an arbitrary value.

When k-1=0, i.e., k=1, x has no solution.

When (k+1)(k-1)≠0, then x=2(k+1)(k+2) [k+1)(k-1)]=2(k+2) (k-1).

Integer. Equation means that all the unknowns in the equation appear on the numerator, the denominator.

Equations such as attitude cavities that are just constants and have no unknowns. For example, equation 3 x 5 + 2 = 0 is an integral equation, while equation 3 (x-1)+2=1 is not an integral equation (both with x as an unknown). In an integer equation, we call it a multi-element equation if there are several different unknowns, and if the highest number of unknowns is a few times, we call it a few equations.

Fractional equationsDifference from integer equations

1. The definitions are different

Fractional equation is a kind of equation, which refers to a rational equation with an unknown number or an unknown integer in the denominator, and this part of the knowledge belongs to elementary mathematical knowledge.

All the unknowns in the equation appear on the numerator, and the denominator is just a constant and there is no match for the unknown.

2. The steps of solving the problem are different

Fractional equations

Go to the denominator. Both sides of the equation are multiplied by the simplest common denominator at the same time, and the fractional equation is transformed into an integral equation. Raiding refers to when there is a situation where numbers are opposite. Don't forget to change the symbols.

Lowest common denominator: The coefficient is the lowest common multiple.

The unknown number takes the highest power and the factor in which it appears.

take the highest power).

Transposition. Move items, if there are parentheses, you should remove the parentheses first, pay attention to changing the number, and merge similar items.

Convert the coefficient to 1 to find the value of the unknown;

Root inspection. After finding the value of the unknown, it is necessary to check the root, because in the process of converting the fractional equation into an integral equation, the range of the value of the unknown is expanded, and the root may be increased.

If the simplest common denominator is equal to 0, the root is an incremental root. Otherwise this root is the root of the original fractional equation. If the solved roots are all incremental roots, then there is no solution to the original equation.

If the fraction itself is divided, it should also be substituted for inspection.

When solving a problem with a column equation, it is not only necessary to test whether the obtained solution satisfies the equation.

It is also necessary to check whether it matches the topic.

In general, when solving a fractional equation, the solution of the integral equation obtained after removing the denominator may make the denominator in the original equation zero, so the solution of the integral equation should be substituted into the simplest common denominator, and if the value of the simplest common denominator is not zero, it is the solution of the equation.

Integer equations:

Denominator { Multiply both sides of the equation by the simplest common denominator (simplest common denominator: the coefficient is the lowest common multiple).

Remove the parentheses (remove the parentheses and remember to look at the symbols).

Shift term (add or subtract the same number or the same integer on both sides of the equation, usually placing unknowns to the left of the equation and constants to the right.) ）

Merge items of the same kind.

The coefficient is reduced to 1

An integral equation is an equation that if there is only one unknown in the equation, and both sides are integers about the unknowns, such an equation is called a one-dimensional integral equation. For example, 3x 5+2=0 is an integer equation, and 3 (x-1)+2=1 is not an integer equation. For example, ax+b=c integer is for some "unknown pose" (usually denoted by x, y, etc.).

These "unknown quantities", numbers, other letters representing numbers, and some algebraic formulas that do not contain these "unknown quantities" from the source, are formed by a finite number of addition, subtraction, and multiplication. It's called integers about these "unknowns". Integer 0 (or two different integers connected with an equal sign).

It's an integer equation. Concepts just need to be understood.

What is called an integral equation is as follows:An integral equation is one in which all the unknowns appear on the numerator, and the denominator is only a constant and there are no unknowns. For example, 3x, 5+2=0 is an integer equation, and 3 (x-1)+2=1 is not an integer equation, e.g. ax+b=c, an integer is for some "unknowns" (usually represented by x, y, etc.).

These "unknown quantities", numbers, other letters representing numbers, and some algebraic formulas that do not contain these "unknown quantities", are formed by adding, subtracting, and multiplying a finite number of equations. It's called integers about these "unknowns". Integer 0 (or two different integers connected with an equal sign).

It's an integer equation. The concept only needs to be understood to be suppressed.

1. Integral equations, corresponding to fractional equations, refer to a class of equations in which all the unknowns in the equation appear on the fraction or pickpocket, and the denominator is only a constant and there are no unknowns. For example, equation 3 x 5 + 2 = 0 is an integral equation, while equation 3 (x-1) + 2 = 1 is not an integral equation (both regret to be unknown to x).

2. In the integer equation, we call it a few yuan equations if there are several different unknowns, and the highest number of unknowns is a few times, so we call it a few equations.

1. Integral equations, corresponding to fractional equations, refer to a class of equations in which all the unknowns in the equation appear on the numerator, the denominator is only a constant, and there are no unknowns. For example, equation 3 x 5 + 2 = 0 is an integral equation, while equation 3 (x-1)+2=1 is not an integral equation (both with x or unknown).

2. In the integer equation, we call it a few yuan equations if there are several different unknowns, and the highest number of unknowns is a few times, so we call it a few equations.

An integral equation is one in which all the unknowns appear on the numerator, and the denominator is only a constant and there are no unknowns. For example, 3x, 5+2=0 is an integer equation, and 3 (x-1)+2=1 is not an integer equation, e.g. ax+b=c, an integer is for some "unknowns" (usually represented by x, y, etc.).

These "unknown quantities", numbers, other letters representing numbers, and some algebraic formulas that do not contain these "unknown quantities", are formed by adding, subtracting, and multiplying a finite number of equations. It's called integers about these "unknowns". Integer 0 (or two different integers connected with an equal sign).

It's an integer equation. Concepts just need to be understood.

Good evening, dear!

What is an integer equation? To concept! To punish copying, hey...

To the textbook, thank you for the latest 2 small happy mononomials and polynomials are collectively referred to as integers. A rational form in algebra. If there is no division operation or fraction, and if there is a division operation and a fraction, there are no variables in the division or denominator, it is called an integer.

Integers can be divided into definitions and operations, definitions can be divided into monomials and polynomials, and operations can be divided into addition, subtraction, and multiplication and division. Addition and subtraction include merging similar terms, multiplication and division include basic operations, rules and formulas, basic operations can be divided into power operation properties, laws can be divided into integers, division, formulas can be divided into multiplication formulas, zero exponential powers and negative integer exponential powers.

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Denominator { Multiply both sides of the equation by the simplest common denominator (simplest common denominator: the coefficient is the lowest common multiple).

Remove the parentheses (remove the parentheses, remember to look at the symbols) Move the item (add or subtract the same number or the same integer on both sides of Fang Chunchangcheng.

Ulnar bending merges similar terms.

The coefficient is turned into one.

Example: x 2-5=2 (x-4).

Remove the denominator x-10=4(x-4).

Remove the parentheses x-10=4x-16

Shift x-4x=-16+10

Merge homogeneous items -3x=-6

The coefficient is reduced to one x=2