How to solve inequality equations, how to solve inequality equations

When solving an inequality, you can treat the inequality as an equation, solve the solution of the equation, that is, divide the inequality into the interval boundary, and then choose different intervals according to the meaning of the problem.

For example, x 2 9, solve this according to the equation x = 3, that is, 3 divides ( into three intervals, i.e. ,3],[3, 3],[3, and then according to the sign of the inequality, just select some of these three intervals, and the solution set of x 2 9 is ( 3],[3,

The process of solution must follow the infinitive nature.

The most basic property of inequality.

If x>y, then yy, y>z; Then x>z; (Transitivity).

If x>y, and z is an arbitrary real number or integer, then x+z>y+z; (Addition Rule).

If x>y,z>0, then xz>yz; If x>y,z<0, then xzy,z>0, then x z>y z; If x>y,z<0, then x zy,m>n, then x+m>y+n (sufficient unnecessary).

If x>y>0 and m>n>0, then xm>yn

If x>y>1, then the nth power of x" the nth power of y (n is a positive number), 1>x>y>0, then the nth power of x > y to the nth power (n is a positive number), If we start from the basic properties of inequalities, through logical reasoning, we can prove a large number of elementary inequalities, the above are the more famous of them.

The principle of solving inequalities.

The main ones are: the inequality f(x) g(x) is the same as the inequality g(x) > f(x).

If the equation f(x) is not in order. 1.Symbol: Multiply or divide a negative number on both sides of the inequality to change the direction of the inequality.

2.Determine the solution set:

If it is greater than both values, it is greater than the largest;

Smaller than both values, smaller than the smaller;

Bigger than the big, smaller than the small, there is no solution;

Bigger than the small, smaller than the big, there is a solution in the middle.

A group of inequalities consisting of three or more inequalities, and so on.

3.Alternatively, the solution set can be determined on the number line:

The solution set of each inequality is represented on the number line, and the points on the number line divide the number line into segments, and if the number of lines representing the solution set on a certain segment of the number line is the same as the number of inequalities, then this section is the solution set of the inequality group. A few will cost a few.

4.If both sides of an inequality are added or subtracted, the direction of the unequal sign remains unchanged for the same number or formula. (Change the number of the move item).

5.Multiply or divide the two sides of an inequality with the same positive number, and the direction of the inequality sign does not change. (Equivalent to a coefficient of 1, which can only be used if it has to be positive).

6.Multiply or divide both sides of an inequality by the same negative number, and the direction of the inequality sign changes. (or 1 negative number).

Firstly, the solution set of each inequality is solved separately, and the specific steps are to remove the denominator, remove the parentheses, shift the terms, merge the same terms, and coefficientize 1. After that, draw two solution sets on the number line; Finally, find the overlapping part of the two solution sets, that is, the solution set of the inequality group.

Classification: 1. Integer inequality: Integer inequality is an integer on both sides (i.e., the unknown number is not on the denominator).

2. Unary one-time inequality: an inequality that contains an unknown number and the number of unknowns is one.

3. Binary one-time inequality: an inequality that contains two unknowns, and the number of unknowns is one.

Inequality Properties:1. Add (or subtract) the same number or the same integer on both sides of the inequality, and the direction of the inequality sign remains unchanged.

2. Both sides of the inequality are multiplied (or divided) by the same positive number, and the direction of the inequality sign remains unchanged.

3. Multiply (or divide) the same negative number on both sides of the inequality, and the direction of the inequality sign changes.

Hello, I'm Xuan Ya Fei Bu 8 and I'm glad to serve you. Your question has been received and is being sorted out, about 5 minutes for you, please wait

Hello, I'm Xuan Ya Fei Bu 8 and I'm glad to serve you. Your question has been received and is being sorted out, about 5 minutes for you, please wait

According to the known conditions and the conclusions, the unknowns are set, and some wholes are represented by the known and hidden conditions, so as to list the inequality equations, and finally the inequalities can be solved according to the established laws.

For example: I have 10 yuan, and you have more money than me, and if the amount of your money is x, then x > 10

Extended information: With the inequality sign (, the concatenated formula is called an inequality. Usually the number in the inequality is a real number, and the letter also represents the real number, and the inequality can represent both a proposition and a problem.

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, operations), and the value of the unknown number that makes the equation true is called the "solution" or "root". The process of finding the solution of an equation is called "solving an equation".

By solving the equation, you can avoid the difficulty of reverse thinking, and directly list the equation containing the quantity you want to solve. Equations have a variety of forms, such as unary linear equations, binary linear equations, unary quadratic equations, etc., and can also form a system of equations to solve multiple unknowns.

In mathematics, an equation is a statement that contains an equation of one or more variables. Solving the equation involves determining which values of the variable make the equation true. Variables are also known as unknowns, and the value of the unknowns that satisfies equality is called the solution of the equation. [1]

Hope mine can help you! [Love you].

Solution: Basically, it is the same as the equation Qin Gao, just pay attention to the variable sign.

Give a few examples of solving differential equations.

<> hope it helps you.

The methods of solving inequality equations can be divided into the following:

Image method, algebra method, mathematical reasoning method, and number axis method. According to the specific form and difficulty of the inequality, the appropriate method is selected to solve it.

1. Image method:

The image method is an intuitive way to solve inequalities by drawing the region represented by the inequality on a coordinate system. For example, for a unary one-time inequality, it can be converted into a straight line and the position of the solution set can be determined according to the direction of the inequality sign.

2. Algebraic method:

Algebraic is a method of solving inequality equations using algebraic operations. Inequality equations are transformed into simpler problems by applying mathematical rules and properties for deformation and simplification. For example, for a quadratic inequality of one element, it can be converted into a quadratic equation by a fitting method or a root-finding formula, and the solution set can be obtained by solving the equation.

3. Mathematical reasoning:

Mathematical deduction is a method of solving inequality equations through logical reasoning and proof. By applying mathematical theorems and properties, the set of solutions to inequality equations is derived. For example, for some complex inequality equations, mathematical reasoning methods, such as mathematical induction or mathematical recursion, can be used to find the characteristics and laws of the solution.

4. Number axis method:

The number line method is a visual solution based on the number line that is used to solve unary inequality equations. The range and position of the solution are determined by marking the interval represented by the unequal sign on the number line. For example, for a unary one-dimensional inequality, it can be converted into an interval representation on the number line, and the position of the solution set is determined according to the direction of the inequality sign.

5. Summary:

Methods for solving inequality equations are image method, algebra method, mathematical reasoning method, and number axis method. Choosing the right solution depends on the form of the inequality equation and the difficulty of the equation.

The image method is suitable for areas where inequalities are explained visually; Algebraic methods simplify problems through algebraic operations; Mathematical reasoning uses logical reasoning and proof to find the characteristics and laws of solutions; The number holder method determines the position of the solution by means of an interval representation on the number line. Depending on the situation, there is flexibility to choose different methods to solve inequality equations.

x²-3x+2＜0

x-1)(x-2)<0

The 1 x 2 solution set is x 1 x 2

Usually the numbers in inequalities are real numbers, and letters also represent real numbers, and the general form of inequality is f(x,y,......z)≤g(x，y，……z) (where the inequality sign can also be <, one of them), the common domain of the analytic formula on both sides is called the definition domain of the inequality, and the inequality can express both a proposition and a problem.

If x>y, then yy;

If x>y, y>z; Then x>z;

If x>y, and z is an arbitrary real number or integer, then x+z>y+z;

If x>y,z>0, then xz>yz; If x>y,z<0, then xz If x>y,z>0, then xz>y z; If x>y,z<0, then xzAdditional Information:

Solve the inequality group step:

1.Set the inequalities in the inequality group separately

2.Solve the inequalities separately.

The format is: Solution. Solution.

3.It can be represented separately on the number line.

4.Stand up the original dissociation to form a solution set.

5.If there is no solution, then write: This group of inequalities has no solution.

If the inequality f(x)0 is the same solution as the inequality f(x)h(x)g(x).

Content from users: You're right.

1 Solution Inequality:.

2 Solve the inequality: and represent its solution set on the number line 3 Solve the inequality and represent the solution set on the number line

4.Solve the inequality and represent its solution set on the number line 5 Solve the inequality and represent its solution set on the number line.

6.Solve the inequality and represent its set of solutions on the number line.

7.Solve the group of inequalities and express the set of its solutions on the number line 8 to solve the group of inequalities:

9 Solve the inequality group:

10 Solving Inequality Groups:

11 Finding the integer solution of a group of inequalities

12 Finding the integer solution of the group of inequalities.

13 Solve the group of inequalities: and write the integer solutions of the groups of inequalities.

14 Solve an inequality group and determine whether it is a solution to the inequality group 15 Solve an inequality group represents its solution set on a number line and finds its integer solution

16 Solve the group of inequalities and represent the set of solutions on the number line

x²-3x+2＜0

x-1)(x-2)<0

The 1 x 2 solution set is x 1 x 2

It is not easy to answer the question, if you are dissatisfied, please understand

x²-3x+2＜0

x-1)(x-2)<0

1 Inequalities can be understood as equations to solve, and then use formulas with symbols.

（x-1)(x-2)<0

1. x-1<0 x-2>0

x1<1 x2>2

There is no solution to this one.

2. x-1>0 x-2<0

x1>1 x2<2

1So, the set of solutions to the inequality is 1

x2-3x+2 0 (x-1)(x-2)<0 1 x 2 The solution set is x 1 x 2 Usually the numbers in inequalities are real numbers, and letters also represent real numbers, and the general form of inequalities is f(x,y,......z)≤g(x，y，……z) (where the inequality sign can also be <, one of them), the common domain of the analytic formula on both sides is called the definition domain of the inequality, and the inequality can express both a proposition and a problem. If x>y, then yy; If x>y, y>z; Then x>z; If x>y, and z is an arbitrary real number or integer, then x+z>y+z; If x>y,z>0, then xz>yz; If x>y,z>0, then xz>yz; If x>y, z<0, then x z0, then the inequality f(x)h(x)g(x) is the same solution.

Regardless of how this inequality equation came about.

It should be said that there are three conditions for this equation:

2m+4+1-3m>=0①

m-2+1-3m>=0②

The solution of m≠2 m must meet the above three conditions at the same time.

Result: -5m+5>=0

5m<=5

m<=1④

Derives: -2m-1>=0

2m<=-1

m<=-1/2⑤

Synthesizing Agnosticism, the solution of the inequality equation is:

m<=-1/2

Since it is determined that the fraction is a positive value, it is enough to find the reciprocal inequality directly

The solution of the inequality is a set (or several) sets, a range of values (or several); The solution of an equation is one (or several) specific values. For example, "all numbers greater than 2" and "equal to 2" can be distinguished, right?