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What is the concept of inequality?
The relation of numbers in a formula is not all equal sign. The formula with unequal sign is an inequality. For example, the inequality connected by 2x + 2Y ≥ 2XY, SiNx ≤ 1, ex > 0 "" is called strict inequality, The inequality connected with no less than sign (greater than or equal to sign) and not greater than sign (less than or equal to sign) ≥ "≤ is called non strict inequality or generalized inequality
If the even function f (x) defined in [- 1,1] is a decreasing function when x belongs to [0,1], then the solution set of the inequality f (1 / 2-x) < f (x) is
When x belongs to [0,1], it is a minus function
When x belongs to [- 1,0], it is an increasing function
F (1 / 2-x) < f (x) is equivalent to | 1 / 2-x | > | X|
The square of both sides is 1 / 4 + x ^ 2 - x > x ^ 2
X < 1 / 4
Because of | 1 / 2-x|
It is known that the function f (x) = (- 2 ^ x + b) / (2 ^ (x + 1) + a) is an odd function. (1) find the value of a and B, (2) if for any, the inequality F Let f (x) = - 2 ^ x + b) / (2 ^ (x + 1) + a) be odd functions. (1) find the values of a and B, (2) if the inequality f (T ^ 2-2t) + F (2 (T ^ 2-k) < 0 holds for any t ∈ R, find the value range of K
1. Odd function f (0) = 0 B = 1
f(1)=-1/(4+a)
F (- 1) = (1 / 2) / (1 + a) odd function f (- 1) + F (1) = 0
1/(2+2a)-1/(4+a)=0 a=2
2.f(x)=12(1-2^x)/(1+2^x)
F (x) is a decreasing function on R
f（t^2-2t）+f（2（t^2-k）＜0
f（t^2-2t）2k-2t^2
3T ^ 2-2t-2k > 0 holds
T + 244
In order to solve a system of inequalities of degree one, we can usually find the solution set of the system of inequalities directly by using the number axis as soon as possible
In order to solve a system of one variable linear inequalities, we can first (find out the solution set of each inequality in the inequality group) and then (find their common parts). Using the number axis, we can directly help us to find the solution set of the inequality system
How to solve a system of inequalities of order one variable?
1. De denominator (if any); X + 1 / 3 > 5x + 6
2. Remove brackets (if any); X + 1 > 15x + 18
3. Shift item (pay attention to changing sign); x-15x > 18-1
4. Merge similar terms (same as equation); - 14x > 17
5. Change the coefficient into one (note the sign change of "<" > "); x < - 14 / 17
There are also a few things you would like to use:
1:
Solving practical problems with inequalities is a new hot topic in the senior high school entrance examination. Practical problems are closely related to our life, especially the problems of resources and environment. The key to solve such problems is to find out the equal and unequal relations in practical problems, and list equations and inequalities. Here, we illustrate the solution of such problems with examples``
2:
1. The main types of inequality and inequality group are single choice, filling in blank, calculation and solution 2. The knowledge of inequality and inequality group mainly includes: the basic properties of inequality, the solution set of one variable linear inequality and the expression of the solution set of inequality on the number axis, the inequality system composed of two univariate linear inequalities, and the simple application of the number axis to determine the solution set, inequality and inequality group
3:
1. The knowledge points examined in the part of equations and inequalities mainly include: listing, solving and testing equations according to the quantitative relations in specific problems, being able to estimate the solutions of equations, solving unary first-order equations, simple binary linear equations, fractional equations that can be converted into unary first-order equations, and univariate quadratic equations with simple coefficients, as well as the significance and basic properties of inequalities, This paper solves the linear inequality of one variable and expresses the solution set on the number axis. It solves the system of linear inequalities and determines the solution set of the inequality system by using the number axis. It solves simple application problems
That's about it!
Hope to be helpful to your achievement ~!
The steps of solving univariate linear inequality are as follows （1）______ ; （2）______ ; （3）______ ; （4）______ ; （5）______ .
The steps of solving univariate linear inequality are as follows
(1) De denominator;
(2) Remove brackets;
(3) Transfer;
(4) Merge similar items;
(5) The coefficient is reduced to 1
So the answer is: (1) remove the denominator;
(2) Remove brackets;
(3) Transfer;
(4) Merge similar items;
(5) The coefficient is reduced to 1
Representation of the solution set of the system of inequalities of degree one, X>2 X
There is no solution to the inequality
The second volume of seventh grade mathematics univariate linear inequality group about X inequality group x-a ≥ B 2x-a < 2b-1 x solution set is 3 ≤ x < 5, find the value of a, B
x-a≥b
X>=a+b
2x-a＜2b-1
2x
On the inequality system x + b > 2a, the solution set of X + a < 2b is - 3 < x < 3
The correct solution is as follows:
x+b＞2a
x+a＜2b
The above inequalities are solved respectively
x>2a-b
X
The value of an unknown number that makes an inequality tenable is called inequality (). All solutions of an inequality containing an unknown number, The value of the unknown number that can make the inequality tenable is called inequality (). All solutions of an inequality containing an unknown number constitute the inequality's (). Help me solve it
Solution set
RELATED INFORMATIONS
- 1. In the inequalities with unknowns, () is called inequality solution of inequality
- 2. Find the solution set of the inequality system 1.2x-75 3x-2≥4 3.1-2（1+y)-3/4 x≥5
- 3. After y = SiNx (2x + π / 4) image translation vector (π / 4,0), the function corresponding to the new image is y=
- 4. How to find tangent equation of curve at a certain point according to the geometric meaning of derivative
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- 6. The equation of conic curve. Find the hyperbolic equation with two vertices of ellipse x squared / 16 + y squared / 9 = 1 as focus and ellipse focus as vertex
- 7. The problem of finding tangent by derivative If the function y = f (x) passes through the tangent line of point P (x, f (x)), there are two cases, one is that the point is tangent point, the other is that the point is not tangent point, so there may be two answers My question is, isn't the tangent line only one intersection point with the image of y = f (x)? Since the point P (x, f (x)) is on y = f (x), isn't p the tangent point? If not, isn't the tangent point more than one intersection point with the image of y = f (x)?
- 8. In the triangular vertebrae with o as the vertex, the intersection angle of the three edges passing through O is 30 degrees. Take two points AB on one edge, OA = 4cm, OB = 3cm. At the end point of AB, a rope is used to tightly wrap the side of the triangular pyramid (there is no friction between the rope and the side), and find the shortest rope length between AB and ab
- 9. Can we prove that the line m is perpendicular to the line n?
- 10. The derivative of the function y = sin2x - cos2x is () A. 2 2cos(2x-π 4) B. cos2x-sin2x C. sin2x+cos2x D. 2 2cos(2x+π 4)
- 11. What is the solution formula of quadratic inequality of one variable Isn't the result of two values? It doesn't become to understand the quadratic equation of one variable
- 12. How to solve the inequality with absolute value? For example: | 1-3x | 4 problem solving process, as long as detailed steps, don't say a lot, I think we all understand a kind of problem do not understand, as long as you look at the problem-solving process can roughly understand it? So don't copy some theories to send up! At present, just read senior one, senior one solution priority, other night can!
- 13. Solving inequality: 1 + SiNx + cosx ≠ 0
- 14. The graph of the function y = - 3x + 12 is drawn, and the solution set of inequality - 3x + 12 > 0 is obtained by using the image. (2) the solution set of inequality - 3x + 12 ≤ 0 is obtained
- 15. Using function image to solve inequality 5x-1 > 2x + 5
- 16. What is the area of the plane area represented by the absolute value of inequality x + absolute value y less than or equal to 3
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- 18. Using monotonicity of function to prove inequality Prove x-x ^ 2 > 0, X ∈ (0,1) by monotonicity of function
- 19. On Sunday, the class leader Wang Xiaoming organized 50 students to go to Nanhu Park. There are two kinds of boats available for hire in the park. Each big boat can seat 5 people at most, and the rent is 30 yuan for each boat, and the rent is 20 yuan for each boat. Please use what you have learned to design a scheme so that the boat does not leave vacant seats and pays the least rent. Remember: use the solution of one variable linear inequality equation~
- 20. A practical problem of inequality in grade two To welcome the Universiade and beautify Shenzhen, the garden department decided to use the existing 3490 pots of A-type flowers and 2950 pots of B-type flowers with 50 gardening styles of a and B on both sides of Yingbin Avenue. It is known that 80 pots of A-type flowers and 40 pots of B-type flowers are needed to match a type-A flower, and 50 pots of A-type flowers are required to match a B-type flower, The extracurricular activity group of class 1 of the third grade of a school undertook the design of the horticultural modeling collocation scheme?