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When the linear function y > 0, the value of X is a linear inequality of one variable_______ The solution set of the model; When a linear function y
If the linear function is expressed as y = KX + B
When a linear function y
The solution set of one variable linear inequality KX + b > 0 (k is not 0) can be regarded as the value range of X when y = KX + B takes () value
1 from KX + b > 0, x > - B / K
When k > 0, b > 0, the value range of X is x > - B / K (one two three quadrants)
When k > 0, BB / K (one three four quadrants)
When K0, the value range of X is X
Linear inequality of one variable - x + 2
Linear inequality of one variable - x + 2
Linear function and linear inequality of one variable
If the intersection coordinates of the image of the linear function y = - x + A and the image of y = x + B are (m, 8), find the value of a + B
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The intersection coordinates of images are the solutions of the equations
Y=-X+A
Y=X+B
The solution is: x = (a-b) / 2, y = (a + b) / 2
That is: (m, 8) is ((a-b) / 2, (a + b) / 2)
So: (a + b) / 2 = 8
A+B=16
One variable linear inequality and two ways of linear function
1. It is known that the image of function y = (A-2) x + 1 is a straight line, and the image passes through the first, second and fourth quadrants. According to this, we can simplify (radical a & sup2; - 4A + 4) + (radical 16-8a + A & sup2;)
2. In the linear function y = ax + B (a ≠ 0), when a, B are what values, y increases with the increase of X? When a, B are what values, y decreases with the increase of X?
Well written. I can score
1. Because the image of the function y = (A-2) x + 1 passes through the first, second and fourth quadrants, so A-2
Inequality of one variable of one degree applies to function of one degree
1. The ticket of Hongfeng Lake is 45 yuan per person. There is a 25% discount for group tickets for more than 20 people (including 20 people). Now 18 tourists buy group tickets for 20 people
(1) How much cheaper than a regular ticket?
(2) When there are less than 20 people, how many people buy a group ticket for 20 people to be cheaper than an ordinary ticket? (write down the relationship between the ticket price and the number of people first)
18 people is 18 × 45 = 810
20 persons 20 × 45 × 0.75 = 675
810-675=135
So it's 135 yuan cheaper
Set X people, x675
x>15
So more than 15 people
Linear function and linear inequality of one variable
6 + 3x greater than 4x-2
Using function image to solve x
Draw two function images so that y = 6 + 3x, y = 4x-2
The range of X is the x value of 6 + 3x image higher than 4x-2 image
What is the relationship between linear inequality of one variable and linear function?
The solution of one variable linear inequality is the geometric property of the corresponding linear function image
For example, the solution of KX + b > 0 is the value range of the first-order function y = KX + B above the x-axis
It is known that the solution of 5-3k = x + 3 is a negative number, and the range of K is one variable linear inequality
5-3k-3=x
2-3k=x
x(2/3)
It is known that (m-2) x + 5 ＞ m + 4 is the range of the value of (1) to find M
M is not equal to 2
Because when m = 2, the coefficient of X is 0, X is not an inequality of X
RELATED INFORMATIONS
- 1. If (M + 1) x | m | + 2 ＞ 0 is a linear inequality with respect to x, then the value of M is________ ．
- 2. A T-shirt is priced at 200 yuan and can sell 500 pieces per month. According to the survey, 50 more T-shirts can be sold for every 3 yuan price reduction. There are 1000-1200 T-shirts at present. If you want to sell them out in a month, how much should you sell?
- 3. A mathematical problem about the linear inequality of one variable? When a supermarket purchases a batch of fruits, the quality loss is 5% in the transportation process, assuming that the supermarket does not include other costs (1) If the supermarket takes 5% of the purchase price as the selling price, please use the calculation to explain whether the supermarket is losing money (2) If the supermarket wants to make at least 20% profit, what is the minimum price increase of this fruit? (the result is accurate to 0.1%) It's a simple inequality
- 4. It is known that f (x) = asin (π x + α) + bcos (π X - β), where α, β, a and B are non-zero real numbers. If f (2012) = - 1, then f (2013) =? [the answer is 1]
- 5. If a belongs to a, then (1 / 1-A) belongs to a, and 1 does not belong to a.1). If 2 belongs to a, and a has three elements, find the set a 2) Verification: if a belongs to a, then (1-1 / a) belongs to a
- 6. Proof: when m is a real number, at least one of the quadratic equation x2-5x + M = 0 and the equation 2x2 + x-6-m = 0 has a real root
- 7. It is known that the quadratic equation 2x2 + 4x + k-1 = 0 has real roots 1) Find the value of K; (2) When the equation has two non-zero integer roots, the image of the quadratic function y = 2x ^ 2 + 4x + k-1 about X is translated down 8 units, and the analytic expression of the translated function is obtained; (3) Under the condition of (2), the image of the translated quadratic function below the x-axis is folded along the x-axis, and the rest of the image remains unchanged to get a new image. Try to explore whether the new image intersects with the line y = 1 / 2x + B? If there are several intersections?
- 8. The four real roots of the equation x2 + MX + 16 / 3 x2 + NX + 16 / 3 = 0 form an equal ratio sequence of A1 = 3 / 2 If the four real roots of the equation (X & # 178; + MX + 16 / 3) · (X & # 178; + NX + 16 / 3) = 0 form an equal ratio sequence with the first term of 3 / 2, then | M-N|=_______
- 9. Given that m and N are two equations x ^ 2 + 5x + 2 = 0, find the median term of M and n
- 10. It is known that M is the equal proportion median of two positive numbers 2 and 8, then the eccentricity of conic x ^ 2 + y ^ 2 / M = 1 is As long as the result (two solutions)
- 11. How to solve the sum of X + 1 of quadratic inequality x with one variable less than or equal to 3?
- 12. Shanghai Science Edition mathematics basic training 8.5 expand space answer
- 13. The solution of inequality (6x-x2-x3) (x2-7x + 10) is greater than 0
- 14. If inequality (5-a) x2-6x + A + 5 > 0 holds for any real number x, then the value range of real number a is______ ．
- 15. Solve the following inequality. (1) x2-7 + 12 > 0 (2) - x2-2x + 3 ≥ 0 (3) x2-2x + 1 < 0 (4) x2-2x + 12 < 0
- 16. What is the maximum distance between circle x2 + y2-2x + 4Y + 4 = 0 and straight line 3x-4y + 9 = 0?
- 17. The distance from the point (- 1,2) to the line 3x + 4y-7 = 0 is___
- 18. If the distance between two parallel lines 3x + 4Y + 5 = 0 and + 6x + ay + 30 = 0 is D, then a + D =? Find the specific process,
- 19. Find a point m on the parabola x ^ 2 = 1 / 4Y, so that the distance from m to the straight line y = 4x-5 is the shortest
- 20. It is known that P is on the straight line L: x + Y-1 = 0 and Q is on the circle C: (X-2) 2 + (Y-2) 2 = 1. (1) make the tangent PM, PN and tangent point of circle C through P It is known that P is on the straight line L: x + Y-1 = 0 and Q is on the circle C: (X-2) 2 + (Y-2) 2 = 1. (1) through P, make the tangent PM, PN of circle C, and the tangent points are m, N, and find the minimum value of cos ∠ MPN. (2) through P, make the tangent PM, PN of circle C, and the tangent points are m, N, and find cos ∠ MPN ≤ 35, calculate the value range of abscissa of point P