Solving inequalities for mathematical problems Solving inequality system brace 2 (x-1) ≤ 3x + 1 x/3

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• 1. Solving inequality |How to solve x-500 | 5 | 2x + 5 | ≤ 7 | 2x-5 | > 3 | 7-5x | ≤ 3 1 ≤ | 2x-1 | < 2
• 2. √(y+1)≤4÷(y-1)
• 3. A certain market bought a batch of clothes worth 80000 yuan. When the price of each piece was 280 yuan, 150 pieces were sold. In order to promote sales, the shopping mall decided to reduce the price, but hoped to get back the cost when another 200 pieces were sold. So how much yuan can the clothing store reduce the price at most?
• 4. X / (X-2) - 1 = 6 / (square of x-4)
• 5. X2 + y2 = (x + y) 2 + P = (X-Y) 2 + Q, then p=______ ，Q=______ ．
• 6. To solve the equations: {5x-4y = 12} {3x-y = 7}
• 7. Solving a mathematical problem about proposition and proof The following is the definition of "mysterious number": a positive integer that can be expressed as the square difference of two consecutive even numbers is called a mysterious number. Please judge 4, 12, 20, 28, 2012 as a mysterious number according to the definition of "mysterious number". Why?
• 8. Let u = {positive integer no more than 5}, a = {x | x ^ 2-5x + q = 0}, B = {x | x ^ 2 + PX + 12 = 0}, (CUA) UB = {1,3,4,5}. Find P, Q, AUB I just learned the basic operation of set. The teacher left this question as a thinking question. I've read your explanation, but I still don't quite understand it
• 9. Let u = {positive integer no more than 5}, a = {x | x2-5x + q = 0}, B = {x | x2 + PX + 12 = 0}, (∁ UA) ∪ B = {1, 3, 4, 5}, find P, Q and set a, B
• 10. Given the complete set a = {1,2,3,4,5,6,7,8,9}, anb = {2}, (CUA) n (cub) = {1,9}, (CUA) NB = {4,6,8}, determine a, B Sorry, wrong number. It's the complete U
• 11. Prove by analysis: a square b square + b square C square + C square a square ≥ ABC (a + B + C) I just asked. Unfortunately, I read the answer. Here is the analytical method, not the difference method, Using basic inequalities and so on
• 12. 1. Compare the size ①a^2+b^2___ (a+b)^/2 ②ab_____ (a^2+b^2)/2 ③(a+b)^2____ 4ab ④[(a+b)/2]^2_____ (a^2+b^2)/2 2. Given x > 0, Y > 0, xy = 4, then the minimum value of X + y? 3. Given x > 0, Y > 0, x + y = 6, then the maximum value of XY? 4. Given that x > 0, then the minimum value of (32 / x) + 2x is? Trouble has a process
• 13. Inequality | x-4 | + | x-3|
• 14. System of inequalities In a visit activity, students are divided into eight groups. If each group is more than one person, the number of visitors is more than 156. If each group is less than one person, the number of visitors is not more than 150.
• 15. A math problem (high school inequality) Let the plane region represented by inequality x > 0 be o [n] y>0 y
• 16. Given the function f (x) = x2-2ax + 5, if f (x) is a decreasing function in the interval (- ∞, 2), and for any x1, X2 ∈ [1, a + 1], there is always | f (x1) - f (x2) | ≤ 4, the value range of real number a is obtained
• 17. If the function f (x) = x ^ 3-4x ^ 2-ax + 3 is a monotone function in [1,2], find the value range of A
• 18. When x tends to ∞, find the limit of [(x-1 Λ 10) (3x-1)) ^ 10] / (x + 1) Λ20
• 19. If the solution of equation x2-5x + 6 = 0 and equation x2-x-2 = 0 is m, then the number of elements in M is () A. 1B. 2C. 3D. 4
• 20. Given the set a = {x | x2-2x-3 ＞ 0}, then the number of elements in the set Z ∩ ∁ RA is () A. 5B. 4C. 3D. 2