Why do negative numbers multiplied by both sides of inequality change sign

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1. If both sides of the inequality divide or multiply by a number at the same time, the inequality does not change, right
2. Linear equations and inequalities of one variable 1. Let X / (a + B-C) = Y / (B + C-A) = Z / (a + C-B), find the value of (a-b) x + (B-C) y + (C-A) Z 2. Given / x + 5 / + / x-4 / = 9, find the value range of X (/ represents absolute value) 3. Cut two pieces of equal weight from two alloys of 7kg and 3kg respectively with different percentage of copper. Put the remaining part of each cut piece together with the rest of the other piece. After melting, the percentage of copper in the two alloys is equal. What is the weight of the cut alloy? 4. It is known that a, B and C are any real numbers, and it is proved that a ^ 2 + B ^ 2 + C ^ 2 > = AB + BC + ca 5. Given that x is a real number, prove 3 (1 + x ^ 2 + x ^ 4) > = (1 + X + x ^ 2) Only answer the third question, and don't answer the rest
3. Seeking: the procedure of solving the inequality of linear equation of one variable
4. Solving the inequality of linear equation with one variable The wage is divided into two parts, one is the basic wage of 200 yuan, and the other is the reward of 5 yuan for each garment processed. Worker Xiao Hong hopes that the wage will not be less than 1200 yuan. Then how many garments does Xiao Hong have to process at least one month?
5. Elementary inequality system or inequality equation of first degree with one variable (the more, the better)
6. A-B = 3, B-C = 2, a & # 178; + B & # 178; + C & # 178; = 1, find the value of AB + BC + ca
7. Given a / 3 = B / 4 = C / 5, find a & # 178; + B & # 178; + C & # 178; / AB + BC + ca （a²+b²+c²）/（ab+bc+ca）
8. If inequality | X-1|
9. The solution of inequality is 2 × & # 178; - 3 × - 2 ≤ 1?
10. In high school inequality, there is a common inequality ab ≤ [(a + b) / 2] &# 178; or ab ≤ (A & # 178; + B & # 178;) / 2 There is a common inequality in senior high school, which is ab ≤ [(a + b) / 2] &# 178; or ab ≤ (A & # 178; + B & # 178;) / 2. Is there any difference between [(a + b) / 2] &# 178; and (a & # 178; + B & # 178;) / 2, or is it equal?
11. Does the direction of the inequality sign change with the sign For example, | 2-x | > 3 2-x > 3, or 2-x < - 3 2-x > 3 x < 1 2-x < -3 x > -5 The meaning of the original formula | 2-x | > 3 on the number axis is that the distance from the far point is greater than 3 But in solving those two equations, the direction of the unequal sign changed So the solution set of the original formula should be {x | x < 1, or x > - 5} Or {x | - 5 < x < 1}
12. Under what circumstances does the direction of one variable linear inequality change When moving to? {x-4
13. The expression of relation is called inequality
14. Inequalities are formulas that use symbols (), (), (), () to denote inequality relations The answers at the midpoint are greater than, less than, greater than or equal to, less than or equal to and not equal to But there are only the first four items in the book, which is not equal to the answer Please give me some advice But there is no sign "not equal" in the textbook, only greater than, less than, greater than or equal to, less than or equal to It is said in the textbook that, in general, formulas connected by the symbols "< (or" less than or equal to "), and" greater than "(or" ≥) are called inequalities. There is no ≠ sign
15. Inequality is the expression of () relation
16. An inequality is a formula that uses (), (), or () to represent the size relationship
17. If two points a and B on the number axis represent real numbers a and B respectively, the length of line AB is () A. a-bB. a+bC. |a-b|D. |a+b|
18. The positions of real numbers a and B on the number axis are shown in the figure ────┴──┴─────┴─────┴─┴──＞ b -1 0 a 1 A.a+b>0 B.ab>0 C.a-b>0 D.|a|>|b|
19. The positions of real numbers a and B on the number axis are shown in the figure. Try to simplify | a + B | + | A-B | + | ab| -----b--------0--------a--------》
20. The position of the known real number AB on the number axis is shown in the figure: try to simplify: root (a-b) &# 178; - | a + B|