高一數學問題 請高手指導拜託..20點

1.
|2x - 1| + |x - 5| - |x - 7| = 15

情況一： 當 x ≤ 1/2
-(2x - 1) + [-(x - 5)] - [-(x - 7)] = 15
-2x + 1 - x + 5 + x - 7 = 15
2x = -16
x = -8

情況二：當 1/2 ≤ x ≤ 5
(2x - 1) + [-(x - 5)] - [-(x - 7)] = 15
2x - 1 - x + 5 + x - 7 = 15
2x = 18
x = 9
但 x= 9 不在 1/2 ≤ x ≤ 5 的範圍，故情況二無解。

情況三：當 5 ≤ x ≤ 7
(2x - 1) + (x - 5) - [-(x - 7)] = 15
2x - 1 + x - 5 + x - 7 = 15
4x = 28
x = 7

情況四：當 x ≥ 7
(2x - 1) + (x - 5) - (x - 7) = 15
2x - 1 + x - 5 - x + 7 = 15
2x = 14
x = 7

答案：x = -8 或 x = 7


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2.
|x - 1| ≤ 2
-2 ≤ (x - 1) ≤ 2
-1 ≤ x ≤ 3

|y - 3| ≤ 2
-2 ≤ y - 3 ≤ 2
1 ≤ y ≤ 5

x/y 的最小值 = -1/1 = -1
x/y 的最大值 = 3/1 = 3

答案： -1 ≤ x/y ≤ 3


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3.
a = 622/733 = (733 - 111)/733 = 1 - (111/733)
b = 833/944 = (944 - 111)/833 = 1 - (111/833)
c = 432/543 = (543 - 111)/543 = 1 - (111/543)

111/833 < 111/733 < 111/543
-111/833 > -111/733 > -111/543
[1 - (111/833)] > [1 - (111/733)] > [1 - (111/543)]
所以，b> a > c

1. 2x-1+x-5-x+7=15 x=7#
1-2x+5-x-7+x=15 x=-8#
2. -2≦x-1≦2 -1≦x≦3
-2≦y-3≦2 1≦y≦5
-1≦x/y≦3 #
3. b>a>c#(!!) 第一題有2個答案ㄛ^^