英语数学题：The integer solutions of the inequalities about"x" [3(x-a)+2≥2(1-2x-a)] and [(x+b)÷3＜(b-x)÷2] are 1,2,3,then the number of integer pairs (a,b) is ( )先翻译

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英语数学题：The integer solutions of the inequalities about"x" [3(x-a)+2≥2(1-2x-a)] and [(x+b)÷3＜(b-x)÷2] are 1,2,3,then the number of integer pairs (a,b) is ( )先翻译
英语数学题：
The integer solutions of the inequalities about"x" [3(x-a)+2≥2(1-2x-a)] and [(x+b)÷3＜(b-x)÷2] are 1,2,3,then the number of integer pairs (a,b) is ( )
先翻译

英语数学题：The integer solutions of the inequalities about"x" [3(x-a)+2≥2(1-2x-a)] and [(x+b)÷3＜(b-x)÷2] are 1,2,3,then the number of integer pairs (a,b) is ( )先翻译
大家都写错了,我的才对,
翻译：所给的关于x的不等式的整数解是1,2,3.,那么由整数a跟b组成的组合有几个?
由[3(x-a)+2≥2(1-2x-a)] 得x≥ a/7
由[(x+b)÷3＜(b-x)÷2] 得x＜b/5
所以a/7≤x＜b/5
因为x的不等式的整数解是1,2,3
所以1≥a/7>0,解得7≥a>0,a可以取7,6,5,4,3,2,1,共7种可能
3

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integer是整数的意思，solution是解决方法的意思，inequality是不等式的意思。
就是说，这个关于x的不等式的整数解是1,2,3.。
那么由整数a跟b组成的组合有几个？？
3(x-a)+2 ≥ 2(1-2x-a) 先看这个，
当x分别等于1,2,3的时候
a≤7, a≤14, a≤21.
(x+b)÷3＜(b-x)÷2 看这个，
当x分别等于1,2,3的时候
b＞5, b＞10, b＞15
那各式的共同解就是 a≤7 跟 b＞15 了。
这个整数对很多呀。。。无数个~~~ （楼上的第一个不等式貌似解错了~）
。额，你上哪得到的这个英文数学题啊？？

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意思就是所给的关于x的不等式的整数解是1,2,3.让你求ab可以是几个整数对
先分开解不等式 [3(x-a)+2≥2(1-2x-a)] ，3x-3a+2≥1-2x-a,
5x+1≥2a ,x≥2/5a-1/5
[(x+b...

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意思就是所给的关于x的不等式的整数解是1,2,3.让你求ab可以是几个整数对
先分开解不等式 [3(x-a)+2≥2(1-2x-a)] ，3x-3a+2≥1-2x-a,
5x+1≥2a ,x≥2/5a-1/5
[(x+b)÷3＜(b-x)÷2] ，x/3+b/3须同时满足两个不等式，当x=1时，1≥2/5a-1/5，1<1/5b
当x=2时，2≥2/5a-1/5，2<1/5b
当x=3时，3≥2/5a-1/5，3<1/5b
很显然只要满足1≥2/5a-1/5和3<1/5b这两个不等式就ok了。
解这俩不等式1≥2/5a-1/5，6/5≥2/5a ，a<=3, 3<1/5b b>15
就是a小于等于3，b大于15的就可以
具体是多少对，无穷啊。感觉少个条件什么的再限制一下

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最终答案及标准答案：
翻译：关于x的不等式
3(x-a)+2≥2(1-2x-a)
（x+b)÷3＜(b-x)÷2
的整数解是1,2,3.，那么由整数a、b组成的组合有几个？
由[3(x-a)+2≥2(1-2x-a)] 整理得x≥ a/7
由[(x+b)÷3＜(b-x)÷2] 整理得x＜b/5
所以a/7≤x＜b/5
...

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最终答案及标准答案：
翻译：关于x的不等式
3(x-a)+2≥2(1-2x-a)
（x+b)÷3＜(b-x)÷2
的整数解是1,2,3.，那么由整数a、b组成的组合有几个？
由[3(x-a)+2≥2(1-2x-a)] 整理得x≥ a/7
由[(x+b)÷3＜(b-x)÷2] 整理得x＜b/5
所以a/7≤x＜b/5
因为x的不等式的整数解是1,2,3
所以1≥a/7>0，解得7≥a>0，因为a为整数，a可以取1,2,3,4,5,6,7，共7种可能
3所以整数a跟b组成的组合有5×7=35个

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