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How to explain?

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电梯直达

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发表于 2005-2-21 20:40:19 | 显示全部楼层回帖奖励

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I try to teach my daughter to solve some equations with absolute value signs, such as

|x-1| + |2x+1| = 12

We can break it into x-1+2x+1=12 and -(x-1)-(2x+1)=12.

How can I explain to her that she cannot use

x-1-(2x+1)=12 or -(x-1)+2x+1=12 to get the answers?

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1 主题	38 帖子	265 积分

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沙发

楼主| 发表于 2005-2-22 23:18:06 | 显示全部楼层

Here is a general question

Thank both of you for your help. In general, how many solutions exist for this type of equation?

|ax+b|+|cx+d|+...+|mx+n|=constant.

(It is better to use a1x..., but I cannot write 1 as subscript)

If the answer is bigger than 2, can you show me an example?

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板凳

楼主| 发表于 2005-2-23 03:44:02 | 显示全部楼层

No solution

It is easy to find a case of no solution, such as |x|=-1 or |x-1|+|x|=0.

Could show an example for infinitely many solution and 3 solutions

Thank you a lot. It seems so easy for you. But I just could not find them.

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