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earboth · #3 November 10th, 2008, 06:45 AM

As I've told you there are three distinct intervals. To each interval belongs one equation without any absolute values:

A) $x<-5:~~~~~~~~-(2x-1)-(-(x+5))=3$

B) $-5\leq x < \frac12:~-(2x-1)-(x+5)=3$

C) $x\geq \frac12:~~~~~~~~~~~(2x-1)-(x+5)=3$

Expand the brackets and solve for x. Afterwards you have to check if the solution is possible:

A) $-(2x-1)-(-(x+5))=3~\iff~-x+6=3~\iff~x=3$ .......BUT: 3 is not smaller than -5

B) $-(2x-1)-(x+5)=3~\iff~-3x-4=3~\iff~-3x=7~\iff~x=-\frac73$

I'll leave the last one for you.

Btw: If you need some additional informations ask in the original thread, please.

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