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I know the method of solving the equation like this $|2x+1|=|3x+9|$ but the problem is if the same equation would be like this $| 2x+1 | = x | 3x+9 |$, how can I solve this?

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    Again, the point that has been raised to you in your past few questions: treat the absolute value as a function with two cases. $|2x+1|=\mathrm{something}$ can mean either of $2x+1=\mathrm{something}$ or $-(2x+1)=\mathrm{something}$. You will have four "cases" since you have two absolute values; work from that.2010-08-23
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    actuall we can solve the first example as 2x+1=3x+9 or 2x+1=-(3x+1) we have only two cases to solve , now i want to discover that how we can solve the second example in this way2010-08-23
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    The same technique still applies, Zia.2010-08-23
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    Lastly, making a good plot: http://tinyurl.com/28lkzje helps greatly when trying to solve such things.2010-08-23
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    Eleven exclamation marks look like someone's shouting. What shall I picture for myself in the face of eleven interrogation marks?2010-08-23
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    Rasmus: extreme curiosity?2010-08-23
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    Solving an equation with n absolute values by using $2^n$ cases can be a lot harder than with $n+1$ cases (since $2^n-n-1$ of the $2^n$ cases for $n>1$ are impossible anyway); the solutions using only two cases are restricted to equations with an essentially-multiplicative relationship between the absolute values and won't generalize to equations like $|x+1|+|x-3|=4$.2010-08-23
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    I disagree that this is an *exact* duplicate of a previous question. Consider me to have voted to reopen.2010-08-24

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