So everyone knows (I hope) how to solve equations like $5x-2=4$ however how would you solve equations like $2x-1=3x-2=4x$. How, do you manipulate the equation? I've tried to use the common algebra rules however they don't work in these cases.
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1Well, look at what you wrote. $2x-1=4x\implies 2x=-1\implies x=-\frac 12$. But $3x-2=4x\implies x=-2$. Thus, your system is inconsistent and there is no solution. – lulu Apr 09 '18 at 22:58
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A string of equations like $a=b=c$ implies that $a=b$ and that $b=c$ as well as $a=c$, so the string of equations $2x-1=3x-2=4x$ can be rewritten as $\begin{cases}2x-1=3x-2\2x-1=4x\3x-2=4x\end{cases}$ (the third line is technically unnecessary, but it doesn't hurt). From there you can rearrange terms to get the variables all on one side and the constants all on the other and then use standard techniques for solving a system of linear equations such as gaussian elimination. As mentioned, your system in your example is inconsistent. – JMoravitz Apr 09 '18 at 23:14
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Basically, split it into two (or three, but the third is redundant) equations. – amd Apr 09 '18 at 23:39