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I have simple equation, $a = b - c$. For instance $8 = 12 - 4$. If I want to compute $b$, I have to transform this equation to $b = a + c$. So we have three variable, $a=8,b=12,c=-4$. I calculated it this way: $12 = 8 + (-4) = 8 - 4 = 4$. Why the result is incorrect?

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    $\begingroup$ $c=4$, not $c=(-4)$. That is all. $\endgroup$
    – Janik
    Nov 2, 2016 at 15:57
  • $\begingroup$ Given $a = b+c$ we have $ 8 = 12 - 4 \iff 8+4 = 12$ If you start with $c = -4$, when $4$ is added to each side of the equation in order to isolate $b$, we have $8+4 = 12.$ $\endgroup$
    – amWhy
    Nov 2, 2016 at 16:40

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Your error is in this line

So we have three variable, $a = 8, b = 12$ and $c = -4$

Here $c$ is not equal to $-4$. Actually, $c = 4$, because we define $-a$ as $-(+a)$.

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