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In the second half of the picture where it says

$$ 1 = 4 - 1 \cdot (11 - 2 \cdot 4)\\ 1 = 3 \cdot 4 - 1 \cdot 11 $$

How did they jump from that first equation to the next? Where'd the $3$ come from?

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up vote 3 down vote accepted

You have $$ 4-1\cdot(11-2\cdot 4)=4-1\cdot 11+2\cdot 4=3\cdot 4-1\cdot 11 $$ by distributing the $-1$ in front of $(11-2\cdot 4)$ and collecting multiples of $4$.

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