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When solving for unknowns why does the symbols sometimes change from $a + $ to $a -$ or vice versa or stays the same?

For example (using solutions from text): $2x+6 = x+16\quad$ and the solution is $2x-x = 16-6\quad \Rightarrow \quad x=10$.

Or

$8x-12 = -3x+21\quad $Solution: $8x+3x = 21+12\quad \Rightarrow \quad 11x = 33\quad \Rightarrow \quad x=3$

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