Why is 7 handled as a negative number in the following equation?Here is a very simple multi-step equation that bothered me for a specific reason:20-7x=6x-6I started by subtracting 6x from both sides and for a second I thought I would find "1x" as a result of subtracting 6x from the left side of the equation (and write it as 20-1x=-6). then I realized that it should have been "-13 x" (20-13x=-6)Although I could solve it mechanically, I couldn't internalize the logic behind evaluating a subtraction sign as a negative number symbol in algebraic equations. Why should one get the "-" sign before 7x as a negative sign and conduct the subtraction operation accordingly? I would appreciate an answer that covers the logic behind this action.

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Why is 7 handled as a negative number in the following equation?Here is a very simple multi-step equation that bothered me for a specific reason:20-7x=6x-6I started by subtracting 6x from both sides and for a second I thought I would find &quot;1x&quot; as a result of subtracting 6x from the left side of the equation (and write it as 20-1x=-6). then I realized that it should have been &quot;-13 x&quot; (20-13x=-6)Although I could solve it mechanically, I couldn&#039;t internalize the logic behind evaluating a subtraction sign as a negative number symbol in algebraic equations. Why should one get the &quot;-&quot; sign before 7x as a negative sign and conduct the subtraction operation accordingly? I would appreciate an answer that covers the logic behind this action.

Angelo Murray · Accepted Answer

Subtraction is not an associative operation, i.e.,   (  a  −  b  )  −  c  ≠  a  −  (  b  −  c  ) When you bring the   6  x over to get   20  −  7  x, you should interpret it as   −  6  x   (  20  −  7  x  )  −  6  x  =  20  −  (  7  x  +  6  x  )  =  20  −  13  x, not   20  −  (  7  x  −  6  x  )  =  20  −  x

Why is 7 handled as a negative number in the following equation? Here is a very simple multi-step e

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