Why does the sign need to change?

[mauricev]

I submitted (2(1-x))/3 - 8/1=1/(6x)-(2x-3)/3 to cymath. In solving it, it gets to a step

(2(1-x))/3 - 8/1=1/(6x)-((2x)/3-1)

Then it removes the brackets around the last term like so

(2(1-x))/3 - 8/1=1/(6x)-(2x)/3-1

But this also resulted in the sign of the last term being changed to a + like so

(2(1-x))/3 - 8/1=1/(6x)-(2x)/3+1

Why does removing the brackets require the sign to be changed? Without the sign change, of course, the final answer would be totally different.

 

[Deleted member 4993]

I submitted (2(1-x))/3 - 8/1=1/(6x)-(2x-3)/3 to cymath. In solving it, it gets to a step

(2(1-x))/3 - 8/1=1/(6x)-((2x)/3-1)

Then it removes the brackets around the last term like so

(2(1-x))/3 - 8/1=1/(6x)-(2x)/3-1

But this also resulted in the sign of the last term being changed to a + like so

(2(1-x))/3 - 8/1=1/(6x)-(2x)/3+1

Why does removing the brackets require the sign to be changed? Without the sign change, of course, the final answer would be totally different.

(-1) * (-1) = ?

 

[mmm4444bot]

I submitted [an equation] to cymath.

I cannot recommend the cymath site.

Their software seems confused by certain expressions using standard Function Notation, and cymath sometimes fails to find certain solutions.

 

[mauricev]

I figured it out. Consider

10 - (3 -2) = 9

Now
10 - 3 + 2 = 9

Taking out the parentheses and changing the sign of the last term results in the same answer. What's happening is that in the first expression, the whole expression 3-2 is being subtracted from 10, so when the parentheses are taking away the minus sign must be distributed to the -2 and minus a minus is positive.