**Example A:**

2x + 4y - 3z = 3

after re-shuffling, becomes

-3z +2x + 4y - 3 = 0

**Example B:**

3x - 4y + z = 2

becomes, after re-shuffling,

**-z**-4y

**-3z**-2 = 0

Example A can be seen to be correct mathematically, whereas, Example B isn't.

Why so?

*Example B, after having the terms re-shuffled, has the*

**signs**of those terms**changed!**The explanation to this sign change is that since, the terms were moved from left to right, and right to left, the sign must change. A shocking mistake has been made!

This is a mis-understanding and also a mis-conception.

*What was missed out here is that the movement of left to right (or vice versa) has to*

**cross over**the "**equal**" symbol.4x -5y = 1

0 = 1 - 4x + 5y <== This is correct sign change after re-shuffling across the "=" symbol.

-5y + 4x = 1 <== This is correct re-shuffled terms with no change in sign.

**Message:****As long as the terms remain on the same side of the "=" symbol, the terms will not have their signs changed, even though their positions may have shifted.**

**The sign change results only when the term moves across the "equal" symbol, crossing over the opposite side.**

Thus, do not confuse re-shuffling of terms within the same side to crossing the "equal" symbol.

This simple mistake can produce a big mistake through wrong understanding of math principles.

Math make us think properly and logically with reasoning to every steps taken. It is a good subject that aids mankind. Treasure the learning.

Cheers!

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