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Transposing a number is the same as adding its additive inverse to both sides. The result is that (1) the number disappears from the side it was on and (2) its additive inverse appears on the other side.

Lots of uncommon words: easier to explain with an example.

Suppose you have x + 3 = y

The additive inverse of 3 is the number that you have to add to three to get an answer of 0. And that number is -3.

Adding -3 to both sides of the above equation gives:

x + 3 - 3 = y - 3

But x + 3 - 3 = x

So that x = y - 3

and in effect, you have transposed 3 to the other side along with the sign change.

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Q: Why do need to change the sign of a number when transposing?
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