major task. For instance, using “the rules of algebra” to get X on the other side of 7 = X, X would have to be subtracted from both sides, yielding 7 – X = 0. Then 7 would have to be subtracted from both sides, yielding –X = –7. Then both sides of the equation would have to be multiplied by –1, finally yielding X = 7 (because a negative times a negative is a positive, which is hardly intuitive).
In spite of laborious procedures like the above in some algebra texts, don't expect to ever meet a mathema-tician who would perform them. Most likely, if one wanted X on the other side in 7 = X, they would just flip everything around, which is what one would see if they just turned a math balance around! Note that in flipping an inequality, the sense or direction of the inequality changes. For example, flipping 5 < 7 results in 7 > 5, which, again, is what one would see if they just turned a math balance around.