# Delightful Division 4

## In Algebra, a variable's value will "flip" into its reciprocal when moved over to the other side of an equal sign! But only if each side has a specific number instead of a complicated formula.

__Examples:__

If 4x = 5, then x = 5/4 or 1 + 1/4; If 4 = 5x, then x = 4/5

If 7x = 8, then x = 8/7 or 1 + 1/7; If 7 = 8x, then x = 7/8

If 12x = 84, then x = 7; If 12 = 84x, then x = 1/7

If x√(2) = π, then x = π/√(2) or π√(2)/2; If √(2) = πx, then x = √(2)/π

This math trick works with any 2 numbers, except **zero(0)** because division by **zero(0)** is *undefined.* Any number multiplied by **zero(0)** is still **zero(0)**, **zero(0)** divided by any other number is still **zero(0)**, but watch what happens in the counterexample below:

If 25x = 0, then x = 0; If 25 = 0x, then... Wait a minute, there's no solution because the sides aren't equal!

If the 2 numbers on both sides of the equal sign are the same, then *x* = 1; simple as that!

If 9x = 9, then x = 1; If 9 = 9x, then x = 1

If 0x = 0, then x is indeterminate!; If 0 = 0x, then x is indeterminate!

Oops! I almost forgot! If both of those numbers are **zero(0)**, then **x** is *indeterminate*, meaning that the value can be anything you want to be! But according to math, an algebra problem is supposed to have a determinate solution.

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© Derek Cumberbatch