inverse operation
Every action that can be undone has an opposite. If you walk 5 steps forward, walking 5 steps back returns you to the start. In arithmetic, an inverse operation is one that undoes another: subtraction undoes addition, and addition undoes subtraction. Add 7 then subtract 7, and you are exactly where you began.
The pairs are: addition and subtraction undo each other, and multiplication and division undo each other. Each undoing returns you to the identity for that operation — adding then subtracting the same number nets to adding 0; multiplying then dividing by the same nonzero number nets to multiplying by 1. Squaring and taking a square root are inverse processes too, with a caveat about signs.
Inverse operations are the secret engine of solving equations. To free a variable you apply the inverse of whatever is attached to it, doing the same thing to both sides to keep the balance. If 3x + 4 = 19, subtract 4 (undoing the addition) to get 3x = 15, then divide by 3 (undoing the multiplication) to get x = 5.
Solve x − 8 = 5. Apply the inverse of subtracting 8, namely add 8 to both sides: x − 8 + 8 = 5 + 8, so x = 13.
Undo each operation with its inverse, applied equally to both sides, to isolate the variable.
Squaring and square-rooting are inverses only with care: sqrt(x^2) equals the absolute value of x, not x itself, because both 3 and −3 square to 9. The square root returns only the non-negative result.