isolating the variable

Isolating the variable is like peeling an onion to reach its center. The variable is wrapped in layers of operations — added numbers, multipliers — and you strip them away one at a time until the variable sits bare on one side, with its value laid out on the other.

You undo each layer using its inverse operation, and you do it to both sides so the equation stays balanced. Undo addition with subtraction, multiplication with division. Crucially, peel in reverse order: deal with what is added or subtracted before what multiplies or divides.

Once the variable stands alone — x = something — you have solved the equation, because the right side is its value. This single skill is the engine behind almost every linear-equation solution and behind formula rearrangement too.