solution of an equation

Think of an equation as a balance scale with a mystery weight. The solution is the exact value of that mystery weight that makes both pans level — the number you can drop in for the variable so the two sides truly match.

Formally, a solution of an equation is any value of the variable that, when substituted, turns the equation into a true statement. For 2x = 10 the solution is 5, because 2 times 5 really does equal 10. A value that does not balance the equation simply is not a solution.

An equation may have one solution, several, infinitely many, or none at all. Solving an equation means finding every value that works — not just one lucky guess. The collection of all of them is the solution set.