solution set
A single solution answers “does this one value work?” The solution set answers the bigger question: “which values work, all of them?” It is the complete roster of every number that satisfies the equation or inequality — no member missing, no impostor included.
It is written using set notation. A finite list goes in braces, like {2, −3}; an empty solution set is written ∅, the symbol for nothing at all. For inequalities, where the answer is usually a whole range, interval notation or a number-line picture is more compact than listing.
Thinking in terms of the solution set keeps you honest. An equation with one solution has a one-element set; an identity has the set of all real numbers; a contradiction has the empty set. Naming the set forces you to account for how many solutions there truly are.
The solution set of |x| = 3 is {−3, 3}; of x < 1 it is (−∞, 1).
Equations often give a list; inequalities give a range.