solve

USSAHLV/sɑlv/UKSOLV/sɒlv/AUSSAWLV/sɔlv/

7 meanings of solve

1
verbtransitive
To work out how to resolve a problem or answer a question.
Engineers worked all night to solve the cooling problem.
It took the team weeks to solve the scheduling conflict.
Similarresolve, fix, crack, settle
Note
The sense once reached past puzzles and sums. Robert South has true piety solve scruples, and Thomas Tickell has God solve "the dark decrees of fate": doubts and mysteries untangled rather than problems worked out. Today the usual object is a problem, puzzle or question. The older reach still shows in the detective's sense, where what gets solved is a mystery.
2
verbtransitive
To discover who committed a crime and what their motive was.
The detective solved the murder by tracing a single phone call.
Investigators hope new evidence will help them solve the cold case.
Similarcrack, unravel, resolve
3
verbtransitive
To determine the values of the variables that make a system of equations, inequalities, or both true.
The algorithm can solve large systems of linear equations quickly.
He solved the inequality and graphed the solution set.
Note
In mathematics the object is the equation, system or inequality itself, and the outcome is the set of values that makes every condition true at once, often called the solution set. That separates it from solving for a variable, where the answer is a rearranged formula rather than a set of numbers.
4
verbtransitive
To rearrange an equation or inequality so that a chosen variable is isolated on one side, with the other side giving an expression for it.
To find velocity, solve the equation for v.
He solved the formula for temperature before plugging in the numbers.
Note
The preposition gives this sense away: you solve an equation for a variable, and the for names the quantity to be isolated. The result is an expression, not a number. Solving a formula for v leaves v alone on one side, ready to take values once the others are plugged in. In practice the equation is often left unsaid, as in the familiar "solve for x."

Less common meanings

5
verbarchaictransitive
To cause a substance to dissolve, mixing it fully into a liquid.
The apothecary solved the crystals in warm vinegar.
Gentle heat will solve the resin in oil.
Note
An old chemist's and apothecary's verb, and a narrowing of the loosening sense: dissolving loosens a solid's parts into a liquid. Where present-day usage dissolves a salt or resin, earlier writers could simply solve it. The verb is now archaic, so keep it for historical writing or deliberate period flavor. In modern technical prose, write dissolve.
6
nounarchaic
An answer or explanation, especially the resolution of a difficult or puzzling matter.
The council awaited a solve to the question of the missing funds.
The solve is this, that thou dost common grow.
1609, William Shakespeare, “Sonnet 69”
Note
A noun with two lives. In Shakespeare's Sonnet 69 (1609), "The solve is this" means the explanation of a riddle. It returns in investigators' talk as a compliment on cracking a case: "Good solve, Detective" in The Party (2014), "Nice solve, Nancy Drew" in Elodia Strain's The Dating Experiment (2017). It is at home after good or nice. In formal writing, solution is the safer word.
Good solve, Detective. That alibi never held up.
Nice solve. I would have missed the timestamp entirely.
7
verb
To loosen the parts of something, or to separate them from one another.

Practice

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Origin

The word comes from Middle English "solven," which came from the Latin verb "solvō."