A small family of words with the root word solve refer in some way to changing the physical or figurative state of something—naturally, since the Latin root of solve, solvere, means “dissolve, loosen, or solve.”
Solve itself means “find an answer, explanation, or solution for.” One who solves is a solver (rarely used in isolation but part of the common phrase “problem solver”); something solved is a solution, and solution is also defined as a liquid in which something has been dissolved.
To dissolve, in turn, is to cause something to pass into a solution (the liquid type), though it also means “destroy, disintegrate, or terminate” or “make legally void.” The noun for such an action is dissolution (not to be confused with disillusion, a synonym for disenchant as a verb and the noun disenchantment). Dissolve has also acquired a sense as a noun, used in cinematography to describe a transition achieved by gradual imposition of one image onto another, and it serves as a verb in that context as well.
A solvent, meanwhile, is a liquid used to dissolve another substance, or anything that solves a problem or eliminates or diminishes an obstacle. Solvent can also be an adjective meaning “able to dissolve” or “able to pay debts.” The adjective soluble, by contrast, has the former sense but not the latter, though it also means “able to be explained or solved.” (The antonyms are insolvent and insoluble.)
Absolve means “forgive” or “free from blame or responsibility”; an act taken to absolve someone is an absolution. (One is said to give or grant absolution.) Interestingly, the adjective absolute, meaning “complete” or “unlimited,” is related; it derives from the Latin term absolutus, meaning “absolve” or “set free.”
Resolve, too, is related: To resolve is to find an answer or solution, or to make a serious decision or take a formal vote to do something. The noun form is resolution, though one can also use resolve as a noun, employing it as a synonym for determination, and the adjectival form is resolute. (The antonyms for the adjectives resolved and resolute are unresolved and irresolute, and a lack of resolution is irresolution.)