'inconsistently-used' originates from Modern English, combining the adverb 'inconsistently' (from the adjective 'inconsistent' + the adverbial suffix '-ly') and the past participle 'used' of the verb 'use'.

'inconsistent' derives from Latin elements 'in-' (not) + 'consistere' (to stand together) via Old French and Middle English; 'use' comes from Old French 'user' and Latin 'uti'/'usus' and became 'use' in Middle English; the compound 'inconsistently-used' was formed in Modern English by combining these elements.

Initially the components meant 'not consistent' and 'to employ or make use of'; over time they combined to mean 'employed or applied without consistency', which is the current meaning.