word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."
In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
1620s, "given to profuse expenditure," from expense (n.) + -ive. Meaning "costly, requiring profuse expenditure" is from 1630s. Earlier was expenseful (c. 1600). Expenseless was in use mid-17c.-18c., but there seems now nothing notable to which it applies, and the dictionaries label it "obsolete." Related: Expensively; expensiveness.
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Harper, D. (n.d.). Etymology of inexpensive. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/inexpensive