Problem: Leviticus 16:30 commanded that a fast should be kept in connection with the Day of Atonement. However, Solomon did not observe a fast in connection with the Day of Atonement celebration that he held here in 2 Chronicles 7:8–10 (cf. also 1 Kings 8:65–66).
Solution: First of all, it cannot be shown from the texts that Solomon failed to keep the fast as Leviticus had commanded. The text declares that Solomon celebrated for “fourteen days” (1 Kings 8:65). It is quite possible that on the actual Day of Atonement, which was the tenth day of the seventh month, that Solomon did keep the fast.
Furthermore, strictly speaking, the Leviticus passage does not use the word “fast.” It simply says they were to “afflict their souls” (Lev. 16:29). This could mean to keep the celebration with appropriate solemnity, not necessitating that no food be eaten. It does forbid that no work be done (v. 29), but it does not really say that no food could be eaten, although this has been the general understanding of the phrase throughout Jewish history.
Finally, even if it could be shown that Solomon did not keep the Law correctly, all this would prove is that Solomon erred in not keeping the fast. It would not show that the Bible erred in recording what Solomon in truth did.