Solomon"s sin in going after other gods was the quintessence of covenant infidelity. David had sinned against God deliberately on occasion when tempted ( 2 Samuel 11), but his heart remained devoted to Yahweh. His sin was not as serious as Solomon"s was (cf. Deuteronomy 6:5). [source][source][source]
"One of the most puzzling aspects of the life of Solomon was the fact that Hebrews , the wisest of all men, could be so foolish, particularly in the last years of his reign. What must be understood is that the very basis, in fact, the essence of biblical wisdom is to fear God ( Proverbs 1:7). It was precisely when Solomon neglected this principle that he began the slippery slope to folly ( 1 Kings 11:9)." [1][source]
The one tribe Solomon"s heir would retain was Judah. Judah had absorbed the tribe of Simeon almost entirely by this time, though some Israelites from Simeon had moved north ( 2 Chronicles 15:9; 2 Chronicles 34:6). [source][source][source]