Solomon did not remain faithful to God, and how his heart got turned from the LORD, was not at first by breaking a big commandment, like I am the LORD your God, worship Me only. That was not the first commandment Solomon broke.
The first commandment Solomon broke was, do not intermarry with the nations around about you, who do not worship the LORD God (Exo 34:12-16, Deu 7:3). Maybe he thought that since he was wise, and feared the LORD, he could intermarry with foreign wives and not be tripped up. He had been taught the word of the LORD from his youth after all.
So perhaps he thought that if he broke one of the small commands which was not one of the Ten Commandments, that it would not matter that much, as long as he did not let his heart stray from the LORD.
However, the minute he justified breaking a small command, his heart was already straying from the LORD. We can see from today’s reading, that breaking a small command leads to breaking a large one, even for the wisest man who had ever lived. But a simpleton who keeps his heart pure before the LORD all the days of his life, is wiser than Solomon.
The other thing that jumped out at me in today’s reading, was that the division of the kingdom of Israel was from the LORD. Why this might be so turned out to be a whole post on its own.
Continued in: 1 kings 11-12, division of the kingdom