Jeremiah 11:10
They are turned back to the iniquities of their forefathers, which refused to hear my words; and they went after other gods to serve them: the house of Israel and the house of Judah have broken my covenant which I made with their fathers.
Jeremiah 11:10 stands among the prophecies of Jeremiah 3 to 21 whose meaning is very clear in awful denunciation against sin, showing sorrow of heart over transgression and making a touching appeal to return to God amid utter lack of response from the mass of the people. The verse means the house of Israel and the house of Judah turned back to the iniquities of their forefathers, refusing to hear God's words and going after other gods to serve them, and by turning from God in this way they broke His covenant.
The covenant they broke was the covenant God made with their fathers when He brought them out of Egypt. About six hundred years before Christ, in the days when the new covenant was promised, the Ten Commandments proclaimed by the Lord who brought Israel out of Egypt were still acknowledged as His law and as the condition of the old covenant, so the old covenant was still in force then. If the Ten Commandments were not His law at that time the old covenant would have been a nullity six hundred years before Christ, and therefore the law God promised to put in minds and hearts in the new covenant is the Ten Commandments, since no other law is intimated where the new covenant is spoken of.
By breaking the covenant Israel and Judah forfeited its blessings, so God regarded them not and justly finds fault with them, announcing that forfeiture as the breaking off of many branches of their olive tree, the good olive tree representing the family of Abraham. This failure explains the need for a second covenant, foretold a few years later about six hundred years before Christ and before the birth of Christ. The first covenant was established upon promises conditioned on perfect obedience that fallen man could not meet, so because Israel broke it place was sought for a second and better covenant established upon better promises, and from Jeremiah's time the first covenant was old and ready to vanish away until Christ took away the first to establish the second. The first covenant made at the departure from Egypt and the new covenant made at the time of Christ's ministry and death were both made with the same Hebrew people, so by the new covenant those broken off for breaking the covenant can be grafted in again, and the Gentiles with them, until the tree stands complete as the twelve tribes of the Israel of God.