Jesus explains very clearly that murder is the result of anger toward one another. While murder is unapologetically horrible, it is the anger within one's mind toward another that literally murders the image of God that is in all of humanity. The right way to obey the Law of God is to reconcile with someone whom we have anger toward. In doing so, we imitate Christ and imitate the true gospel. Just as we forgive and reconcile with one another, God first reconciled us to Himself through Christ and forgave us therefore putting away HIS wrath against our sin.
The Sermon on the Mount from Jesus teaches about what the true citizenship of the Kingdom of Heaven is. In this text, Jesus begins to explore the damage that the extra-canonical teachings of the Rabbinic Law has done to the original and purest intent of God's Law. The "you have heard that it was said" passages are partly from the Decalogue of Moses (10 Commandments) and also from the Levitical law of the Old Testament Pentateuch. Jesus now takes the literal expectations of obedience imposed by the Rabbinic teachers and uncovers God's design that the Law was to lead to a change of the inner heart.