IT IS POSSIBLE TO NOT BREAK ANY OF THE TEN COMMANDMENTS.
According to the Bible, Jesus of Nazareth followed them and did not break one.
According to Jesus, his cousin John The Baptist is declared to be the greatest of all men, presumably because he had not broken any of the Ten Commandments up until that time.
Truly, I say to you, among those born of women there has arisen no one greater than John the Baptist. Yet the one who is leastinthekingdom of Heaven is greater than he. (Matthew 11:11)
The answer to the question is YES, it is possible to follow all the Ten Commandments and not break one.
However, the likelihood of a person keeping the Ten Commandments without breaking one is remote.
If a person is born and raised in a cave or some location where coveting never becomes an issue and pubescent concerns never cause a problem, then a person could live without breaking one of the Ten Commandments.
The one difficulty that each one of us has today is that our bodies are affected by sin. We could live for six hundred years (as did the righteous Shem after the flood), or even 969 years (as Methuselah did before the flood), but overcoming death is the problem. Even if we never sinned once, biological death is the result of the fall.
John the Baptist was overshadowed or protected by the Holy Spirit from birth.
But the angel said to him, “Do not be afraid, Zechariah, for your prayer has been heard, and your wife Elizabeth will bear you a son, and you shall call his name John. And you will have joy and gladness, and many will rejoice at his birth, for he will be great before the Lord. And he must not drink wine or strong drink, and he will be filled with the Holy Spirit, even from his mother's womb. (Luke 1:13-15)
Moreover, we learn that those who become members of the Kingdom of Heaven (i.e. Kingdom of God) are greater than John the Baptist.
Because they have overcome death.
Unless a person accepts that Jesus died and paid the price for sin and provided the means by which a person can be born into eternal life, rather than the temporal biological life that is known from being born into this world, there is a judgment: where each one will be given his or desire.
Those who desire to blame and abuse and reject God and trust their own self-righteousness (as opinionated fools) rather than reason with the Almighty Lord God as to why they exist and what eternity has for them, are considered willful individuals who refuse to take responsibility for themselves and their actions. They fail their moral responsibility of loving their neighbor as themselves, not to mention seeking out the truth for their existence.
Call such people arrogant, ignorant, fools, if you like. They hate hearing the truth. But then again the truth is always hated by those who do not want to admit it; especially, by those who have no power over death but think their assumptions (and their opinions based on those assumptions) are superior to the knowledge possessed by the Creator.
Jesus pointed out what was required to get into the Kingdom of God. But in such a way that unless you are truly humble and honest with yourself, you would miss it.
For I tell you, unless your righteousness exceeds that of the scribes and Pharisees, you will never enter the kingdom of heaven. (Matthew 5:20)
Hypocrites are the ones who are judged as unworthy.
What is a hypocrite?
Some people call them cockroaches. But a hypocrite is merely someone who bears false witness and thinks it does not matter. You know the kind. As long as it is good for me: up yours, Jack! And up yours, Jill!! Only, usually, they are not so blunt. Hypocrites do it with finesse. They like to leave you thinking you are special; meanwhile, they are organizing the digging of your grave behind your back.
If you are interested in understanding the purpose of the Ten Commandments and why they ought to be acknowledged and understood with all their implications, read the FREE book: The Only Words Written By The Finger of God.
From reading some of the comments to this question, by reading The Only Words Written By The Finger of God, you will be enlightened, indeed. Those who have read the complete book say that they are amazed at how much more enlightened they have become as to the reason the Ten Commandments exist. How important it is for us to understand them, even if we fail to keep them, and not merely pay lip service to the only words that were written by God Himself.