Jesus has plainly said that repentance means ceasing to sin:
42 Behold, he who has repented of his sins, the same is forgiven, and I, the Lord, remember them no more.
43 By this ye may know if a man repenteth of his sins—behold, he will confess them and forsake them. (D&C 58)
He has plainly said that only those who obey his commandments are forgiven of their sins:
Who am I that made man, saith the Lord, that will hold him guiltless that obeys not my commandments? (D&C 58:30)
We have been told plainly what it will be like in the resurrection for those who do not keep all of his commandments:
3 …Do ye suppose that ye shall dwell with him under a consciousness of your guilt? Do ye suppose that ye could be happy to dwell with that holy Being, when your souls are racked with a consciousness of guilt that ye have ever abused his laws?
4 Behold, I say unto you that ye would be more miserable to dwell with a holy and just God, under a consciousness of your filthiness before him, than ye would to dwell with the damned souls in hell.
5 For behold, when ye shall be brought to see your nakedness before God, and also the glory of God, and the holiness of Jesus Christ, it will kindle a flame of unquenchable fire upon you. (Mormon 9)
He came to earth to show men it was possible to keep all of God's commandments:
7 Know ye not that he was holy? But notwithstanding he being holy, he showeth unto the children of men that, according to the flesh he humbleth himself before the Father, and witnesseth unto the Father that he would be obedient unto him in keeping his commandments.
8 Wherefore, after he was baptized with water the Holy Ghost descended upon him in the form of a dove.
9 And again, it showeth unto the children of men the straitness of the path, and the narrowness of the gate, by which they should enter, he having set the example before them.
10 And he said unto the children of men: Follow thou me. Wherefore, my beloved brethren, can we follow Jesus save we shall be willing to keep the commandments of the Father? (2 Nephi 32)
If you sin knowingly, you are ineligible for salvation.
For if we sin wilfully after that we have received the knowledge of the truth, there remaineth no more sacrifice for sins…. (Hebrews 10:26)
Therefore God gave unto them commandments, after having made known unto them the plan of redemption, that they should not do evil...for on such the plan of redemption could have no power, for the works of justice could not be destroyed, according to the supreme goodness of God. (Alma 12:32)
For behold, there is a wo pronounced upon him who listeth to obey that spirit; for if he listeth to obey him, and remaineth and dieth in his sins, the same drinketh damnation to his own soul; for he receiveth for his wages an everlasting punishment, having transgressed the law of God contrary to his own knowledge. (Mosiah 2:33)
And I say unto you again that he cannot save them in their sins; for I cannot deny his word, and he hath said that no unclean thing can inherit the kingdom of heaven; therefore, how can ye be saved, except ye inherit the kingdom of heaven? Therefore, ye cannot be saved in your sins. (Alma 11:37)
But remember that he that persists in his own carnal nature, and goes on in the ways of sin and rebellion against God, remaineth in his fallen state and the devil hath all power over him. Therefore, he is as though there was no redemption made, being an enemy to God; and also is the devil an enemy to God. (Mosiah 16:5)
And he hath power given unto him from the Father to redeem them from their sins because of repentance; therefore he hath sent his angels to declare the tidings of the conditions of repentance, which bringeth unto the power of the Redeemer, unto the salvation of their souls. (Helaman 5:11)
And now, verily I say unto you, I, the Lord, will not lay any sin to your charge; go your ways and sin no more; but unto that soul who sinneth shall the former sins return, saith the Lord your God. (D&C 82:7)
You have the power not to sin. You can obey everything God tells you, and you must if you desire to be saved and live with him in heaven.
8 Now, the decrees of God are unalterable; therefore, the way is prepared that whosoever will may walk therein and be saved.
9 And now behold, my son, do not risk one more offense against your God upon those points of doctrine, which ye have hitherto risked to commit sin. (Alma 41)
And it came to pass that I, Nephi, said unto my father: I will go and do the things which the Lord hath commanded, for I know that the Lord giveth no commandments unto the children of men, save he shall prepare a way for them that they may accomplish the thing which he commandeth them. (1 Nephi 3:7)
There hath no temptation taken you but such as is common to man: but God is faithful, who will not suffer you to be tempted above that ye are able; but will with the temptation also make a way to escape, that ye may be able to bear it. (1 Corinthians 10:13)
Many people have shown us that sinlessness is possible through their own example. You are left without excuse.
Principle among all examples of sinless people is Jesus Christ. "For we have not an high priest which cannot be touched with the feeling of our infirmities; but was in all points tempted like as we are, yet without sin." (Hebrews 4:15)
Noah: "...Noah was a just man and perfect in his generations, and Noah walked with God." (Genesis 6:9)
An innumerable number: "22 But ye are come unto mount Sion, and unto the city of the living God, the heavenly Jerusalem, and to an innumerable company of angels, 23 To the general assembly and church of the firstborn, which are written in heaven, and to God the Judge of all, and to the spirits of just men made perfect," (Hebrews 12)
There is no darkness in God, and no unclean thing can dwell in his presence. As long as there is darkness in you, you can't be with him. If you come to him, he will show you the darkness that remains in you, or how you are different from him. He will reveal to you, line upon line, how you can be more like him, or in other words how you can more fully take upon you the name of Christ.
As he reveals more to you, you must reconcile yourself to him by remaining faithful to the new information he shows you. If you sin by disobeying the new information, you remove yourself from his promises, and you must repent and renew your dedication to the Lord.
To be perfect in Christ is not to be excused of sins you know you are committing, but those you do not yet know of because you are still learning more about him. To be perfect in Christ, you must actually forsake all sin you know of:
Yea, come unto Christ, and be perfected in him, and deny yourselves of all ungodliness; and if ye shall deny yourselves of all ungodliness, and love God with all your might, mind and strength, then is his grace sufficient for you, that by his grace ye may be perfect in Christ; and if by the grace of God ye are perfect in Christ, ye can in nowise deny the power of God. (Moroni 10:32)
When you actually believe Jesus, you actually do what he says. This starts with baptism, where you promise to God to keep all of his commandments, even unto death. Baptism is "covenant with God that ye should be obedient unto the end of your lives." (Mosiah 5:8)
If you knowingly break a commandment, you have broken the covenant of baptism, and you are in willful rebellion against God. You must repent and renew your commitment to God.
If you believe in Jesus, you will act, think, and desire as he did and does, as far as you understand. If you do not act, think, and desire as he did and does, you do not believe in him.
Verily I say unto you, all among them who know their hearts are honest, and are broken, and their spirits contrite, and are willing to observe their covenants by sacrifice—yea, every sacrifice which I, the Lord, shall command—they are accepted of me. (D&C 97:8)