Wrong.
Romans 11:6-7King James Version (KJV)
6 And if by grace, then is it no more of works: otherwise grace is no more grace. But if it be of works, then it is no more grace: otherwise work is no more work.
7 What then? Israel hath not obtained that which he seeketh for; but the election hath obtained it, and the rest were blinded.
If eternal security is wrong then none of these passages make any sense: John 10:27-30; I Peter 1:5; Ephesians 4:30; Romans 8:35-39; John 5:24
Salvation is by FAITH alone. It's asked ONE SINGLE TIME in the Bible "what must I do to be saved?" The answer is "believe ON the Lord Jesus and thou shalt be saved."
Believe ON. That means you're trusting ONLY in Jesus Christ to get to Heaven. Trusting in anything else will send you to hell. Believe that Jesus will take you to heaven when you die, trust only in Him for your salvation and you will be 100% sure about Heaven.
Jesus says you have eternal life if you believe on Him (John 6:47) - if eternal life could be lost then it was never eternal and God is a liar. Good works are great and everyone should do good works, but that doesn't get to you Heaven. Faith alone does, and it says so countless times in the Bible.
Actually Paul is more referring to boasting in those verses. Ephesians 2:8-10 "For by grace you have been saved through faith, and that not of yourselves;
it is the gift of God, 9 not of works, lest anyone should boast. 10 For we are His workmanship, created in Christ Jesus for good works, which God prepared beforehand that we should walk in them."
In James 2:14-24
What
does it profit, my brethren, if someone says he has faith but does not have works? Can faith save him? 15 If a brother or sister is naked and destitute of daily food, 16 and one of you says to them, “Depart in peace, be warmed and filled,” but you do not give them the things which are needed for the body, what
does it profit? 17 Thus also faith by itself, if it does not have works, is dead.
18 But someone will say, “You have faith, and I have works.” Show me your faith without your works, and I will show you my faith by my works. 19 You believe that there is one God. You do well. Even the demons believe—and tremble! 20 But do you want to know, O foolish man, that faith without works is dead? 21 Was not Abraham our father justified by works when he offered Isaac his son on the altar? 22 Do you see that faith was working together with his works, and by works faith was made perfect? 23 And the Scripture was fulfilled which says, “Abraham believed God, and it was accounted to him for righteousness.” And he was called the friend of God. 24 You see then that a man is justified by works, and not by faith only.
Jesus Himself says in many places to obey His teachings Luke 6:46 But why do you call Me ‘Lord, Lord,’ and not do the things which I say? 47 Whoever comes to Me, and hears My sayings and does them, I will show you whom he is like: 48 He is like a man building a house, who dug deep and laid the foundation on the rock. And when the flood arose, the stream beat vehemently against that house, and could not shake it, for it was founded on the rock. 49 But he who heard and did nothing is like a man who built a house on the earth without a foundation, against which the stream beat vehemently; and immediately it fell. And the ruin of that house was great.”
John 14:23-24 Jesus answered and said to him, “If anyone loves Me, he will keep My word; and My Father will love him, and We will come to him and make Our home with him. 24 He who does not love Me does not keep My words; and the word which you hear is not Mine but the Father’s who sent Me.
Faith is proven through one's actions, not their mind. If you think you don't have to abide by Christ's teachings and have "faith" in Him and be saved then you will become like those described in Mat 7:21-23 Not everyone who says to Me, ‘Lord, Lord,’ shall enter the kingdom of heaven, but he who does the will of My Father in heaven. 22 Many will say to Me in that day, ‘Lord, Lord, have we not prophesied in Your name, cast out demons in Your name, and done many wonders in Your name?’ 23 And then I will declare to them, ‘I never knew you; depart from Me, you who practice lawlessness!’
Lawlessness is sin, in other translations it says iniquity which is sin. If we are practicing or living a sinful lifestyle and say we "believe" in God. Christ will tell us He never knew us according to this verse. So yes, eternal life can be lost if you lose Christ in your life, which is to not live according to His Word.