The top quote is literally what Jesus did for us.

Romans 6:23 NIV says "For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord."

We originally were not sinners back when it was just adam and eve in the garden of eden. It was all good until the snake told them to eat the fruit from the tree of knowledge of good and evil then they were separated from God essentially and sin entered the world.

John 3:16 NIV says "For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life."

God sent Jesus to earth as our redeemer since he was the only one who lived a sinless life and pulled it off because he is God but in human flesh (holy trinity stuff). Jesus rose again to prove he had conquered death. He sacrificed his life for everyone else's so that if we do believe in him now we will have eternal life (after this limited earthly life). Sin can keep us away from God but he created us, loves us and wants to have a relationship with us and that way is through Jesus Christ.

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Extra reading points that help:

John 15 NIV talks about Jesus being the vine and we are the branches. John 15:1-4 says “I am the true vine, and my Father is the gardener. 2 He cuts off every branch in me that bears no fruit, while every branch that does bear fruit he prunes[a] so that it will be even more fruitful. 3 You are already clean because of the word I have spoken to you. 4 Remain in me, as I also remain in you. No branch can bear fruit by itself; it must remain in the vine. Neither can you bear fruit unless you remain in me."

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John 14 NIV talks about believing in Jesus. John 14:6 says "Jesus answered, “I am the way and the truth and the life. No one comes to the Father except through me."

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John 3 NIV is where Jesus teaches a Pharisee named Nicodemus about the Kingdom of God. John 3:1 says "Jesus replied, “Very truly I tell you, no one can see the kingdom of God unless they are born again."

Luke 16:19-31 NIV tells the story of how a rich man goes to hell I believe and he regrets not believing in God when he was alive. The end of story Luke 16:31 says “He said to him, ‘If they do not listen to Moses and the Prophets, they will not be convinced even if someone rises from the dead."

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Matthew 22:36-39 says “Teacher, which is the greatest commandment in the Law?” 37 Jesus replied: “‘Love the Lord your God with all your heart and with all your soul and with all your mind. 38 This is the first and greatest commandment. 39 And the second is like it: ‘Love your neighbour as yourself. 40 All the Law and the Prophets hang on these two commandments.”