Let's see exactly what happened.
Genesis 3, NIV (my comments in red)
Now the serpent was more crafty than any of the wild animals the LORD God had made. He said to the woman, "Did God really say, 'You must not eat from any tree in the garden'?"
2 The woman said to the serpent, "We may eat fruit from the trees in the garden, 3 but God did say, 'You must not eat fruit from the tree that is in the middle of the garden, and you must not touch it, or you will die.' "
This is indeed what God had said in chapter 2, verse 17, although Eve hadn't been created at the time, so she may have only heard this from Adam.
4 "You will not surely die," the serpent said to the woman. 5 "For God knows that when you eat of it your eyes will be opened, and you will be like God, knowing good and evil."
The serpent contradicts God here. He tells Eve she won't die, but will be like God, knowing good and evil.
6 When the woman saw that the fruit of the tree was good for food and pleasing to the eye, and also desirable for gaining wisdom, she took some and ate it. She also gave some to her husband, who was with her, and he ate it. 7 Then the eyes of both of them were opened, and they realized they were naked; so they sewed fig leaves together and made coverings for themselves.
This seems to be closer to what the serpent told Eve, than what God told Adam
8 Then the man and his wife heard the sound of the LORD God as he was walking in the garden in the cool of the day, and they hid from the LORD God among the trees of the garden. 9 But the LORD God called to the man, "Where are you?"
As an aside, I find it interesting that they were able to hide from God.
10 He answered, "I heard you in the garden, and I was afraid because I was naked; so I hid."
11 And he said, "Who told you that you were naked? Have you eaten from the tree that I commanded you not to eat from?"
12 The man said, "The woman you put here with me-she gave me some fruit from the tree, and I ate it."
13 Then the LORD God said to the woman, "What is this you have done?"
The woman said, "The serpent deceived me, and I ate."
14 So the LORD God said to the serpent, "Because you have done this,
"Cursed are you above all the livestock
and all the wild animals!
You will crawl on your belly
and you will eat dust
all the days of your life.
15 And I will put enmity
between you and the woman,
and between your offspring [1] and hers;
he will crush [2] your head,
and you will strike his heel."
16 To the woman he said,
"I will greatly increase your pains in childbearing;
with pain you will give birth to children.
Your desire will be for your husband,
and he will rule over you."
This was never part of the deal. God had said that eating from the tree would result in death, but this is something else that he has chosen to do to Eve to punish her. He has decided that he will actively increase the pain she feels when giving birth, as well as condemning her to be dominated by her husband.
17 To Adam he said, "Because you listened to your wife and ate from the tree about which I commanded you, 'You must not eat of it,'
"Cursed is the ground because of you;
through painful toil you will eat of it
all the days of your life.
18 It will produce thorns and thistles for you,
and you will eat the plants of the field.
19 By the sweat of your brow
you will eat your food
until you return to the ground,
since from it you were taken;
for dust you are
and to dust you will return."
Again, this is a new and deliberate punishment imposed by God, not a "consequence" of eating the fruit.
20 Adam [3] named his wife Eve, [4] because she would become the mother of all the living.
21 The LORD God made garments of skin for Adam and his wife and clothed them. 22 And the LORD God said, "The man has now become like one of us, knowing good and evil. God himself here confirms that what happened is exactly as the serpent predicted
He must not be allowed to reach out his hand and take also from the tree of life and eat, and live forever."
God obviously feels threatened by his creations' new status, so he takes action.
23 So the LORD God banished him from the Garden of Eden to work the ground from which he had been taken. 24 After he drove the man out, he placed on the east side [5] of the Garden of Eden cherubim and a flaming sword flashing back and forth to guard the way to the tree of life.
God deliberately removes Adam and Eve from access to the tree of life. Not an inevitable consequence of their actions but an active and deliberate punishment by God.
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A straightforward reading of the text clearly shows that it was God who lied, not the serpent and that he punished Adam and Eve. They did not die. They were not poisoned by eating the fruit but rather were punished by God for disobeying him. God apparently became afraid because the man had become like him and banished him from the garden so that he could not live forever. He also cursed Adam and Eve, making their lives miserable and more difficult. None of this was a direct consequence of their actions. It was punishment by an insecure god.