אל תצאי מהבית בלי שתבדקי אם הכרטיס בארנק.

In Hebrew, אל + future tense is the normal way to make a negative command:

• אל תצאי = don’t go out / don’t leave
• אל תבדקי = don’t check

By contrast, לא תצאי usually means you will not go out / you won’t leave, which is a statement about the future, not a command.

So here אל תצאי is the correct form for telling someone not to do something.

That -י shows the sentence is addressed to one female.

Both verbs are 2nd person feminine singular:

• תצאי = you (fem.) will go out
• תבדקי = you (fem.) will check

If you were speaking to a man, you would say:

• אל תצא מהבית בלי שתבדוק אם הכרטיס בארנק.

מהבית means from the house or more naturally out of the house / from home.

It is made of:

• מ־ = from
• הבית = the house / the home

So:

• מהבית = from the house

In Hebrew, לצאת מהבית is a very common way to say to leave the house / go out from home.

Here ש־ introduces a clause after בלי.

The pattern is:

• בלי ש + future verb

This means without someone doing something.

So:

• בלי שתבדקי = without you checking

Literally, it is something like without that you check, but in natural English it is just without checking or without you checking.

This is a very common Hebrew structure.

Yes. Both are possible.

• אל תצאי מהבית בלי לבדוק אם הכרטיס בארנק.
• אל תצאי מהבית בלי שתבדקי אם הכרטיס בארנק.

The version with בלי לבדוק uses the infinitive to check and can feel a bit more general or compact.

The version with בלי שתבדקי feels a bit more explicit and personal, because it directly refers to you doing the checking.

Both are natural.

Here אם means whether, even though English often also uses if.

In this sentence, the idea is not a condition like If the card is in the wallet, then...
Instead, it is an indirect yes/no question:

• check if / whether the card is in the wallet

So:

• אם הכרטיס בארנק = whether the card is in the wallet

This is a very common use of אם after verbs like check, see, know, ask, and so on.

It is simply not written, because Hebrew usually leaves out the verb to be in the present tense.

So:

• הכרטיס בארנק literally = the card in the wallet
• natural English = the card is in the wallet

This is normal Hebrew grammar.
The same thing happens in sentences like:

• הוא בבית = He is at home
• הספר על השולחן = The book is on the table

Because הכרטיס is not the direct object here. It is the subject of the clause הכרטיס בארנק.

Compare:

• תבדקי את הכרטיס = check the card
  Here הכרטיס is a direct object, so you need את.

But in your sentence:

• תבדקי אם הכרטיס בארנק = check whether the card is in the wallet

You are not checking the card directly. You are checking whether a situation is true.
So הכרטיס is the subject of the embedded clause, and את is not used.

Literally, בארנק means in the wallet:

• ב־ = in
• הארנק = the wallet

So the literal meaning is definite: in the wallet.

In real usage, though, Hebrew often leaves possession unstated when it is obvious from context. So depending on the situation, בארנק may naturally be understood as in your wallet.

If you want to say it explicitly, you can say:

• בארנק שלך = in your wallet

Yes. כרטיס is a broad word and can mean either card or ticket, depending on context.

For example:

• כרטיס אשראי = credit card
• כרטיס נסיעה = travel ticket / transit card
• כרטיס להופעה = ticket for a show

So if the meaning has already been given to the learner, that is important, because the Hebrew word by itself can be interpreted in more than one way.

Because Hebrew often uses future forms where English uses commands.

For positive commands, Hebrew has imperative forms, but in everyday speech people often use future forms as commands. For negative commands, אל + future is the standard pattern:

• אל תצאי = don’t go out

Also, after certain words like בלי ש־, Hebrew commonly uses future forms in the subordinate clause:

• בלי שתבדקי = without checking / without you checking

So even though the meaning is a present instruction, the grammar uses future-style verb forms.

To one man:

• אל תצא מהבית בלי שתבדוק אם הכרטיס בארנק.

To several people:

• אל תצאו מהבית בלי שתבדקו אם הכרטיס בארנק.

So the main changes are in the verb forms:

• feminine singular: תצאי / תבדקי
• masculine singular: תצא / תבדוק
• plural: תצאו / תבדקו