مضخة الهواء قرب الدراجة المستعملة.

In Arabic, a present-tense sentence often has no spoken or written copula.

So:

مضخة الهواء قرب الدراجة المستعملة
literally looks like:

The air pump near the used bicycle

but it means:

The air pump is near the used bicycle.

This is called a nominal sentence. In the present tense, Arabic usually leaves out is / are.

If you wanted past tense, you would usually add a verb such as كان:

• كانت مضخة الهواء قرب الدراجة المستعملة = The air pump was near the used bicycle.

Because مضخة الهواء is an iḍāfa construction, often called a construct phrase.

In an iḍāfa:

• the first noun does not take الـ
• the second noun is in the genitive
• the whole phrase becomes definite or indefinite based on the second noun

So here:

• مضخة = pump
• الهواء = the air

Together:

• مضخة الهواء = the air pump

Even though مضخة has no الـ, the whole phrase is definite because الهواء is definite.

A useful comparison:

• مضخة هواء = an air pump
• مضخة الهواء = the air pump

قرب here means near and functions like a word of location. In traditional grammar, it is often treated as a ẓarf (adverbial noun of place), but for a learner it is fine to think of it as behaving very much like a preposition.

So:

• قرب الدراجة = near the bicycle

The noun after it is treated as genitive:

• الدراجةِ

A very common alternative is:

• بالقرب من الدراجة المستعملة

That also means near the used bicycle, and many learners find it easier because it works more obviously like a prepositional phrase.

Because it agrees with الدراجة, and دراجة is a feminine singular noun.

Arabic adjectives agree with the noun they describe in:

• gender
• number
• definiteness
• case

So:

• الدراجة = feminine singular definite
• المستعملة = feminine singular definite

That is why the adjective ends with ة and appears in the feminine form.

The masculine form would be:

• المستعمل

For example:

• الكتاب المستعمل = the used book
• الدراجة المستعملة = the used bicycle

Because of its position.

In Arabic, an adjective normally comes right after the noun it describes.

Here we have:

• قرب الدراجة المستعملة

So المستعملة follows الدراجة, which shows that it describes the bicycle.

If you wanted to say the used air pump, you would normally say:

• مضخة الهواء المستعملة

There, المستعملة comes after the whole iḍāfa phrase مضخة الهواء, so it describes the air pump.

So the sentence as written is understood as:

• The air pump is near the used bicycle

not:

• The used air pump is near the bicycle

Because adjectives in Arabic match the noun in definiteness as well.

So if the noun is definite, the adjective must also be definite.

Here:

• الدراجة = the bicycle
• المستعملة = the used

Together:

• الدراجة المستعملة = the used bicycle

If the noun were indefinite, the adjective would also be indefinite:

• دراجة مستعملة = a used bicycle

This matching is very important in Arabic and is one of the clearest signs that a word is acting as an adjective.

A fully vocalized version would be:

مِضَخَّةُ الهَوَاءِ قُرْبَ الدَّرَّاجَةِ المُسْتَعْمَلَةِ

The grammar is:

• مِضَخَّةُ: nominative, because it is the subject of the nominal sentence
• الهَوَاءِ: genitive, because it is the second part of the iḍāfa
• قُرْبَ: accusative as a ẓarf of place
• الدَّرَّاجَةِ: genitive after قرب
• المُسْتَعْمَلَةِ: genitive because it is an adjective describing الدراجة

In normal unvocalized writing, these case endings are not shown, which is why you usually see:

مضخة الهواء قرب الدراجة المستعملة

Because د is a sun letter.

When الـ is attached to a word beginning with a sun letter, the l sound of الـ is not pronounced. Instead, the first consonant of the noun is doubled.

So:

• الدراجة is pronounced ad-darrāja

By contrast, الهواء begins with ه, which is a moon letter, so the l sound stays:

• الهواء = al-hawāʾ

This is a pronunciation rule only. In writing, both still use الـ.

The final ة is called tāʾ marbūṭa.

Its pronunciation depends on context:

• At a pause, it is usually pronounced like -a or -ah
• When grammatical endings are pronounced, it sounds like t

So if you stop on the word:

• مضخة ≈ miḍakhkha
• الدراجة ≈ ad-darrāja
• المستعملة ≈ al-mustaʿmala

But in fully inflected reading:

• مِضَخَّةُ
• الدَّرَّاجَةِ
• المُسْتَعْمَلَةِ

you can hear the t sound before the case ending.

This is very common in formal Arabic: the ة behaves like t when connected grammatically, but like a/ah when you stop.

Yes. Both are correct.

• قرب الدراجة المستعملة = near the used bicycle
• بالقرب من الدراجة المستعملة = near the used bicycle

The second version is a little more explicit and often feels easier for learners because it clearly uses a preposition-like pattern:

• بـ
• القرب
• من

The version in your sentence is shorter and perfectly natural in formal Arabic.

So both are good, but قرب + noun is a useful pattern to learn because it is very common.