الدخل الشهري مهم لميزانية الأسرة.

A careful MSA pronunciation is:

ad-dakhlu ash-shahriyyu muhimmun limīzāniyyati al-usrati

A more natural everyday pronunciation, without full case endings, is often closer to:

ad-dakhl ash-shahri muhimm li-mīzāniyyat al-usra

A few notes:

• الدخل = ad-dakhl
  The ل in ال is pronounced here because د is a sun letter, so al- becomes ad-.
• الشهري = ash-shahriyy
  Same idea: ش is also a sun letter, so al- becomes ash-.
• مهم = muhimm
• لميزانية = li-mīzāniyya...
• الأسرة = al-usra

So the doubled consonants in ad-dakhl, ash-shahri, and muhimm are important to hear and pronounce.

Because in Arabic, the present tense of to be is usually not expressed in simple equational sentences.

So:

• الدخل الشهري مهم
  literally: the monthly income important
• natural English: The monthly income is important

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

If you wanted the past, then Arabic would use a verb, for example:

• كان الدخل الشهري مهمًا
  The monthly income was important.

Because الشهري is an adjective describing الدخل, and Arabic adjectives normally follow the noun and agree with it.

Here:

• الدخل = the income
• الشهري = monthly

Since الدخل is definite (the income), the adjective must also be definite:

• الدخل الشهري = the monthly income

This is a key Arabic pattern:

• noun + adjective
• and the adjective agrees in:
  • definiteness
  • gender
  • number
  • case (in fully vowelled Arabic)

So Arabic says literally:

• the income the-monthly

but in English we translate it as:

• the monthly income

الشهري means monthly.

It comes from شهر (month) and is turned into an adjective using the common nisba pattern, which often gives the meaning related to or pertaining to.

So:

• شهر = month
• شهري = monthly

Other examples of this pattern are:

• يوم = day → يومي = daily
• سنة = year → سنوي = annual / yearly

So الدخل الشهري means monthly income.

Because مهم here is not an adjective inside the noun phrase. It is the predicate of the sentence.

Compare these two ideas:

1. Inside a noun phrase

   • الدخل الشهري = the monthly income
     Here الشهري is an adjective modifying الدخل, so it must match it in definiteness.

2. As the predicate of the sentence

   • الدخل الشهري مهم = The monthly income is important
     Here مهم is not just modifying the noun; it is telling you something about it. So it is normally indefinite.

This is very common in Arabic:

• الولد طويل = The boy is tall
• الكتاب جديد = The book is new

So مهم is indefinite because it is the predicate, not because anything is wrong.

The prefix لـ usually means for, to, or belonging to, depending on context.

In this sentence, مهم لميزانية الأسرة means:

• important for the family budget

So:

• مهم = important
• لـ = for
• ميزانية الأسرة = the family budget

This لـ shows what something is important for or to.

Similar examples:

• هذا مفيد للصحة = This is beneficial for health
• الرياضة مهمة للأطفال = Exercise is important for children

Because Arabic is using an iḍāfa construction, often translated as X of Y or Y's X.

Here:

• ميزانية = budget
• الأسرة = the family

Together:

• ميزانية الأسرة = the budget of the family = the family budget

In an iḍāfa:

1. The first noun usually does not take ال.
2. The second noun can be definite or indefinite.
3. The whole phrase becomes definite if the second noun is definite.

So:

• ميزانية الأسرة = the family budget / the budget of the family

This is one of the most important structures in Arabic.

Because الأسرة means the family, and in the iḍāfa construction it makes the whole phrase definite.

Compare:

• ميزانية أسرة = a family budget
• ميزانية الأسرة = the family budget

Since الأسرة is definite, the whole phrase ميزانية الأسرة is also definite.

So in this sentence, we are talking about a specific kind of budget: the family budget.

It is a nominal sentence:

• الدخل الشهري = the topic / subject
• مهم لميزانية الأسرة = the comment / predicate

More traditionally:

• الدخل الشهري = mubtadaʾ (the thing being talked about)
• مهم لميزانية الأسرة = khabar (what is said about it)

So the sentence structure is:

• [subject/topic] + [predicate]

Literally:

• The monthly income — important for the family budget.

Natural English:

• The monthly income is important for the family budget.

Yes, in fully vowelled formal Arabic there are case endings, even though they are often not written in normal text and are often dropped in pause.

The full grammatical form would be:

الدخلُ الشهريُّ مهمٌّ لميزانيةِ الأسرةِ

A rough breakdown:

• الدخلُ → nominative
• الشهريُّ → nominative, agreeing with الدخل
• مهمٌّ → nominative as the predicate
• ميزانيةِ → genitive after لـ
• الأسرةِ → genitive as the second term of the iḍāfa

In ordinary reading, many learners first meet the sentence without these endings:

الدخل الشهري مهم لميزانية الأسرة

That is completely normal.

Because in Arabic, adjectives usually come after the noun they describe.

So:

• دخل شهري = monthly income
• literally: income monthly

This is the normal Arabic order.

More examples:

• كتاب جديد = a new book
• الكتاب الجديد = the new book
• سيارة كبيرة = a big car

English usually puts the adjective first, but Arabic usually puts it after the noun.

Not very naturally. A word-for-word rendering would be something like:

• the-income the-monthly important for-budget the-family

That shows the Arabic structure, but it is not good English.

A better natural English translation is:

• The monthly income is important for the family budget.

This sentence is a good example of why Arabic and English organize information differently:

• Arabic: noun first, then adjective
• Arabic: no present-tense is
• Arabic: possession often shown through iḍāfa
• English: adjective before noun, and usually an expressed is

Yes, Arabic could say دخل الأسرة الشهري, but that means something slightly different:

• الدخل الشهري = the monthly income
• دخل الأسرة الشهري = the family's monthly income

So the original sentence talks about monthly income in a more general sense, while دخل الأسرة الشهري explicitly says that the income belongs to the family.

That distinction may or may not matter depending on context, but grammatically they are not exactly the same phrase.