Hún athugaði útsvarið því að launamiðinn var rangur.

Athugaði is the past tense of the verb að athuga, which means to check, to examine, or to look into.

In this sentence, hún athugaði means she checked.

A learner may notice that many Icelandic past-tense weak verbs end in -ði or -di, and athugaði is a good example of that pattern.

Hún is the nominative singular form of the feminine pronoun she. It is used because it is the subject of the sentence — the person doing the action.

So in:

Hún athugaði ...
= She checked ...

If the pronoun were in a different grammatical role, Icelandic would use a different case form.

The ending -ið here is the definite article attached to the noun. Icelandic usually adds the to the end of the noun instead of putting a separate word before it.

So:

• útsvar = municipal tax / tax assessment
• útsvarið = the municipal tax / the tax assessment

Also, útsvarið is a neuter noun, and in this sentence it is in the accusative singular, because it is the object of athugaði.

A useful thing to notice is that for many neuter nouns, the nominative singular and accusative singular look the same.

It is in the accusative because að athuga normally takes a direct object, and direct objects in Icelandic are often in the accusative.

So:

• Hún = subject, nominative
• athugaði = verb
• útsvarið = direct object, accusative

This is one of the most important things to get used to in Icelandic: nouns change form depending on their grammatical role.

Yes. Því að means because.

In this sentence:

... því að launamiðinn var rangur
= ... because the payslip was wrong

You may also see af því að, which also means because and is extremely common in everyday Icelandic. In many contexts, því að and af því að are very similar in meaning, though af því að is often more common in speech.

Launamiðinn means the payslip or the wage slip.

It comes from:

• launamiði = payslip
• launamiðinn = the payslip

The -inn is the attached definite article, meaning the.

This noun is masculine, and in the sentence it is in the nominative singular because it is the subject of the clause:

launamiðinn var rangur
= the payslip was wrong

Rangur is the adjective wrong/incorrect in the masculine nominative singular form.

It has to agree with the noun it describes:

• launamiðinn is masculine
• it is singular
• it is in the nominative

So the adjective must also be masculine singular nominative:

• masculine: rangur
• feminine: röng
• neuter: rangt

That is why the sentence says:

launamiðinn var rangur
= the payslip was wrong

Var is the past singular form of að vera (to be).

So:

• er = is
• var = was

In the sentence:

launamiðinn var rangur
= the payslip was wrong

Since the whole sentence is talking about a past situation, Icelandic uses var.

That is a very good question. Icelandic does often follow verb-second word order in main clauses, but after a subordinating conjunction like því að (because), the clause is a subordinate clause, and the word order is more like:

conjunction + subject + verb + complement

So:

því að launamiðinn var rangur

not:

því að var launamiðinn rangur

This is similar to the difference in some other Germanic languages, where main clauses and subordinate clauses follow different word-order patterns.

Yes. It has:

1. a main clause
   Hún athugaði útsvarið
   = She checked the tax assessment

2. a subordinate clause introduced by því að
   því að launamiðinn var rangur
   = because the payslip was wrong

So the structure is:

[main clause] + [reason clause]

This is a very common and useful pattern in Icelandic.

Yes, Icelandic often allows different word orders for emphasis, especially in the main clause.

For example, you could front the reason clause:

Því að launamiðinn var rangur, athugaði hún útsvarið.

That is grammatical, though it may sound more marked or literary depending on context. When a subordinate clause comes first, the finite verb in the main clause still follows the first element, so you get:

• first element: Því að launamiðinn var rangur
• then verb: athugaði
• then subject: hún

That is a classic verb-second pattern in the main clause.

It is a real and useful word, but it is somewhat tied to tax and official/financial contexts, so it may feel more specialized than everyday vocabulary like hús, bíll, or vinur.

A learner should understand it as a word connected with municipal tax or a tax charge/assessment. In real life, people may also use other tax-related vocabulary depending on the exact context.

So even if the grammar is the main lesson here, it is worth remembering that útsvar belongs to the semantic field of taxes and finance.

You can tell from both meaning and case/agreement.

In:

launamiðinn var rangur

• launamiðinn is in the nominative
• rangur agrees with it in masculine nominative singular
• var links the subject to a description

That tells you launamiðinn is the subject.

This is one of the helpful things about Icelandic: even when word order changes, case endings and agreement often show you what goes with what.