kubi ga itai toki ha, muri ni undousinai hou ga ii desu.

Because 痛い is an i-adjective, not a verb like to hurt in English.

In Japanese, the thing that feels painful is usually marked with が, so:

• 首が痛い = My neck hurts / The neck is painful

A native English speaker may expect を because in English we say my neck hurts, where neck feels like the object. But in Japanese, 痛い describes the state of the neck, so が is natural.

You may also hear 首は痛い, which would put extra focus or contrast on the neck.

とき means when or at the time when.

So:

• 首が痛いとき = when your neck hurts
• 首が痛いときは = as for when your neck hurts / when your neck hurts, ...

The は after とき makes that whole time expression the topic of the sentence. It frames the advice:

• As for times when your neck hurts, ...

Without は, the meaning is still similar, but は makes it sound more like general guidance or advice for that situation.

In Japanese, forms before nouns and inside many grammar patterns are usually plain form, not polite form.

Since とき is a noun, the clause before it modifies it:

• 首が痛いとき = the time when your neck hurts

Using 痛いですとき is incorrect.

This is very common:

• 忙しいとき = when busy
• 行くとき = when going
• 食べたとき = when ate / when had eaten

The sentence can still end politely with です:

• ...ほうがいいです

無理に means something like:

• forcibly
• too hard
• beyond one’s limits
• unreasonably

Here it means don’t push yourself to exercise or don’t force yourself to exercise.

無理 by itself often means the impossible, overdoing it, or strain.
Adding に turns it into an adverb:

• 無理に = forcibly / by overdoing it

So the sentence is not saying never exercise. It is saying don’t force yourself to exercise when your neck hurts.

The pattern verb + ほうがいい is used for advice.

Two very common patterns are:

• V-た ほうがいい = it’s better to do ...
• V-ない ほうがいい = it’s better not to do ...

So:

• 運動しないほうがいい = It’s better not to exercise

Literally, ほう means side or option, so the idea is:

• The “not exercising” option is better

This is one of the most important advice patterns in Japanese.

It is usually advice, not a direct command.

• 運動しないほうがいいです = You’d better not exercise / It’s better not to exercise

It sounds softer than an outright prohibition like:

• 運動してはいけません = You must not exercise
• 運動するな = Don’t exercise (very strong/rough)

So 〜ないほうがいい is a natural way to give practical or medical-style advice without sounding too harsh.

This is very normal in Japanese.

Japanese often uses:

• plain forms inside clauses and grammar structures
• polite form at the very end of the sentence

So here:

• 首が痛い → plain form inside the clause
• 運動しない → plain negative inside 〜ほうがいい
• いいです → polite ending

This mix is standard and natural.
You do not need to make every part polite.

Japanese often leaves out the subject when it is obvious from context.

In English, we often need:

• When your neck hurts, you shouldn’t force yourself to exercise.

In Japanese, that you is usually omitted if the sentence is clearly giving advice to the listener.

So the sentence naturally leaves it unstated:

• 首が痛いときは、無理に運動しないほうがいいです。

Depending on context, it could mean:

• you
• one
• someone in that condition

Japanese prefers omission when the meaning is clear.

Yes, that is a good way to think about it.

A more literal breakdown is:

• 首 = neck
• が = subject marker
• 痛い = painful

So literally it is close to:

• The neck is painful

But natural English is:

• My neck hurts
• Your neck hurts
• When you have neck pain

Japanese often does not explicitly say my or your with body parts when it is obvious whose body is being discussed.

The comma is there to make the sentence easier to read and to show a pause.

• 首が痛いときは、無理に運動しないほうがいいです。

It separates the condition/topic part from the main advice.

Japanese commas are often more flexible than English commas.
The sentence could sometimes be written without one, but this comma makes the structure clearer.

Yes, it is the same word as good, but in this pattern it means:

• it is better
• it is advisable

So:

• 運動しないほうがいいです = It is better not to exercise

As for いい vs よい:

• よい is the dictionary/base form historically
• いい is the very common everyday form

Both are correct in many situations, but いいです is much more common in normal speech.

A helpful breakdown is:

• 首が痛い = your neck hurts
• ときは = when / as for when
• 無理に = forcibly / by pushing yourself
• 運動しない = do not exercise
• ほうがいいです = it is better

So the structure is basically:

[When X happens], [it is better not to do Y].

More literally:

• When your neck hurts, it is better not to force yourself to exercise.

This kind of structure is very common in advice, instructions, and health-related Japanese.