Jeg føler sterkt at planen er viktig.

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Breakdown of Jeg føler sterkt at planen er viktig.

• være: to be
• viktig: important
• at: that

Questions & Answers about Jeg føler sterkt at planen er viktig.

Why is it sterkt and not sterk in this sentence?

In Jeg føler sterkt at planen er viktig, sterkt is an adverb, not an adjective.

• sterk = adjective form, used with nouns:
  
  • en sterk mann – a strong man
  • en sterk plan – a strong plan
• sterkt = adverb form, used to modify verbs, adjectives, or whole clauses:
  
  • Jeg føler sterkt – I feel strongly
  • Jeg tviler sterkt – I strongly doubt

Here, sterkt modifies the verb føler (feel), so you must use the adverb form sterkt.
Using sterk would sound ungrammatical to a native speaker in this context.

Can I move sterkt to another place in the sentence, like in English?

Norwegian word order is stricter than English. The natural, neutral position for sterkt here is right after the verb:

• Jeg føler sterkt at planen er viktig. ✔ (normal)

These versions are either unnatural or wrong:

• Jeg sterkt føler at planen er viktig. ✖ (sounds very odd)
• Jeg føler at planen er sterkt viktig. ✖ (unusual and changes meaning; sterkt viktig would be “very important,” not “feel strongly”)
• Jeg føler at planen er viktig sterkt. ✖ (ungrammatical)

So in this sentence, keep sterkt right after føler.