Thank you for your excellent question!
If you sell your home at a loss, can you deduct the amount from your taxes? Unfortunately, the answer is no. A loss on the sale of a personal residence is considered a nondeductible personal expense. You can only deduct losses on the sale of property used for business or investment purposes.
This is covered in great detail in the relevant IRS publication here:
https://www.irs.gov/faqs/capital-gains-losses-and-sale-of-home
If your LLC was formed in the current year, you would have no deductions for the prior year unless you had business operations at that point. In which case you would have home office deductions. However, these will still not offset the vast majority of your capital loss, as depreciation reduces basis and increases the amount of capital gain.
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