Final answer:
The correct journal entries for adjusting a deferred tax asset that is unlikely to be realized are decreasing the Deferred Tax Asset and recording a Valuation Allowance, both by the amount not expected to be realized.
Step-by-step explanation:
The journal entry for Carson's deferred tax asset adjustment involves a decrease in the Deferred Tax Asset by $3,000 and the establishment of a valuation allowance of $3,000. This adjustment acknowledges that $3,000 of the deferred tax asset is unlikely to be realized. The entry does not directly record a loss on the income statement; instead, it addresses the valuation of the deferred tax asset on the balance sheet.
The creation of the valuation allowance is a precautionary measure to adjust the carrying value of the deferred tax asset, reflecting the portion deemed unlikely to be realized. This adjustment does not have a direct impact on the income statement or Income Tax Expense. Hence, the correct options are to decrease the Deferred Tax Asset by $3,000 and record a Valuation Allowance of $3,000, reflecting the conservative assessment of the asset's realizability.