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after entering a transaction into the accounting equation, an increase in total assets can be accompanied by a(n) (increase/decrease) in total liabilities or equity.
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The fundamental accounting equation is $\text{Assets} = \text{Liabilities} + \text{Equity}$. For this equation to remain balanced, an increase in total assets must be matched by an increase in the sum of total liabilities and equity, meaning it can be accompanied by an increase in either liabilities or equity.
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