The balance sheet equation is an accounting rule used in standard double-entry bookkeeping: It says that assets minus liabilities must equal equity, or equivalently assets equal liabilities plus equity.
If a transaction violates the balance sheet equation, that means that it changes some or all of the three terms so that the equation no longer balances; this should not happen in the ordinary course of business, and is generally evidence of an error or possibly even fraud. You should never just increase liabilities by $1,000, for example; that increase in liabilities should be matched by an increase in assets or a decrease in equity.
By requiring accounts to balance in this way, double-entry bookkeeping makes it easier to detect errors and harder to commit fraud.
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