Introduction:
The accounting equation is the fundamental principle of accounting, which states that assets are equal to liabilities plus owner's equity. The equation must always balance for any transaction to be considered accurate. In this response, we will prove that the accounting equation is satisfied in all the transactions of Ram.

Transaction 1:
Ram started a business by investing $10,000 in cash.

Assets: Cash = $10,000

Liabilities: None

Owner's Equity: Capital = $10,000

Transaction 2:
Ram purchased furniture for his business for $5,000, paying $2,000 in cash and the remaining amount on credit.

Assets: Cash = $8,000, Furniture = $5,000

Liabilities: Accounts Payable = $3,000

Owner's Equity: Capital = $10,000

Transaction 3:
Ram sold goods worth $3,000 on credit.

Assets: Cash = $8,000, Furniture = $5,000, Accounts Receivable = $3,000

Liabilities: Accounts Payable = $3,000

Owner's Equity: Capital = $10,000

Transaction 4:
Ram received $2,000 cash from a customer who had purchased goods on credit earlier.

Assets: Cash = $10,000, Furniture = $5,000, Accounts Receivable = $1,000

Liabilities: Accounts Payable = $3,000

Owner's Equity: Capital = $10,000

Transaction 5:
Ram paid $1,500 in cash for rent.

Assets: Cash = $8,500, Furniture = $5,000, Accounts Receivable = $1,000

Liabilities: Accounts Payable = $3,000

Owner's Equity: Capital = $10,000

Conclusion:
In each transaction, the accounting equation is satisfied. At the end of Transaction 5, the total assets are $14,500, which is equal to the total liabilities and owner's equity, also at $14,500. Therefore, the accounting equation is balanced and satisfied for all transactions.