Yes, a business can enter into such transactions where only the left side of the accounting equation is affected.

Example:

The left side of the equation has assets. Therefore:

Purchase of assets for cash is a transaction in which the noncurrent assets increase with the purchase of a fixed asset and also there is a decrease in the current assets as the cash is paid, rendering the total assets to remain the same. Only the left side of the equation is affected and yet the transaction is valid.