Joe's burger shop being left behind in rent for $821 can be represented by the equation x = -$821.
To represent Joe's burger shop being left behind in rent for $821 as an equation, we can let 'x' represent the number of months. Since rent is owed, we can use the subtraction operation (-) to represent the amount owed. The equation would be:
$821 = 0 - x
To solve for 'x', we can simply subtract $821 from both sides of the equation:
x = 0 - $821
Simplifying, we have:
x = -$821
Therefore, the equation representing Joe's burger shop being left behind in rent for $821 is x = -$821.