1. The problem states: "Six times the difference of 11 and a number is -72." We need to write this as an equation using $x$ to represent the number. 2. The phrase "the difference of 11 and a number" means $11 - x$. 3. "Six times" means multiply by 6, so the expression is $6(11 - x)$. 4. The equation is therefore: $$6(11 - x) = -72$$ 5. Let's check the other options: - $6(x - 11) = -72$ means six times the difference of the number and 11, which reverses the order and is incorrect. - $6x - 11 = -72$ means six times the number minus 11, which is not the difference of 11 and the number. - $6(11) - x = -72$ means six times 11 minus the number, which is not the difference multiplied by six. 6. Therefore, the correct equation is: $$6(11 - x) = -72$$