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 "difference of 11 and a number" means $11 - x$. 3. "Six times the difference" means multiply the difference by 6, so the equation is: $$6(11 - x) = -72$$ 4. Now, solve the equation step-by-step: $$6(11 - x) = -72$$ Distribute 6: $$6 \times 11 - 6 \times x = -72$$ $$66 - 6x = -72$$ 5. Subtract 66 from both sides: $$66 - 6x - 66 = -72 - 66$$ $$\cancel{66} - 6x - \cancel{66} = -72 - 66$$ $$-6x = -138$$ 6. Divide both sides by -6: $$\frac{-6x}{-6} = \frac{-138}{-6}$$ $$x = 23$$ 7. The number is $23$.