Final answer:
To solve the equation, we can set up the equation 2(x - 3) = 3(x + 9) and simplify it step by step. The number that satisfies this equation is -33.
Step-by-step explanation:
To solve this problem, we can represent the unknown number as 'x'. According to the information given, twice the difference of 'x' and 3 is equal to three times the sum of 'x' and 9. We can express this as the equation: 2(x - 3) = 3(x + 9).
To simplify the equation, we distribute the 2 and 3 to the terms inside the parentheses: 2x - 6 = 3x + 27.
Next, we can combine like terms by subtracting 2x from both sides: -6 = x + 27.
Finally, to isolate the variable 'x', we subtract 27 from both sides: -33 = x.
Therefore, the number is -33.