Final answer:
The statement cannot be resolved with a single operator because the mathematical operations lead to a result where 4 is being incomparably juxtaposed with -160, and potentially positive figures from 16, making the overall comparison indeterminable.
Step-by-step explanation:
The question asks us to determine which mathematical symbol (<, >, =) makes the statement true: 4 □ 16-16□4 □ [24-2 □ (4×8)]. To solve this, we need to perform the operations within the brackets first.
Within the brackets, we calculate 2 □ (4×8) first, which simplifies to 2 □ 32. Since 2 times a number is just that number doubled, 2 □ 32 equals 64. The expression inside the brackets now is 24-64, which is equal to -40.
Next, we have 4 □ (-40). Since any number multiplied by 4 is four times greater, 4 □ (-40) would yield -160. Finally, we compare 4 with -160 and it is clear that 4 is greater than -160.
Now let's consider the 16-16□4 part of the equation. Here, 16 will cancel out if we choose the multiplication operator, leaving whatever is the result of 16□4. Since 16 multiplied by any number would be a positive number, this comparison cannot balance out the -160 we got earlier.
Therefore, it is impossible to determine a single mathematical operator that would make the initial statement true.