To evaluate the expressions on both sides of the blank, we will solve the left side and the right side separately.
First, let's calculate the left side: \[ 6 - 14 \cdot 28 - 214 \] Following the order of operations:
- Calculate \(14 \cdot 28\): \[ 14 \cdot 28 = 392 \]
- Substitute this back into the expression: \[ 6 - 392 - 214 \]
- Now perform the subtraction: \[ 6 - 392 = -386 \]
- Then subtract 214: \[ -386 - 214 = -600 \]
Now, let's evaluate the right side: \[ 34 + 4 \cdot 2 - 11 \] Following the order of operations:
- Calculate \(4 \cdot 2\): \[ 4 \cdot 2 = 8 \]
- Substitute this back into the expression: \[ 34 + 8 - 11 \]
- Now perform the addition and subtraction: \[ 34 + 8 = 42 \] \[ 42 - 11 = 31 \]
Now we compare the results:
- Left side: \(-600\)
- Right side: \(31\)
The inequality we need to evaluate is: \[ -600 _ 31 \]
The correct operation that satisfies this inequality is: \[ -600 < 31 \]
Therefore, among the options provided, the correct operation to place in the blank is: \[ < \]
However, since this option is not listed, the most accurate selection regarding the choices given would be: \[ \text{is less than} \] (even though you can classify it as "is not greater than" which is more fitting with the given choices of ≥ or >).
But if restricted to the given options, none fit perfectly, as < is not an option to choose from. Therefore, the evaluation leads to:
No valid choice from the given options directly fits the blank—if forced to choose, we select based on the least contradiction, which is: \[ < \text{ (not available in options)} \] but recognize that technically one should say none of these apply.
Thus, from listed choices, none address that effectively.