To determine which operator can be inserted to make the statement true, let's evaluate both sides of the expression:
The left side:
6 - 14 ⋅ 28 - 214.
First, calculate \(14 \cdot 28\): \[ 14 \cdot 28 = 392. \] Now, substitute this back into the expression: \[ 6 - 392 - 214. \] Next, perform the calculations step by step: \[ 6 - 392 = -386, \] and then: \[ -386 - 214 = -600. \]
Thus, the left side evaluates to: \[ 6 - 14 ⋅ 28 - 214 = -600. \]
Now for the right side:
34 + 4 ⋅ 2 - 11.
First, calculate \(4 \cdot 2\): \[ 4 \cdot 2 = 8. \] Now, substitute this back into the expression: \[ 34 + 8 - 11. \] Next, perform the calculations step by step: \[ 34 + 8 = 42, \] and then: \[ 42 - 11 = 31. \]
Thus, the right side evaluates to: \[ 34 + 4 ⋅ 2 - 11 = 31. \]
Final comparison: \[ -600 \text{ (left side) } ? \text{ (operator) } 31 \text{ (right side)}. \]
Now let's check which operators would fit between \(-600\) and \(31\):
- For \(>\): \(-600\) is not greater than \(31\).
- For \(<\): \(-600\) is less than \(31\).
- For \(\geq\): \(-600\) is not greater than or equal to \(31\).
- For \(\leq\): \(-600\) is less than or equal to \(31\).
Thus, the operator that can be inserted to make the statement true is: \[ < \]
So, the answer is \( < \).
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