To find the appropriate operator to insert, we need to evaluate both sides of the equation and see what operation would make them equal.
Let's first simplify each side.
The left side is: \[ 8 - 18 \cdot 12 - 1 \]
Calculating this step-by-step:
- Calculate \( 18 \cdot 12 = 216 \)
- Now, substitute back into the expression: \[ 8 - 216 - 1 = 8 - 216 - 1 = 8 - 217 = -209 \]
Now, for the right side: \[ 9 + 4 - 11 \cdot 2 \]
Calculating this step-by-step:
- Calculate \( 11 \cdot 2 = 22 \)
- Now, substitute back into the expression: \[ 9 + 4 - 22 = 13 - 22 = -9 \]
Now we have:
Left side: \(-209\)
Right side: \(-9\)
To find an operator that balances the equation: \[ -209 ; __ ; -9 \]
We can start testing basic arithmetic operations (+, -, *, /):
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Testing with = The two sides are clearly not equal.
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Testing with + \(-209 + (-9) = -218\) (not equal)
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Testing with - \(-209 - (-9) = -209 + 9 = -200\) (not equal)
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Testing with * (multiplication) \(-209 * (-9) = 1881\) (not equal)
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Testing with / (division) \(-209 / (-9) = 23.222\) (not equal)
Since none equalized, it leads us to reasonable consideration of different type of structure.
After careful calculation and thought, we realize the question may need proper context such as constraints on the results or further expressions.
Given solutions don’t yield an operator match will generally fall down to phrased analysis or examination for correct logic depending on the task request.
Hence, please clarify further rules or conditions required to identify such applied operator—an approach on strict number relations, inequalities or approximate results would guide to better selection which results aren’t yielding exact match but potentially situational through functional application or logical boundaries.
In conclusion, if strictly searching for operators that can insert as numerical back-end matching, none within singular basic operators +, -, *, / fit to yield directly matching scenarios without broader expressions or contextual constraints.
The results show us that there isn’t one operator that isolated would effectively equal the two statements directly.