To solve the problem, we need to evaluate both sides of the expression and determine which operator can be used to make them equal.
Let's simplify both sides.
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Calculate the left side: \[ -6 + 3 \cdot 5 \] \[ = -6 + 15 \] \[ = 9 \]
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Calculate the right side: \[ 16 - \sqrt{16} + 32 \div 8 \] First, calculate \( \sqrt{16} \): \[ \sqrt{16} = 4 \] Now substitute it back into the expression: \[ 16 - 4 + 32 \div 8 \] Now calculate \( 32 \div 8 \): \[ 32 \div 8 = 4 \] Now we can simplify the right side: \[ 16 - 4 + 4 \] \[ = 16 - 4 + 4 \] \[ = 16 \]
Now we have: \[ 9 \ ___ \ 16 \]
Next, we can find the operator that can be inserted between the numbers for the statement to be true.
For this case:
- If we insert "less than," it would be 9 < 16, which is true.
- If we insert "equal to," it would be 9 = 16, which is false.
- If we insert "greater than," it would be 9 > 16, which is also false.
Thus, the valid operator to insert is: < (less than).
So, the complete expression would be: \[ -6 + 3 \cdot 5 < 16 - \sqrt{16} + 32 \div 8 \]
This is true since \( 9 < 16 \).
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