Let's evaluate both sides of the expression to see how we can make them equal.
First, we'll calculate the left side of the expression:
\[ -6 + 3 * 5 \] According to the order of operations, we first multiply \(3\) and \(5\): \[ 3 * 5 = 15 \] Now we can add: \[ -6 + 15 = 9 \]
Next, let's calculate the right side of the expression:
\[ \sqrt{16} + 32 ÷ 8 \] First, calculate \(\sqrt{16}\): \[ \sqrt{16} = 4 \] Now calculate \(32 ÷ 8\): \[ 32 ÷ 8 = 4 \] Now we add these results together: \[ 4 + 4 = 8 \]
Now we can compare the values: \[ 9 \quad \text{(left side)} \quad \text{and} \quad 8 \quad \text{(right side)} \]
To insert an operator that would make the left side equal to 8, we can take an operator like \(<, \leq, >, \geq, =\) or \( \neq \).
Currently, we have: \[ 9 \quad \text{and} \quad 8 \]
We can conclude: \[ 9 > 8 \]
Thus, we can insert the \(>\) operator to complete the expression as: \[ -6 + 3 * 5 > \sqrt{16} + 32 ÷ 8 \]
Therefore, the operator that can be inserted is greater than (>).
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