To solve the expressions, we will evaluate both sides separately:
-
Left Side: \(-6 + 3 \cdot 5\)
- First, perform the multiplication: \(3 \cdot 5 = 15\)
- Now, add: \(-6 + 15 = 9\)
-
Right Side: \(16 - \sqrt{16} + 32 \div 8\)
- First, compute the square root: \(\sqrt{16} = 4\)
- Now compute the division: \(32 \div 8 = 4\)
- Substitute these results into the expression: \(16 - 4 + 4\)
- Perform the operations from left to right: \(16 - 4 = 12\) then \(12 + 4 = 16\)
Now we compare the two results:
- Left Side = 9
- Right Side = 16
Now we can determine the correct operator:
- \(9 < 16\) (less than)
- \(9 > 16\) (greater than) would be false
- \(9 = 16\) (equals) would be false
- \(9 ≤ 16\) (less-than-or-equal-to) is true as well
The correct operators that can be inserted are:
- \( < \) (less than)
- \( ≤ \) (less-than-or-equal-to)
However, since the question typically implies finding one operator to satisfy the comparison, the best answer would be:
< (less than) as it is the most straightforward comparison in this scenario.
So, the final correct response is < (less than).