Let's evaluate both sides of the expression step by step.
Left side: \[ -34 + 6 \times 2 \times \sqrt{16} \] First, calculate \(\sqrt{16}\): \[ \sqrt{16} = 4 \] Now substitute that into the expression: \[ -34 + 6 \times 2 \times 4 \] Calculate \(6 \times 2\): \[ 6 \times 2 = 12 \] Now calculate \(12 \times 4\): \[ 12 \times 4 = 48 \] Now substitute back into the expression: \[ -34 + 48 = 14 \]
Right side: \[ 4(2 + 6) \div 2 - 6 \] First, calculate \(2 + 6\): \[ 2 + 6 = 8 \] Now substitute that into the expression: \[ 4 \times 8 \div 2 - 6 \] Calculate \(4 \times 8\): \[ 4 \times 8 = 32 \] Now divide by 2: \[ 32 \div 2 = 16 \] Now subtract 6: \[ 16 - 6 = 10 \]
Now we have:
- Left Side: \(14\)
- Right Side: \(10\)
Now, we can compare the two sides: \[ 14 , \text{and} , 10 \]
Thus: \[ 14 > 10 \]
Therefore, we should insert the operator \(>\) into the blank space.
The final statement would be: \[ -34 + 6 \times 2 \times \sqrt{16} > 4(2 + 6) \div 2 - 6 \]