Question

Consider the following expressions:

−34+6*2√16 ___4(2+6 )÷2−6
Which operator ( >, <, or =) should be inserted into the blank space to make the statement true?​

(1 point)
___

Answer 1

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:
\[
-34 + 6 \times 2 \times \sqrt{16} > 4(2 + 6) \div 2 - 6
\]