Question

Consider the following expressions: −6+3⋅5 ______ 16−−√+32÷8 . Which operator can be inserted to make the statement true? (1 point) Responses < less than > greater than = equals ≤

Answer 1

Let's evaluate both sides of the expression to find out which operator makes the statement true.

First, we calculate the left side:

\(-6 + 3 \cdot 5\)

Following the order of operations (PEMDAS/BODMAS), we calculate \(3 \cdot 5\) first:

\[
3 \cdot 5 = 15
\]

Now substituting that back into the expression:

\[
-6 + 15 = 9
\]

So, the left side evaluates to \(9\).

Now, let's evaluate the right side:

\(\sqrt{16} + 32 \div 8\)

First, we calculate \(\sqrt{16}\):

\[
\sqrt{16} = 4
\]

Next, we calculate \(32 \div 8\):

\[
32 \div 8 = 4
\]

Now substituting that back into the expression:

\[
4 + 4 = 8
\]

So, the right side evaluates to \(8\).

Now we compare the two sides:

Left side: \(9\)

Right side: \(8\)

Now, we can determine the relation between the two values:

\(9\) is greater than \(8\).

Thus, we can insert the operator \(>\) (greater than) to make the statement true:

\(-6 + 3 \cdot 5 > 16 - \sqrt{16} + 32 \div 8\).

So, the answer is:

**> greater than**