Question

Consider the following expressions:

−6+3⋅5______16−−√+32÷8.

Which operator can be inserted to make the statement true?

(1 point)
Responses

>
greater than

=
equals

≤
less-than-or-equal-to

<

Answer 1

Let's evaluate the expressions on both sides of the inequality.

For the left side:

\[
-6 + 3 \cdot 5
\]
First, we perform the multiplication:
\[
3 \cdot 5 = 15
\]
Now we can add:
\[
-6 + 15 = 9
\]

Now for the right side:

\[
16 - \sqrt{16} + 32 \div 8
\]
First, we calculate \(\sqrt{16}\):
\[
\sqrt{16} = 4
\]
Next, we do the division:
\[
32 \div 8 = 4
\]
Now we can substitute these results back:
\[
16 - 4 + 4
\]
Now we perform the subtraction and addition:
\[
16 - 4 = 12
\]
\[
12 + 4 = 16
\]

Now we have the simplified expressions:
Left side: \(9\)
Right side: \(16\)

We need to compare \(9\) and \(16\). Since \(9 < 16\), we can use the less-than operator.

Thus, the correct operator to insert is:

< (less-than)