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

=
equals

≤
less-than-or-equal-to

>

Answer 1

Let's evaluate both sides of the expression:

**Left Side:**
\[
-6 + 3 \cdot 5
\]
Perform the multiplication first:
\[
3 \cdot 5 = 15
\]
Now, add:
\[
-6 + 15 = 9
\]

**Right Side:**
\[
16 - \sqrt{16} + \frac{32}{8}
\]
First, calculate the square root:
\[
\sqrt{16} = 4
\]
Now, calculate the division:
\[
\frac{32}{8} = 4
\]
So the right side becomes:
\[
16 - 4 + 4
\]
Now, simplify it:
\[
16 - 4 = 12
\]
Then add 4:
\[
12 + 4 = 16
\]

Now we have the values:
- Left side: \(9\)
- Right side: \(16\)

Now we can compare:
\[
9 \, ? \, 16
\]

The appropriate operator to insert here is \( < \) (less than), since \(9 < 16\).

So, the final answer is:
\[
< \, \text{(less than)}
\]