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

≤
less-than-or-equal-to

<
less than

=

Answer 1

To determine which operator can be inserted between the two expressions, let's evaluate each side of the inequality step by step.

First, simplify the left side:

\[
-6 + 3 \cdot 5
\]

Calculating \(3 \cdot 5\):

\[
3 \cdot 5 = 15
\]

So,

\[
-6 + 15 = 9
\]

Now, we have:

\[
-6 + 3 \cdot 5 = 9
\]

Next, simplify the right side:

\[
16 - \sqrt{16} + 32 \div 8
\]

First, evaluate \(\sqrt{16}\):

\[
\sqrt{16} = 4
\]

Then, calculate \(32 \div 8\):

\[
32 \div 8 = 4
\]

Now plug those values into the expression:

\[
16 - 4 + 4
\]

Calculating this step by step:

1. \(16 - 4 = 12\)
2. \(12 + 4 = 16\)

Now we have:

\[
16 - \sqrt{16} + 32 \div 8 = 16
\]

Now, we can compare the two results:

Left side: \(9\)

Right side: \(16\)

Now we can check the possible relationships:

1. \(9 > 16\) is false.
2. \(9 \leq 16\) is true.
3. \(9 < 16\) is true (and also fits).
4. \(9 = 16\) is false.

Since both \(9 \leq 16\) and \(9 < 16\) are true, we could use either. The simplest form is to use the less-than operator.

Thus, the best operator to insert is:

\[
<
\]

So the final answer is: **<** (less than).