Consider the following expressions:

Question

−6+3⋅5______16−−√+32÷8.

Which operator can be inserted to make the statement true?

(1 point)
Responses

>
greater than

=
equals

<
less than

≤

Answer 1

To determine which operator can be inserted to make the statement true, we need to evaluate both expressions:

Left-hand side: \[ -6 + 3 \cdot 5 \] Calculating it step-by-step:

1. Calculate \(3 \cdot 5 = 15\)
2. Then, \(-6 + 15 = 9\)

So, the left-hand side evaluates to 9.

Right-hand side: \[ 16 - \sqrt{16} + \frac{32}{8} \] Calculating it step-by-step:

1. Calculate \(\sqrt{16} = 4\)
2. Calculate \(\frac{32}{8} = 4\)
3. Substitute these values into the expression: \[ 16 - 4 + 4 \]
4. First, \(16 - 4 = 12\)
5. Then, \(12 + 4 = 16\)

So, the right-hand side evaluates to 16.

Now we can compare the two sides:

• Left-hand side: 9
• Right-hand side: 16

Since \(9 < 16\), the correct operator to insert is:

\(<\) (less than)

Thus, the answer is: < (less than).