Question

Consider the following expressions:

6−14⋅28−2146−14⋅28−214_______34+4⋅2−1134+4⋅2−11.

Which operator can be inserted to make the statement true?

(1 point)

Responses

<<

less than

≥≥

greater-than-or-equal-to

==

equals

>

Answer 1

To determine which operator can be inserted to make the statement true, we need to evaluate both expressions on each side of the operator.

Let's simplify the left side (6 - 14⋅28 - 214):

1. Calculate \(14 \cdot 28\):
\[
14 \cdot 28 = 392
\]

2. Substitute this back into the expression:
\[
6 - 392 - 214 = 6 - 392 - 214
\]

3. Calculate \(6 - 392\):
\[
6 - 392 = -386
\]

4. Now calculate \(-386 - 214\):
\[
-386 - 214 = -600
\]

Thus, the left side simplifies to \(-600\).

Now, let's evaluate the right side (34 + 4⋅2 - 11):

1. Calculate \(4 \cdot 2\):
\[
4 \cdot 2 = 8
\]

2. Substitute this back into the expression:
\[
34 + 8 - 11 = 34 + 8 - 11
\]

3. Calculate \(34 + 8\):
\[
34 + 8 = 42
\]

4. Then calculate \(42 - 11\):
\[
42 - 11 = 31
\]

Thus, the right side simplifies to \(31\).

Now we have:
\[
-600 \, ? \, 31
\]

Given the relationship between \(-600\) and \(31\), we see:

-600 is less than 31.

Therefore, we can insert the operator:

**<** (less than)

The final statement will be:
\[
-600 < 31
\]

Thus, the correct response is:

**less than** ( < )