Question

Consider the following expressions:

6−14⋅28−214 _______ 34+4⋅2−11 .

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 between the two expressions \( 6 - 14 \cdot 28 - 214 \) and \( 34 + 4 \cdot 2 - 11 \), we first need to evaluate both expressions.

Let's calculate the left-hand side:

1. \( 14 \cdot 28 = 392 \)
2. \( 6 - 392 - 214 = 6 - 392 - 214 \)
3. \( = 6 - 606 = -600 \)

So, the left-hand side evaluates to \( -600 \).

Next, let's calculate the right-hand side:

1. \( 4 \cdot 2 = 8 \)
2. \( 34 + 8 - 11 = 34 + 8 - 11 \)
3. \( = 34 + 8 - 11 = 31 \)

So, the right-hand side evaluates to \( 31 \).

Now we have:

\[
-600 \, _______ \, 31
\]

To determine the relationship, we observe that \( -600 \) is indeed less than \( 31 \).

Thus, the operator that can be inserted to make the statement true is:

\[
<
\]

The final statement is:

\[
6 - 14 \cdot 28 - 214 < 34 + 4 \cdot 2 - 11
\]

So the answer is "less than" (<).