Consider the following expressions:

Question

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:

$$\text{Missing open brace for subscript}$$

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" (<).