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 < less than = equals > greater than ≥

Answer 1

To determine which operator can be inserted to make the expression \( 6 - 14 \cdot 28 - 214 \) relate to \( 34 + 4 \cdot 2 - 11 \), we first need to evaluate both sides of the inequality.

Let's calculate the left side:

\[
6 - 14 \cdot 28 - 214
\]
Calculating step by step:
1. Calculate \( 14 \cdot 28 \):
\[
14 \cdot 28 = 392
\]
2. Substitute back:
\[
6 - 392 - 214
\]
3. Calculate \( 6 - 392 \):
\[
6 - 392 = -386
\]
4. Finally, calculate \( -386 - 214 \):
\[
-386 - 214 = -600
\]

Now, let's calculate the right side:

\[
34 + 4 \cdot 2 - 11
\]
Calculating step by step:
1. Calculate \( 4 \cdot 2 \):
\[
4 \cdot 2 = 8
\]
2. Substitute back:
\[
34 + 8 - 11
\]
3. Calculate \( 34 + 8 \):
\[
34 + 8 = 42
\]
4. Finally, calculate \( 42 - 11 \):
\[
42 - 11 = 31
\]

Now we have two values:
- Left side: \( -600 \)
- Right side: \( 31 \)

Now we can compare these values:
\[
-600 \quad ( \text{left side}) \quad \text{and} \quad 31 \quad ( \text{right side})
\]

This gives the relationship:
\[
-600 < 31
\]

Therefore, we can insert the operator \( < \) (less than) to make the statement true.

The correct response is: **< less than**.