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 < less than = equals ≥

Answer 1

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

1. **Calculating the left expression**:
\[
6 - 14 \cdot 28 - 214
\]
First, calculate \( 14 \cdot 28 \):
\[
14 \cdot 28 = 392
\]
Now substitute back into the expression:
\[
6 - 392 - 214
\]
Now, calculate \( 6 - 392 \):
\[
6 - 392 = -386
\]
Now, substitute that back:
\[
-386 - 214 = -600
\]
Thus, \( 6 - 14 \cdot 28 - 214 = -600 \).

2. **Calculating the right expression**:
\[
34 + 4 \cdot 2 - 11
\]
First, calculate \( 4 \cdot 2 \):
\[
4 \cdot 2 = 8
\]
Now substitute back:
\[
34 + 8 - 11
\]
Now, calculate \( 34 + 8 \):
\[
34 + 8 = 42
\]
Now, substitute that back:
\[
42 - 11 = 31
\]
Thus, \( 34 + 4 \cdot 2 - 11 = 31 \).

Now we compare the results:
- Left expression: \( -600 \)
- Right expression: \( 31 \)

Now we can determine the relationship between the two values:
\[
-600 < 31
\]

Thus, the correct operator that can be inserted to make the statement true is "< less than".