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 = equals < less than ≥ greater-than-or-equal-to >

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 need to calculate each expression step by step.

1. **Calculate the left expression, \( 6 - 14 \cdot 28 - 214 \)**:

First calculate \( 14 \cdot 28 \):
\[
14 \cdot 28 = 392
\]

Now substitute back into the expression:
\[
6 - 392 - 214
\]

Then perform the subtraction:
\[
6 - 392 = -386
\]
\[
-386 - 214 = -600
\]

So the left expression evaluates to \( -600 \).

2. **Calculate the right expression, \( 34 + 4 \cdot 2 - 11 \)**:

First calculate \( 4 \cdot 2 \):
\[
4 \cdot 2 = 8
\]

Now substitute back into the expression:
\[
34 + 8 - 11
\]

Then perform the operations:
\[
34 + 8 = 42
\]
\[
42 - 11 = 31
\]

So the right expression evaluates to \( 31 \).

3. **Compare the two results**:
- The left expression: \( -600 \)
- The right expression: \( 31 \)

Now, we analyze the relationship between \( -600 \) and \( 31 \):

- \( -600 < 31 \)
- Therefore, we can conclude that:

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

The appropriate operator to insert in the blank is \( < \).

Thus the answer is: **<**.