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 ≥ greater-than-or-equal-to <

Answer 1

Let's evaluate both expressions:

1. The left side: \( 6 - 14 \cdot 28 - 214 \)

First, we perform the multiplication:
\[
14 \cdot 28 = 392
\]
Now substitute this back into the expression:
\[
6 - 392 - 214
\]
Next, perform the subtractions:
\[
6 - 392 = -386
\]
\[
-386 - 214 = -600
\]

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

2. The right side: \( 34 + 4 \cdot 2 - 11 \)

First, we perform the multiplication:
\[
4 \cdot 2 = 8
\]
Now substitute this back into the expression:
\[
34 + 8 - 11
\]
Next, perform the additions and subtractions:
\[
34 + 8 = 42
\]
\[
42 - 11 = 31
\]

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

Now we have the following:
\[
-600 \, \text{____} \, 31
\]

We compare \(-600\) and \(31\):
- \(-600 < 31\), since \(-600\) is less than \(31\).

Hence, the appropriate operator to insert is \(<\) (less than).

So, the complete statement is:
\[
6 - 14 \cdot 28 - 214 < 34 + 4 \cdot 2 - 11
\]

The answer is **<**.