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><≥≤

Answer 1

To determine which operator can be inserted to make the statement true, let's evaluate both sides of the expression:

The left side:

6 - 14 ⋅ 28 - 214.

First, calculate \(14 \cdot 28\):
\[
14 \cdot 28 = 392.
\]
Now, substitute this back into the expression:
\[
6 - 392 - 214.
\]
Next, perform the calculations step by step:
\[
6 - 392 = -386,
\]
and then:
\[
-386 - 214 = -600.
\]

Thus, the left side evaluates to:
\[
6 - 14 ⋅ 28 - 214 = -600.
\]

Now for the right side:

34 + 4 ⋅ 2 - 11.

First, calculate \(4 \cdot 2\):
\[
4 \cdot 2 = 8.
\]
Now, substitute this back into the expression:
\[
34 + 8 - 11.
\]
Next, perform the calculations step by step:
\[
34 + 8 = 42,
\]
and then:
\[
42 - 11 = 31.
\]

Thus, the right side evaluates to:
\[
34 + 4 ⋅ 2 - 11 = 31.
\]

Final comparison:
\[
-600 \text{ (left side) } ? \text{ (operator) } 31 \text{ (right side)}.
\]

Now let's check which operators would fit between \(-600\) and \(31\):
- For \(>\): \(-600\) is **not greater than** \(31\).
- For \(<\): \(-600\) is **less than** \(31\).
- For \(\geq\): \(-600\) is **not greater than or equal to** \(31\).
- For \(\leq\): \(-600\) is **less than or equal to** \(31\).

Thus, the operator that can be inserted to make the statement true is:
\[
<
\]

So, the answer is \( < \).