Question

6−14⋅28−214_______34+4⋅2−11.Which operator can be inserted to make the statement true?(1 point)Responses≥greater-than-or-equal-to=equals<less than>

Answer 1

To find the appropriate operator that can be inserted in the statement \(6−14⋅28−214 \_\_\_\_ 34+4⋅2−11\), we first need to calculate both sides.

Starting with the left side:

\[
6 - 14 \cdot 28 - 214
\]

Calculate \(14 \cdot 28\):

\[
14 \cdot 28 = 392
\]

Now substitute that back into the equation:

\[
6 - 392 - 214
\]

Now we perform the operations step by step:

1. \(6 - 392 = -386\)
2. \(-386 - 214 = -600\)

So, the left side equals \(-600\).

Next, we calculate the right side:

\[
34 + 4 \cdot 2 - 11
\]

Calculate \(4 \cdot 2\):

\[
4 \cdot 2 = 8
\]

Now substitute that back into the equation:

\[
34 + 8 - 11
\]

Now perform the operations step by step:

1. \(34 + 8 = 42\)
2. \(42 - 11 = 31\)

So, the right side equals \(31\).

Now we compare the two results:

\(-600 \_\_\_\_ 31\)

Given the possible operators:

- \(\geq\) (greater than or equal to)
- \(=\) (equals)
- \(<\) (less than)
- \(>\) (greater than)

Since \(-600\) is less than \(31\), the correct operator to insert is:

\[
<
\]

Thus, the statement can be completed as:

\[
6−14⋅28−214 < 34+4⋅2−11
\]

The operator that can be inserted to make the statement true is **"<"**.