Consider the following expressions:

Question

6−14⋅28−2146−14⋅28−214_______34+4⋅2−1134+4⋅2−11.

Which operator can be inserted to make the statement true?

(1 point)

Responses

<<

less than

≥≥

greater-than-or-equal-to

==

equals

>

Answer 1

To determine which operator can be inserted to make the statement true, we need to evaluate both expressions on each side of the operator.

Let's simplify the left side (6 - 14⋅28 - 214):

1. Calculate \(14 \cdot 28\): \[ 14 \cdot 28 = 392 \]

2. Substitute this back into the expression: \[ 6 - 392 - 214 = 6 - 392 - 214 \]

3. Calculate \(6 - 392\): \[ 6 - 392 = -386 \]

4. Now calculate \(-386 - 214\): \[ -386 - 214 = -600 \]

Thus, the left side simplifies to \(-600\).

Now, let's evaluate the right side (34 + 4⋅2 - 11):

1. Calculate \(4 \cdot 2\): \[ 4 \cdot 2 = 8 \]

2. Substitute this back into the expression: \[ 34 + 8 - 11 = 34 + 8 - 11 \]

3. Calculate \(34 + 8\): \[ 34 + 8 = 42 \]

4. Then calculate \(42 - 11\): \[ 42 - 11 = 31 \]

Thus, the right side simplifies to \(31\).

Now we have: \[ -600 , ? , 31 \]

Given the relationship between \(-600\) and \(31\), we see:

-600 is less than 31.

Therefore, we can insert the operator:

< (less than)

The final statement will be: \[ -600 < 31 \]

Thus, the correct response is:

less than ( < )