Consider the following expressions:

Question

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

To find the appropriate operator to insert between the two expressions, we first need to calculate each expression.

Let's start with the numerator:

Numerator: \[ 6 - 14 \cdot 28 - 214 \] Calculating step-by-step:

1. Calculate \( 14 \cdot 28 = 392 \)
2. Now substitute it back: \[ 6 - 392 - 214 \]
3. Calculate \( 6 - 392 = -386 \)
4. Then \( -386 - 214 = -600 \)

So the numerator evaluates to: \[ -600 \]

Now let's calculate the denominator:

Denominator: \[ 34 + 4 \cdot 2 - 11 \] Calculating step-by-step:

1. Calculate \( 4 \cdot 2 = 8 \)
2. Now substitute it back: \[ 34 + 8 - 11 \]
3. Calculate \( 34 + 8 = 42 \)
4. Then \( 42 - 11 = 31 \)

So the denominator evaluates to: \[ 31 \]

Now we have the two results:

• The numerator = -600
• The denominator = 31

Next, we evaluate the full expression: \[ \frac{-600}{31} \]

To compare the two sides using potential operators:

The left side, \(-600\), is clearly less than the right side, which is \(31\).

Thus: \[ -600 < 31 \]

So the appropriate operator to insert is: \[ < \]

Final answer: < (less than)