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

≥
is greater than or equal to

>
>

<

Answer 1

To determine which operator can be inserted to make the expression true, we need to evaluate both sides of the inequality:

The expression can be simplified as follows:

**Numerator Calculation:**
1. Calculate \(14 \cdot 28\):
\[
14 \cdot 28 = 392
\]
2. Therefore, the numerator becomes:
\[
6 - 392 - 214 = 6 - 392 - 214 = 6 - 606 = -600
\]

**Denominator Calculation:**
1. Calculate \(4 \cdot 2\):
\[
4 \cdot 2 = 8
\]
2. Therefore, the denominator becomes:
\[
34 + 8 - 11 = 34 + 8 - 11 = 31
\]

Now we need to compare the two values:
- Numerator: \(-600\)
- Denominator: \(31\)

Now we need to place an operator between -600 and 31:

- \(-600 \geq 31\) (false)
- \(-600 > 31\) (false)
- \(-600 < 31\) (true)

Thus, the operator that can be used to make the statement true is **<**.