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

≥
greater-than-or-equal-to

<
less than

>
greater than

=

Answer 1

To determine which operator can be inserted to make the statement true, we need to evaluate both the numerator and the denominator of the expression.

Let's simplify the numerator and denominator step by step.

**Numerator:**
\[ 6 - 14 \cdot 28 - 214 \]

First, calculate \( 14 \cdot 28 \):
\[ 14 \cdot 28 = 392 \]

Now substitute back into the expression:
\[ 6 - 392 - 214 \]
Calculate \( 6 - 392 \):
\[ 6 - 392 = -386 \]

Finally, do:
\[ -386 - 214 = -600 \]

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

**Denominator:**
\[ 34 + 4 \cdot 2 - 11 \]

First, calculate \( 4 \cdot 2 \):
\[ 4 \cdot 2 = 8 \]

Now substitute back into the expression:
\[ 34 + 8 - 11 \]
Calculate \( 34 + 8 \):
\[ 34 + 8 = 42 \]

Finally, do:
\[ 42 - 11 = 31 \]

So, the denominator evaluates to:
\[ 31 \]

**Putting it all together:**
We have:
\[ \frac{-600}{31} \]

Now we need to compare this to possible operators:

1. **\(\ge\)** (greater than or equal to) - This means -600/31 is not greater than or equal to 31.
2. **<** (less than) - This means -600/31 is less than 31. This is true.
3. **>** (greater than) - This means -600/31 is not greater than 31.
4. **=** (equal to) - This means -600/31 is not equal to 31.

**Conclusion:**

The correct operator is:
**< (less than)**

Thus, the answer is:
**< (less than)**