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 = equals < less than ≥ greater-than-or-equal-to > greater than Skip to navigation

Answer 1

To solve the problem, we need to evaluate both expressions:

**Left side:**
\( 6 - 14 \cdot 28 - 214 \)

Let's do the multiplication first:
\( 14 \cdot 28 = 392 \)

Now substituting back into the expression:
\( 6 - 392 - 214 \)

First, calculate \( 6 - 392 \):
\( 6 - 392 = -386 \)

Now subtract \( 214 \):
\(-386 - 214 = -600\)

So, the left side evaluates to:
**Left side = -600**

**Right side:**
\( 34 + 4 \cdot 2 - 11 \)

Again, we do the multiplication first:
\( 4 \cdot 2 = 8 \)

Now substituting back into the expression:
\( 34 + 8 - 11 \)

So, calculate \( 34 + 8 = 42 \), then \( 42 - 11 = 31 \).

So, the right side evaluates to:
**Right side = 31**

Now, we have:
\(-600\) (left side) _____ \(31\) (right side)

Now we have to determine which operator can be inserted. The comparison is:
\(-600\) _____ \(31\)

Since \(-600\) is less than \(31\), we can insert the less than symbol "<".

Therefore, the correct operator that can be inserted to make the statement true is:
**< (less than)**