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 < less than = equals > greater than ≥

Answer 1

To determine which operator can be inserted to make the expression \( 6 - 14 \cdot 28 - 214 \) relate to \( 34 + 4 \cdot 2 - 11 \), we first need to evaluate both sides of the inequality.

Let's calculate the left side:

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

1. Calculate \( 14 \cdot 28 \): \[ 14 \cdot 28 = 392 \]
2. Substitute back: \[ 6 - 392 - 214 \]
3. Calculate \( 6 - 392 \): \[ 6 - 392 = -386 \]
4. Finally, calculate \( -386 - 214 \): \[ -386 - 214 = -600 \]

Now, let's calculate the right side:

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

1. Calculate \( 4 \cdot 2 \): \[ 4 \cdot 2 = 8 \]
2. Substitute back: \[ 34 + 8 - 11 \]
3. Calculate \( 34 + 8 \): \[ 34 + 8 = 42 \]
4. Finally, calculate \( 42 - 11 \): \[ 42 - 11 = 31 \]

Now we have two values:

• Left side: \( -600 \)
• Right side: \( 31 \)

Now we can compare these values: \[ -600 \quad ( \text{left side}) \quad \text{and} \quad 31 \quad ( \text{right side}) \]

This gives the relationship: \[ -600 < 31 \]

Therefore, we can insert the operator \( < \) (less than) to make the statement true.

The correct response is: < less than.