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 >

Answer 1

To determine which operator can be inserted between the two expressions \( 6 - 14 \cdot 28 - 214 \) and \( 34 + 4 \cdot 2 - 11 \), we need to calculate each expression step by step.

1. Calculate the left expression, \( 6 - 14 \cdot 28 - 214 \):

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

   Now substitute back into the expression: \[ 6 - 392 - 214 \]

   Then perform the subtraction: \[ 6 - 392 = -386 \] \[ -386 - 214 = -600 \]

   So the left expression evaluates to \( -600 \).

2. Calculate the right expression, \( 34 + 4 \cdot 2 - 11 \):

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

   Now substitute back into the expression: \[ 34 + 8 - 11 \]

   Then perform the operations: \[ 34 + 8 = 42 \] \[ 42 - 11 = 31 \]

   So the right expression evaluates to \( 31 \).

3. Compare the two results:

   • The left expression: \( -600 \)
   • The right expression: \( 31 \)

Now, we analyze the relationship between \( -600 \) and \( 31 \):

• \( -600 < 31 \)
• Therefore, we can conclude that:

\[ 6 - 14 \cdot 28 - 214 < 34 + 4 \cdot 2 - 11 \]

The appropriate operator to insert in the blank is \( < \).

Thus the answer is: <.