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 = equals ≥ greater-than-or-equal-to <

Answer 1

Let's evaluate both expressions:

1. The left side: \( 6 - 14 \cdot 28 - 214 \)

   First, we perform the multiplication: \[ 14 \cdot 28 = 392 \] Now substitute this back into the expression: \[ 6 - 392 - 214 \] Next, perform the subtractions: \[ 6 - 392 = -386 \] \[ -386 - 214 = -600 \]

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

2. The right side: \( 34 + 4 \cdot 2 - 11 \)

   First, we perform the multiplication: \[ 4 \cdot 2 = 8 \] Now substitute this back into the expression: \[ 34 + 8 - 11 \] Next, perform the additions and subtractions: \[ 34 + 8 = 42 \] \[ 42 - 11 = 31 \]

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

Now we have the following: \[ -600 , \text{____} , 31 \]

We compare \(-600\) and \(31\):

• \(-600 < 31\), since \(-600\) is less than \(31\).

Hence, the appropriate operator to insert is \(<\) (less than).

So, the complete statement is: \[ 6 - 14 \cdot 28 - 214 < 34 + 4 \cdot 2 - 11 \]

The answer is <.