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 < less than = equals ≥

Answer 1

To compare the two expressions \( 6 - 14 \cdot 28 - 214 \) and \( 34 + 4 \cdot 2 - 11 \), we first need to evaluate each expression.

1. Calculating the left expression: \[ 6 - 14 \cdot 28 - 214 \] First, calculate \( 14 \cdot 28 \): \[ 14 \cdot 28 = 392 \] Now substitute back into the expression: \[ 6 - 392 - 214 \] Now, calculate \( 6 - 392 \): \[ 6 - 392 = -386 \] Now, substitute that back: \[ -386 - 214 = -600 \] Thus, \( 6 - 14 \cdot 28 - 214 = -600 \).

2. Calculating the right expression: \[ 34 + 4 \cdot 2 - 11 \] First, calculate \( 4 \cdot 2 \): \[ 4 \cdot 2 = 8 \] Now substitute back: \[ 34 + 8 - 11 \] Now, calculate \( 34 + 8 \): \[ 34 + 8 = 42 \] Now, substitute that back: \[ 42 - 11 = 31 \] Thus, \( 34 + 4 \cdot 2 - 11 = 31 \).

Now we compare the results:

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

Now we can determine the relationship between the two values: \[ -600 < 31 \]

Thus, the correct operator that can be inserted to make the statement true is "< less than".