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-or-equal-to > greater than Skip to navigation

Answer 1

To determine which operator can be inserted to make the statement true, we need to evaluate both sides of the expression individually.

1. Left Side: \( 6 - 14 \cdot 28 - 214 \)

   First, we handle the multiplication:
   \( 14 \cdot 28 = 392 \)

   Now substitute this into the expression:
   \( 6 - 392 - 214 \)

   Now perform the operations from left to right:
   \( 6 - 392 = -386 \)
   \( -386 - 214 = -600 \)

   So, the left hand side is \( -600 \).

2. Right Side: \( 34 + 4 \cdot 2 - 11 \)

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

   Substitute this into the expression:
   \( 34 + 8 - 11 \)

   Now perform the operations from left to right:
   \( 34 + 8 = 42 \)
   \( 42 - 11 = 31 \)

   So, the right hand side is \( 31 \).

Now we compare the left hand side and the right hand side:
\( -600 \) (left side) and \( 31 \) (right side).

The final step is to choose the appropriate operator:

• \( -600 < 31 \): This is true.
• \( -600 = 31 \): This is false.
• \( -600 \geq 31 \): This is false.
• \( -600 > 31 \): This is false.

Based on these, the answer is that the operator that can be inserted is:

< (less than).