6−14⋅28−214_______34+4⋅2−11.Which operator can be inserted to make the statement true?(1 point)Responses≥greater-than-or-equal-to=equals<less than>

Answer 1

To find the appropriate operator that can be inserted in the statement \(6−14⋅28−214 ____ 34+4⋅2−11\), we first need to calculate both sides.

Starting with the left side:

\[ 6 - 14 \cdot 28 - 214 \]

Calculate \(14 \cdot 28\):

\[ 14 \cdot 28 = 392 \]

Now substitute that back into the equation:

\[ 6 - 392 - 214 \]

Now we perform the operations step by step:

1. \(6 - 392 = -386\)
2. \(-386 - 214 = -600\)

So, the left side equals \(-600\).

Next, we calculate the right side:

\[ 34 + 4 \cdot 2 - 11 \]

Calculate \(4 \cdot 2\):

\[ 4 \cdot 2 = 8 \]

Now substitute that back into the equation:

\[ 34 + 8 - 11 \]

Now perform the operations step by step:

1. \(34 + 8 = 42\)
2. \(42 - 11 = 31\)

So, the right side equals \(31\).

Now we compare the two results:

\(-600 ____ 31\)

Given the possible operators:

• \(\geq\) (greater than or equal to)
• \(=\) (equals)
• \(<\) (less than)
• \(>\) (greater than)

Since \(-600\) is less than \(31\), the correct operator to insert is:

\[ < \]

Thus, the statement can be completed as:

\[ 6−14⋅28−214 < 34+4⋅2−11 \]

The operator that can be inserted to make the statement true is "<".