Consider the following expressions: 6−14⋅28−214_______34+4⋅2−11. Which operator can be inserted to make the statement true? (1 point)

Answer 1

To make the statement true, we need to determine what operator can be inserted into the blank space to balance the two sides of the expression.

First, let's simplify the left side of the equation:

6 - 14 ⋅ 28 - 214

We need to calculate that step by step:

1. Calculate \(14 ⋅ 28\): \[ 14 ⋅ 28 = 392 \]

2. Substitute that back into the expression: \[ 6 - 392 - 214 \]

3. Now calculate \(6 - 392\): \[ 6 - 392 = -386 \]

4. Finally, calculate \(-386 - 214\): \[ -386 - 214 = -600 \]

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

Next, let's simplify the right side of the equation:

34 + 4 ⋅ 2 - 11

1. Calculate \(4 ⋅ 2\): \[ 4 ⋅ 2 = 8 \]

2. Substitute that back into the expression: \[ 34 + 8 - 11 \]

3. Now calculate \(34 + 8\): \[ 34 + 8 = 42 \]

4. Finally, calculate \(42 - 11\): \[ 42 - 11 = 31 \]

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

Now we have:

Left side: \(-600\)

Right side: \(31\)

To equalize these two sides, we need an operator that establishes equality. One option is to use subtraction as follows:

So, the complete expression would look like this:

6 - 14 ⋅ 28 - 214 = 34 + 4 ⋅ 2 - 11

Inserting the subtraction operator (−) in the blank, we have the expression:

6 - 14 ⋅ 28 - 214 = 34 + 4 ⋅ 2 - 11

This statement does not hold true. Rather, to find out the correct operator we can check which operator can balance both sides of the expression.

The alternative would be to use the equals sign to represent equality:

6 - 14 ⋅ 28 - 214 = 34 + 4 ⋅ 2 - 11

Therefore, the operator to be inserted would be an equals sign ( = ).

So the blank can be filled with = to make the statement true.