Question

Fill in the parts-whole model for the following equation.
minus, 3, x, squared, plus, 6, x, minus, 10, equals, left parenthesis, 3, x, squared, plus, 4, x, minus, 10, right parenthesis, minus, left parenthesis, start underline, end underline, right parenthesis
−3x
2
+6x−10=(3x
2
+4x−10)−(
​
)

Answer 1

To fill in the parts-whole model for the equation

\(-3x^2 + 6x - 10 = (3x^2 + 4x - 10) - ( \_ )\),

we want to identify the parts and the whole.

In this case, the left side of the equation represents one part, and the right side consists of the whole minus another part.

Let's denote the part that is being subtracted on the right side as \( P \).

We can rewrite the equation as:

\[
-3x^2 + 6x - 10 = (3x^2 + 4x - 10) - P
\]

To find \( P \), we can rearrange the equation to isolate \( P \):

\[
P = (3x^2 + 4x - 10) - (-3x^2 + 6x - 10)
\]

Now, we simplify this expression by distributing the negative sign on the left side:

\[
P = (3x^2 + 4x - 10) + (3x^2 - 6x + 10)
\]

Now let's combine like terms:

\[
P = (3x^2 + 3x^2) + (4x - 6x) + (-10 + 10)
\]

This simplifies to:

\[
P = 6x^2 - 2x + 0
\]

Thus, the filled form of the equation can be expressed as:

\[
-3x^2 + 6x - 10 = (3x^2 + 4x - 10) - (6x^2 - 2x)
\]

In this setup, our parts-whole model for the equation is:

- Whole: \(3x^2 + 4x - 10\)
- Part 1 (left side): \(-3x^2 + 6x - 10\)
- Part 2 (subtracted part on the right): \(6x^2 - 2x\)

So the answer is \( P = 6x^2 - 2x \).