Question
When solving an equation, Drew's first step is shown below. Which property justifies Drew's first step?
Original Equation:
Original Equation:
minus, 10, left parenthesis, minus, 2, x, squared, minus, 9, right parenthesis, plus, 1, equals, 10, x, squared, minus, 7
−10(−2x
2
−9)+1=
10x
2
−7
First Step:
First Step:
minus, 10, left parenthesis, minus, 2, x, squared, minus, 9, right parenthesis, equals, 10, x, squared, minus, 8
−10(−2x
2
−9)=
10x
2
−8
Answer
Original Equation:
Original Equation:
minus, 10, left parenthesis, minus, 2, x, squared, minus, 9, right parenthesis, plus, 1, equals, 10, x, squared, minus, 7
−10(−2x
2
−9)+1=
10x
2
−7
First Step:
First Step:
minus, 10, left parenthesis, minus, 2, x, squared, minus, 9, right parenthesis, equals, 10, x, squared, minus, 8
−10(−2x
2
−9)=
10x
2
−8
Answer
Answers
GPT-4o mini
Drew's first step involves distributing the \(-10\) into the expression \(-2x^2 - 9\). The property that justifies this step is the **Distributive Property**.
The Distributive Property states that \(a(b + c) = ab + ac\). In Drew's case, \(-10\) is being distributed to both terms inside the parentheses:
\[
-10 \cdot (-2x^2) + (-10) \cdot (-9) = 20x^2 + 90
\]
However, it looks like there's a small error in the arithmetic given in the problem. The correctly distributed term would actually result in:
\[
20x^2 + 90
\]
Then adding \(1\) (as seen in the original equation), we'd actually get:
\[
20x^2 + 90 + 1 = 20x^2 + 91
\]
Thus, Drew should have ended up with \(20x^2 + 91\) before equating it to anything else on the right side of the equation.
So, the correct justification for Drew's first step would still be the **Distributive Property**, but the arithmetical outcome might require reevaluation based on the original setup.
The Distributive Property states that \(a(b + c) = ab + ac\). In Drew's case, \(-10\) is being distributed to both terms inside the parentheses:
\[
-10 \cdot (-2x^2) + (-10) \cdot (-9) = 20x^2 + 90
\]
However, it looks like there's a small error in the arithmetic given in the problem. The correctly distributed term would actually result in:
\[
20x^2 + 90
\]
Then adding \(1\) (as seen in the original equation), we'd actually get:
\[
20x^2 + 90 + 1 = 20x^2 + 91
\]
Thus, Drew should have ended up with \(20x^2 + 91\) before equating it to anything else on the right side of the equation.
So, the correct justification for Drew's first step would still be the **Distributive Property**, but the arithmetical outcome might require reevaluation based on the original setup.