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Alexis solved this equation:\newline−2(4p−11)+7p=−10p−14-2(4p - 11) + 7p = -10p - 14\newline−8p+22+7p=−10p−14-8p + 22 + 7p = -10p - 14\newline−p+22=−10p−14-p + 22 = -10p - 14\newline9p+22=−149p + 22 = -14\newline9p=−369p = -36\newlinep=−4p = -4\newlineWhich property is not needed to justify any of the steps?\newlineChoices:\newline(A) division property of equality\newline(B) identity property of addition\newline(C) addition property of equality\newline(D) distributive property

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Q. Alexis solved this equation:\newline−2(4p−11)+7p=−10p−14-2(4p - 11) + 7p = -10p - 14\newline−8p+22+7p=−10p−14-8p + 22 + 7p = -10p - 14\newline−p+22=−10p−14-p + 22 = -10p - 14\newline9p+22=−149p + 22 = -14\newline9p=−369p = -36\newlinep=−4p = -4\newlineWhich property is not needed to justify any of the steps?\newlineChoices:\newline(A) division property of equality\newline(B) identity property of addition\newline(C) addition property of equality\newline(D) distributive property
  1. Review Equation Solution: Review the equation and the steps Alexis took to solve it.\newline- Alexis first distributed −2-2 across (4p−11)(4p - 11), then combined like terms, and finally isolated pp to solve for it.
  2. Properties Analysis: Analyze the properties used in each step.\newline- Distributive property: Used to expand −2(4p−11)-2(4p - 11) to −8p+22-8p + 22.\newline- Addition property of equality: Used to add 10p10p to both sides to isolate the pp terms.\newline- Division property of equality: Used to divide both sides by 99 to solve for pp.
  3. Property Check: Check each property against the choices given.\newline- (A) Division property of equality: Used in the final step to solve for pp.\newline- (B) Identity property of addition: Not explicitly used in any step.\newline- (C) Addition property of equality: Used to add 10p10p to both sides.\newline- (D) Distributive property: Used in the first step to expand the equation.

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