(x + 2) (x + 3) = (x - 2) (x - 3) + 10 Which of the following is a solution to the given equation?

The correct answer is A. Choice A is correct. Applying the distributive property on the left- and right-hand sides of the given equation yields x^2 + 2x + 3x + 6 = x^2 - 2x - 3x + 6 + 10 , or x^2 + 5x + 6 = x^2 - 5x + 16 . Subtracting x^2 from and adding 5x to both sides of this equation yields 10x + 6 = 16 . Subtracting 6 from both sides of this equation and then dividing both sides by 10 yields x = 1 .

SAT Question 802549ac: Answer, Explanation & Desmos Solution

Choice B

Choice B is incorrect. Substituting $0$ , $- 2$ , or $- 5$ for $x$ in the given equation will result in a false statement. If $x = 0$ , the given equation becomes $6 = 16$ ; if $x = - 2$ , the given equation becomes $0 = 30$ ; and if $x = - 5$ , the given equation becomes $6 = 66$ . Therefore, the values $0$ , $- 2$ , and $- 5$ aren't solutions to the given equation.

Choice C

Choice C is incorrect. Substituting $0$ , $- 2$ , or $- 5$ for $x$ in the given equation will result in a false statement. If $x = 0$ , the given equation becomes $6 = 16$ ; if $x = - 2$ , the given equation becomes $0 = 30$ ; and if $x = - 5$ , the given equation becomes $6 = 66$ . Therefore, the values $0$ , $- 2$ , and $- 5$ aren't solutions to the given equation.

Choice D

Choice D is incorrect. Substituting $0$ , $- 2$ , or $- 5$ for $x$ in the given equation will result in a false statement. If $x = 0$ , the given equation becomes $6 = 16$ ; if $x = - 2$ , the given equation becomes $0 = 30$ ; and if $x = - 5$ , the given equation becomes $6 = 66$ . Therefore, the values $0$ , $- 2$ , and $- 5$ aren't solutions to the given equation.

Explanation

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Why the other choices are wrong

SAT Question 802549ac: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

Explanation

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Why the other choices are wrong