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- - - -_(x−a)(x−29) - - ~ x−29 = Which of the following are solutions to the given a > 30 equation, where a is a constant and? I. a a+1 II. 29 III.
Correct answer: C (parsed from the explanation — this source omits an answer key for this item)
Explanation
-29 Choice C is correct. Subtracting the expression ^x h from both sides of the 0= - -29 - -29 given equation yields ^x ah^x h ^x h, which can be rewritten as 0= - -29 + -1 -29 ^x ah^x h ^ h^x h. Since the two terms on the right-hand side -29 of this equation have a common factor of ^x h, it can be rewritten as 0= -29 - + -1 0= -29 - -1 - - ^x h^x a ^ hh, or ^x h^x a h. Since x a1 is equivalent - + 0= -29 - -1 to x ^a 1h, the equation ^x h^x a h can be rewritten as 0= -29 - +1 -29=0 ^x h^x ^a hh. By the zero product property, it follows that x or - +1 =0 29 -29=0 =29 x ^a h . Adding to both sides of the equation x yields x . + - +1 =0 = + Adding a 1 to both sides of the equation x ^a h yields x a1 . Therefore, 29 + + 29 the two solutions to the given equation are and a 1. Thus, only a 1 and , not a, are solutions to the given equation. 38 SAT PRACTICE TEST #8 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 1 Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.
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