- - - - - - -_=_b−15x - - The linear function g is defined by g(x), g(c+7) = where b is a constant. If c/4, where c is a constant, which of the following expressions represents the value of b?
Correct answer: C (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice C is correct. It’s given that g^c +7 h = 4c . Therefore, for the given linear = + =c + c function g, when x c 7, g^xh . Substituting c 7 for x and for g^xh in 4 4 g^xh = b -15 x yields 4c= b -15 ^c +7 h. Applying the distributive property to the right-hand side of this equation yields 4c= b -15 c -105 . Adding 15 c to both sides of this equation yields 4c+15 c = b -105 . Adding 105 to both sides of this equation yields 4c+15 c +105= b, or 6 4 1 c+105= b. Therefore, the expression that represents the value of b is 6 4 1 c+105 . 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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