The expression 24 6 x + 42 is equivalent to 4 x + b , where b is a constant

Question

The expression 24 6 x + 42 is equivalent to 4 x + b , where b is a constant and x > 0 . What is the value of b ?

Accepted Answer

Choice A is correct. Since the given expressions are equivalent and the numerator of the second expression is 1 6 of the numerator of the first expression, the denominator of the second expression must also be 1 6 of the denominator of the first expression. By the distributive property, 1 6 6 x + 42 is equivalent to 1 6 6 x + 1 6 42 , or x + 7 . Therefore, the value of b is 7 . Choice B is incorrect and may result from conceptual or calculation errors. Choice C 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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