M:N:MC:3

Calculator: Not Permitted

If $fraction numerator 2 over denominator a minus 1 end fraction equals 4 over y$ where $y not equal to 0$ and $a not equal to 1 comma$ what is $y$ in terms of $a ?$

Select an Answer

$y equals 2 a minus 2$

Correct Answer:

Yes

$y equals 2 a minus 4$

Correct Answer:

$y equals 2 a minus 1 half$

Correct Answer:

$y equals 1 half a plus 1$

Correct Answer:

View Correct Answer

Choice A is correct. Multiplying both sides of the equation by the denominators of the rational expressions in the equation gives $2 y equals 4 a minus 4.$ The student should then divide both sides by 2 to isolate the $y$ variable, yielding the equation $y equals 2 a minus 2.$

Choice B is not the correct answer. This equation may result if a student does not divide both terms by 2 when isolating $y$ in the equation $2 y equals 4 a minus 4.$

Choice C is not the correct answer. This equation may result from the student not distributing the 4 when multiplying 4 and $open parentheses a minus 1 close parentheses.$

Choice D is not the correct answer. This equation may result from solving $2 y equals 4 a minus 4$ for $a comma$ yielding $a equals 1 half y plus 1.$ A student who does not understand the meaning of the variables may then switch them to match the answer choice.