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Question 4 of 18

beginning of content:

M:N:MC:3

Tags:
SAT

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Passport to Advanced Math

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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: 
No

y equals 2 a minus 1 half

Correct Answer: 
No

y equals 1 half a plus 1

Correct Answer: 
No

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.

Question Difficulty: 
medium
Objective: 

Students must complete operations with multiple terms and manipulate an equation to isolate the variable of interest.