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Question 9 of 18

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M:N:MC:9

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SAT

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PSAT 10

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Heart of Algebra

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table row cell fraction numerator 5 left parenthesis k plus 2 right parenthesis minus 7 over denominator 6 end fraction end cell equals cell fraction numerator 13 minus left parenthesis 4 minus k right parenthesis over denominator 9 end fraction end cell end table

In the equation above, what is the value of k?

Select an Answer

9 over 17

Correct Answer: 
No

9 over 13

Correct Answer: 
Yes

33 over 17

Correct Answer: 
No

33 over 13

Correct Answer: 
No

View Correct Answer

Choice B is correct. Simplifying the numerators yields fraction numerator 5 k plus 3 over denominator 6 end fraction equals fraction numerator 9 plus k over denominator 9 end fraction comma and cross-multiplication gives 45 k plus 27 equals 54 plus 6 k. Solving for k yields k equals 9 over 13.

Choice A is not the correct answer. This value may result from not correctly applying the distributive property on the right-hand side, resulting in the expression 13 minus 4 minus k in the numerator. Correctly applying the distributive property yields 13 minus left parenthesis 4 minus k right parenthesis equals 13 minus 4 plus k in the numerator.

Choice C is not the correct answer. This value may result from not correctly applying the distributive property on the left-hand side, resulting in the expression 5 k space plus space 2 space minus space 7. Correctly applying the distributive property yields 5 left parenthesis k plus 2 right parenthesis minus 7 equals 5 k plus 3 in the numerator.

Choice D is not the correct answer. This value may result from not using the appropriate order of operations when simplifying either numerator.

Question Difficulty: 
medium
Objective: 

Students must solve an algebraic equation in one variable.