Question

While grading her students' most recent quiz on equation solving, Mrs. Jones calculated that approximately forty percent of her students answered question number 14 with multiple choice option B, while the other sixty percent answered A or C.Question #14 from Mrs. Jones's students' most recent quiz:14) Solve the single variable equation for n .3(-n+4) + 5n =2na.n = 3b.no solutionc.infinitely many solutionsPart 1: Use inverse operations and rules of equation solving to determine the correct answer to Mrs. Jones's quiz question number 14. Include all of your work in your final answer.Part 2: Use complete sentences to compare the similarities and differences of each of the multiple choice answer options A-C. In your answer, rationalize why a student would choose each of the options as the correct answer.

Answer 1

The given equation is,

$3(-n+4)+5n=2n$

Part 1:

Solve the above equation for n.

Using distributive property of multiplication,

$\begin{gathered} -3n+3\times4+5n=2n \\ -3n+12+5n=2n \end{gathered}$

Now, group the like terms.

$-3n+5n-2n+12=0$

Now, add the like terms.

$\begin{gathered} -5n+5n+12=0 \\ 0=-12 \end{gathered}$

0=-12 is a false statement.

Since we obtained a false statement, the given equation has no solution.

So, option b is correct.

Part 2:

The option (a) is n=3.

If while solving an equation, a single value is obtained for the variable, then the equation has only a single solution. If n=3 is obtained after solving the equation, then the student should chose option (a) as the answer.

The option (b) is "no solution".

While solving an equation, if we obtain an equation which is mathematically false, then the equation will have no solution. So, no solution is chosen when no value is obtained for n and the final equation is mathematically false.

The option (c) is "infinitely many solutions".

While solving an equation, if we obtain an equation which is mathematically correct such as 0=0, 7=7 etc., then the equation will have infinietly many solutions. So, infinitely many solutions is chosen when no value is obtained for n and the final equation is mathematically correct.