Solve |-4t| = -24 ..... trick question

[pka]

possible values of t that make -2|2t| = -24 a true statement.
Her answer was wrong. Could anyone take a look at what she tried and help us figure out what she is doing wrong?

Multiply by -1/2 :
-1/2 * -2|2t| = |2t|
-1/2 * -24 = 12
|2t| = 12

This Question, $\displaystyle \large{-2|2t|=-24}$ is exactly the same as $\displaystyle \large{|t|=6}$
which is exactly the same as $\displaystyle \large{|-4t|=24}$ which is exactly the same as $\displaystyle \large{|2t|=12}$.

It is a sad commentary on the state of basic mathematics education if
anyone cannot see the solution of $\displaystyle \large{|-4t|=-24}$ is less than 3 seconds.

 

[Otis]

$\displaystyle \large{|-4t|=-24}$

The right side should be 24, not -24.

 

[pka]

The right side should be 24, not -24.

Absolutely NOT! That is the whole point.
Given the question is: what are the solutions to $\displaystyle \Large{|-4t|=-24}$ and you cannot see the solution is less than three seconds then you have no business teaching mathematics. Do you see the solution? I think not. That is sad.

 

[Otis]

Absolutely NOT! That is the whole point.
Given the question is: what are the solutions to $\displaystyle \Large{|-4t|=-24}$ and you cannot see the solution is less than three seconds then you have no business teaching mathematics. Do you see the solution? I think not. That is sad.

How can the absolute value of an expression equal a negative quantity?

 

[pka]

How can the absolute value of an expression equal a negative quantity?

Otis, how dense can you be? That is the whole point. There is no solution! That is the answer. Every nation-wide that I have ever worked on, there is a similar question. The point being to catch students who teachers never prepared them to look for such questions. That why such test are called College Aptitude Test.

 

[Harry_the_cat]

Otis, how dense can you be?

Yeah Oats! (bit harsh though!)

 

[Otis]

... if anyone cannot see the solution of $\displaystyle \large{|-4t|=-24}$ ...

... the solutions to $\displaystyle \Large{|-4t|=-24}$ ...

... you cannot see the solution ... That is sad.

My point in posting that the right side needs to be 24 is because the equation has no solution as posted.

You implied (more than once!) that it does have a solution.

I think that you have confused the words "solution" and "answer".

 

[stapel]

This Question, $\displaystyle \large{-2|2t|=-24}$ is exactly the same as ... $\displaystyle \large{|-4t|=24}$....

It is a sad commentary on the state of basic mathematics education if anyone cannot see the solution of $\displaystyle \large{|-4t|=-24}$ is less than 3 seconds.

True, but "|-4t| = -24" is not the same equation as "-2|2t| = -24", since |-4t| is non-negative and -2|2t| is non-positive.

 

[Deleted member 4993]

In my opinion, this type of question:

Solve for 't': |-4t| = -24

Is only good for class-room discussion and should not be used in exam nor as a homework.

 

[lookagain]

In my opinion, this type of question:

Solve for 't': |-4t| = -24 $\displaystyle \ \ \ \ \ \ \ \$ This could be the one example given in class for the notes.

Is only good for class-room discussion and should not be used in exam nor as a homework.

No, that type of question should always be used in exams or in homework of "sufficient length."

The instructor will stress that the absolute value of an expression is non-negative. He/she should show the class one related example, such as the above, so they will recognize it,
even if they have to tweak the exam problem ** or homework problem more to solve it.

The instructor is not to say "There is no answer." The instructor can say, "'no solution' is
the answer."




** Example of an exam question/HW question:$\displaystyle \ \ \ \$ |-3x| + 4 = 25

(Here, the instructor is looking for the answer of "no solution.")

 

[pka]

In my opinion, this type of question:
Solve for 't': |-4t| = -24
Is only good for class-room discussion and should not be used in exam nor as a homework.

Have you experience with test-prep for the SAT or ACT?

 

[Steven G]

Absolutely NOT! That is the whole point.
Given the question is: what are the solutions to $\displaystyle \Large{|-4t|=-24}$ and you cannot see the solution is less than three seconds then you have no business teaching mathematics. Do you see the solution? I think not. That is sad.

Personally I think giving three second is generous.

 

[Steven G]

No, that type of question should always be used in exams or in homework of "sufficient length."

The instructor will stress that the absolute value of an expression is non-negative. He/she should show the class
one related example, such as the above, so they will recognize it, even if they have to tweak the exam problem **
or homework problem more to solve it.

I agree with you

** Example of an exam question/HW question:$\displaystyle \ \ \ \$ |-3x| + 4 = 25

(Here, the instructor is looking for the answer of "no solution.")

I think that x= +/- 7 would work

 

[Deleted member 4993]

Have you experience with test-prep for the SAT or ACT?

Yes .. I do. I have 3 children whom I prepped for SAT (math) since their 6 th grade. They all scored 650+ in their 7 th grade test - one of them scored 780 (he is a fantastic multiple-choice-test taker).
But in SAT test the correct answer is one of the choice (I don't remember seeing "none of the above" as choice). So that (correct answer) prompts the student - which is different from "essay" answers.

 

[pka]

But in SAT test the correct answer is one of the choice (I don't remember seeing "none of the above" as choice). So that (correct answer) prompts the student - which is different from "essay" answers.

Surely you have seen e) no solution as one of the distractors?

 

[Deleted member 4993]

The whole objective of this thread was to torture you .... torture you till you say "uncle"

You have not cried "uncle" - so objective has not been met - so the thread cannot be closed....

 

[Otis]

I do not believe in tricking beginning algebra students because there is too great a risk of demoralization or of frustration secondary to wasted time. Instructors ought to adopt a growth-mindset approach here, particularly in beginning algebra, as this is where too many students become turned-off to mathematics.

There's nothing wrong with testing beginning students' comprehension by challenging a concept, but, instead of implying that unsolvable equations have a solution, these types of questions ought to be qualified with phrases like "If possible, find..." or "...if solution(s) exist...".

Who (or what) exactly is being served by tricking beginning algebra students?