As I write this, I've graded the final exams for one of my three Algebra 2 classes. I'm going to schedule this post to show up on the blog as my last Algebra 2 class starts its final tomorrow, so that none of my students could possibly stumble upon this post and have an advantage when taking the test.
My final consists of a department-wide 15-question multiple choice section, as well as a Darren-made 15-question short answer section. Students did the multiple guess part first, then started the short answer part.
The second question on the short answer section (so there's no excuse for brains having already been turned to mush) was something like this: |something|=-6x . It doesn't matter what was in the absolute value sign, but it was something simple and linear like x-5. Since you, my reader, don't know what was in the absolute value sign, you can't solve the problem, but I ask you this: what can you tell me about the answer x?
Look at the problem and think for a moment.
I understand it's been awhile since many of you have worked with absolute values, so here's what I'm looking for: since the absolute value of a real number is never negative, then x must be negative because -6 times a negative number would be positive.
Solving the problem would give two answers, one positive and one negative--the positive one is extraneous, meaning that when you substitute it back into the original equation it doesn't work.
This was one of the easiest problems on the test, and yet only 3 of my 30 or so students wrote down the correct answer (which is just the negative answer). Most did all this work and then didn't even take the time (and they had plenty of time) to substitute their answers back in to check them. To say I'm disappointed would be an understatement.