Lesson 46a.

NOTE 1: Be sure to read Homework Format, Homework Writing Policy, and Explanations Expected BEFORE writing up your solutions to be turned in.

Due Monday, November 30
This Lesson is essentially the same as Lesson 46. Two warnings have been added, and some comments have been added in boldface. If you have a printout of Lesson 46, you can use it, but you should make sure you answer all the questions given below.

WARNING 1.

In order to answer these questions correctly, you will have to THINK about what you are doing. The worksheet done in class on Thursday, Nov 19, Inequalities (pdf document), especially the first part (the first four problems) is very relevant and should be understood thoroughly.

WARNING 2.

As usual, you answers should contain the context of the questions you are answering. See the links above and below for the instructions on how to answer questions in homework; see especially Homework Format.

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A student is asked to solve the inequality
          2y(y-4) < 0.
The following questions refer to attempts to solve this inequality.

NOTE: To “solve” the inequality means (as with solving equations) to find all values of the variable (in this case,  y)  which make the inequality true. This set, the set of all values of the variable which make the inequality true, is called the “solution set” for the inequality. In other words, “solving” the inequality means finding the solution set.

1. Starting with the original inequality  2y(y-4) < 0,  a student obtains as the next step in the solution process
             y - 4 < 0;
   presumably this is obtained by dividing both sides of the original inequality by  2y.  Discuss the validity of this. I.e., is it legitimate to divide the given original inequality by  2y  to obtain  y - 4 < 0  as the next step in the solution process? If “yes”, explain why. If “no”, explain why not.
   
   
2. Starting with the original inequality  2y(y-4) < 0,  a student writes as the next step in the solution process
             y < 0,       y - 4 < 0.
   Discuss the validity of this; i.e., do the two inequalities  y < 0,   y - 4 < 0  follow from the original inequality?. If “yes”, explain why. If “no”, explain why not.
   
   
3. A student obtains the “solution”  y < 4. In other words, the student claims that the solution set is the set of all numbers  y  satisfying  y < 4.
   
   a. Does  y = 0  belong to the student's “solution set” ?  I.e., does  y = 0  satisfy the student’s solution?
   
   b. Does  y = 0  satisfy the original inequality,  2y(y-4) < 0?
   
   c. What conclusion can you draw about the student's solution? NOTE: The point here is NOT for you to say that “I know what the solution is, and it is different from the student's solution, so the student's solution is wrong”. The point is to analyze the student's solution on its own terms, based on your answers to a. and b. above, as if you did NOT know the correct solution.
   

NOTE: As stated on the Course Home Page, all due dates are tentative. Assignments, or parts of assignments, may be postponed to a later date.

Last modified Nov 24, 2009 7:13 AM

Go to Lesson 44a (due Nov 30).

Go to Lesson 50 (due Nov 30).

Go to Lesson 47 (due Nov 23).

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