NOTE 1: Be sure to read Homework Format, Homework Writing Policy, and Explanations Expected BEFORE writing up your solutions to be turned in.
Due Friday, November 20
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.
- 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?
- 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?.
- A student obtains the “solution” 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?
c. What conclusion can you draw about the student's 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 17, 2009 11:17 PM
Go to Lesson 44 (due Nov 20).
Go to Lesson 47 (due Nov 23).
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