Problem:
Find the value(s) of x such that 8xy−12y+2x−3=0 is true for all values of y.
Answer Choices:
A. 32
B. 23 or −41
C. −32 or −41
D. 23
E. −23 or −41
Solution:
The given equation can be factored as
0=8xy−12y+2x−3=4y(2x−3)+(2x−3)=(4y+1)(2x−3).
For this equation to be true for all values of y we must have 2x−3=0, that is, x=3/2.
Answer: D.
The problems on this page are the property of the MAA's American Mathematics Competitions