The discussion revolves around solving equations involving the greatest integer function, specifically equations like 99 = [2x+1]/3 and 48 = 4[2x/3]. Participants are exploring how to handle the multipliers and constants within the brackets of these equations.
Some participants have provided insights on interpreting the equations and have confirmed understanding of the relationships between the variables. There appears to be a productive exchange of ideas regarding the implications of the greatest integer function in the context of the problems posed.
Participants are navigating through the specifics of the greatest integer function and its application in the given equations, with some assumptions about the behavior of the function being questioned.
statdad said:Think about how the greatest integer function works. For example,
[tex] \lfloor 3.2 \rfloor = \lfloor 3.582 \rfloor = 3[/tex]
and in fact, if [tex]3 \le x < 4[/tex] it is true that
[tex] \lfloor x \rfloor = 3[/tex]
So, if you know that
[tex] \frac{\lfloor 2x+1\rfloor}{3} = 99[/tex]
you also know that
[tex] \lfloor 2x+1 \rfloor = 297[/tex]
(the [tex]3[/tex] in the denominator is not in the function). What does the final
statement above tell you about how large [tex]2x + 1[/tex] must be?
statdad said:Yup.