solving equations with greatest integer function

[Bea77]

1. The problem statement, all variables and given/known data
I can't find a step by step explanation for solving these types of equations

eg.
99 = [2x+1]/3


2. Relevant equations

eg.
99 = [2x+1]/3

or

48 = 4[2x/3]

How do you handle the multipliers iand constants inside the brackets?
thx
[b]3. The attempt at a solution[b]

[statdad]

Think about how the greatest integer function works. For example,


\lfloor 3.2 \rfloor = \lfloor 3.582 \rfloor = 3


and in fact, if 3 \le x < 4 it is true that


\lfloor x \rfloor = 3


So, if you know that


\frac{\lfloor 2x+1\rfloor}{3} = 99


you also know that


\lfloor 2x+1 \rfloor = 297


(the 3 in the denominator is not in the function). What does the final
statement above tell you about how large 2x + 1 must be?

[Bea77]

Think about how the greatest integer function works. For example,


\lfloor 3.2 \rfloor = \lfloor 3.582 \rfloor = 3


and in fact, if 3 \le x < 4 it is true that


\lfloor x \rfloor = 3


So, if you know that


\frac{\lfloor 2x+1\rfloor}{3} = 99


you also know that


\lfloor 2x+1 \rfloor = 297


(the 3 in the denominator is not in the function). What does the final
statement above tell you about how large 2x + 1 must be?

--------------------
so 297 <= 2x+1 < 298

296 <=2x and 2x < 297
148 <=x and x < 148.5

Did I get it?

[statdad]

Yup.

[Bea77]

Yup.


Thanks!