Solving equations with greatest integer function

[Bea77]

Homework Statement

I can't find a step by step explanation for solving these types of equations

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

Homework Equations

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

or

48 = 4[2x/3]

How do you handle the multipliers iand constants inside the brackets?
thx
3. The Attempt at a Solution

 

[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!