- #1

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## Main Question or Discussion Point

A bit of a newbie question, but I was wondering how does one go about solving these?

For example: (I was working on a problem posted on another thread on Homework Help)

[tex]

|3n-4| < 9\epsilon n^2 + 3 \epsilon

[/tex]

Epsilon is a small positive number of course :P

The tricky part is when I split it up..

[tex]

\begin{align*}

-9\epsilon n^2 - 3n - 3\epsilon + 4 < 0 \\

9\epsilon n^2 -3n + 3\epsilon + 4 > 0

\end{align*}

[/tex]

Wouldn't the solution for n then be 4 inequalities? That doesn't make sense, does it?

For example: (I was working on a problem posted on another thread on Homework Help)

[tex]

|3n-4| < 9\epsilon n^2 + 3 \epsilon

[/tex]

Epsilon is a small positive number of course :P

The tricky part is when I split it up..

[tex]

\begin{align*}

-9\epsilon n^2 - 3n - 3\epsilon + 4 < 0 \\

9\epsilon n^2 -3n + 3\epsilon + 4 > 0

\end{align*}

[/tex]

Wouldn't the solution for n then be 4 inequalities? That doesn't make sense, does it?