How to solve the inequality $\frac {5x+1}{4x-1}\geq1$ Please help me solve the following inequality.

\begin{eqnarray}
\\\frac {5x+1}{4x-1}\geq1\\
\end{eqnarray}

I have tried the following method but it is wrong. Why?

\begin{eqnarray}
\\\frac {5x+1}{4x-1}&\geq&1\\
\\5x+1&\geq& 4x-1\\
\\x &\geq& -2
\end{eqnarray}


Thank you for your attention

$$
\frac{5x+1}{4x-1}\geq 1\Leftrightarrow \frac{5x+1}{4x-1}-1\geq 0\Leftrightarrow\frac{5x+1-(4x-1)}{4x-1}\geq 0 \Leftrightarrow \frac{5x+1-4x+1}{4x-1}\geq 0 
$$
$$
\Leftrightarrow \frac{x+2}{4x-1}\geq 0
$$
Now $x+2=0 \Rightarrow x=-2$, and $4x-1=0\Rightarrow x=\frac{1}{4}$
For $x\in (-\infty, -2]$, and $x\in(\frac{1}{4}, +\infty)$, $\frac{x+2}{4x-1}\geq 0$ 
