Aligning multiple equations to both the left and to a specific place

Question

I have some long equations. I want to achieve the followings:

1. How to justify the equation to the left?
2. How to align the equations as in the blue arrow?
3. Just one equation number is required.

For Example;

\begin{small}
\begin{equation} \label{Eq:1}
      \begin{aligned}
& f(x):\; && x^3+4 x +2\\
& g(x):\;  &&x^3+3 x +4\\
&&-5 x^4+x^6\\
& h(x):\; && 0\leq x^5+6 x +7 
      \end{aligned}
  \end{equation}
\end{small}

where \cref{Eq:1} is an example. 

I read the environments alignat, flalign* etc. But I still can't achieve what I want.

Answer 1

You may use the IEEEeqnarray environment from the IEEEtrantools package.

\documentclass{article}

\usepackage{IEEEtrantools}
\usepackage{showframe} %to show page layout
\usepackage{cleveref}

\begin{document}

\begin{IEEEeqnarray*}{*rCl} % * before r aligns the full equation to left margin
    f(x)&:\; & x^3+4 x +2\\
    g(x)&:\; & x^3+3 x +4 \IEEEyesnumber\label{Eq:1}\\ 
        &    & = 5 x^4+x^6\\
    h(x)&:\; & 0\leq x^5+6 x +7 
\end{IEEEeqnarray*}

where \cref{Eq:1} is an example.
\end{document}

Answer 2

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{flalign}
f(x)\colon& x^3+4x+2       &\notag\\
g(x)\colon& x^3+3x+4       &\label{Eq:1}\\
          & =5x^4+x^6      &\notag\\
h(x)\colon& 0\leq x^5+6x+7 &\notag
\end{flalign}
where \eqref{Eq:1} is an example. 
\end{document}

Another solution:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{flalign}
\begin{aligned}
f(x)\colon& x^3+4x+2\\
g(x)\colon& x^3+3x+4\\
          & =5x^4+x^6\\
h(x)\colon& 0\leq x^5+6x+7
\end{aligned}
&&\label{Eq:1}
\end{flalign}
where \eqref{Eq:1} is an example. 
\end{document}