You can do that nesting your equations in a fleqn
environment (from nccmath
). This environment accepts an optional argument for the distance from the left margin ( 0 pt
by default):
\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[showframe]{geometry}
\usepackage{mathtools, nccmath}
\begin{document}
\begin{equation}
d_j =
\begin{cases}
\text{newval}_i, & \quad i = j\\
\text{randval}_k, & \quad k = j\\
\text{bestval}_j, & \quad \text{otherwise}
\end{cases}
\end{equation}
\begin{fleqn}
\noindent\texttt{With fleqn: }
\begin{equation}
d_j =
\begin{cases}
\text{newval}_i, & \quad i = j\\
\text{randval}_k, & \quad k = j\\
\text{bestval}_j, & \quad \text{otherwise}
\end{cases}
\end{equation}
\end{fleqn}
\begin{fleqn}[3em]
\noindent\texttt{With fleqn and optional argument [3em]: }
\begin{equation}
d_j =
\begin{cases}
\text{newval}_i, & \quad i = j\\
\text{randval}_k, & \quad k = j\\
\text{bestval}_j, & \quad \text{otherwise}
\end{cases}
\end{equation}
\end{fleqn}
\end{document}

\mathit{newval}_i
and similarly the other names, never use the default math italic for multi-letter words.