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I'm trying to achieve the following: enter image description here So I'd like to have in-line lists, that our flush with the left margin and vertically aligned with each letter. I achieved the result above by manually spacing, which is not ideal. I can't seem to find an environment that covers each of the above conditions.

Using the following answers: How to make horizontal lists? I can achieve the following:

\usepackage{tasks}
\begin{tasks}[counter-format={(tsk[a])}, label-align=left, label-offset={0mm}, label-width={5mm}, item-indent={5mm}, label-format={\bfseries}, column-sep=-30mm, after-item-skip=-1mm, after-skip={3mm}](2)
\task $f(5)$
\task $f(x+h)$
\task $f(x+h) - f(x)$
\task $\dfrac{f(x+h)-f(x)}{h} \quad h\neq 0$ \end{tasks}

enter image description here

I don't know how to put a space between the letter and the expression. For example: (a)[INSERT SPACE HERE] f(5). Adjusting the parameters listed in the code above seems to adjust other things. Using ":/" in math mode works, but it's not an ideal solution.

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You need to adjust the label-width and item-indent settings to be larger:

enter image description here

\documentclass{article}

\usepackage{amsmath,tasks}

\begin{document}

\begin{tasks}[
    label={(\alph*)}, 
    label-align=left, 
    label-offset={0mm}, 
    label-width=20pt, 
    item-indent=20pt, 
    label-format={\bfseries}, 
    column-sep=-30mm, 
    after-item-skip=-1mm, 
    after-skip={3mm}](2)
  \task $f(5)$
  \task $f(x + h)$
  \task $f(x + h) - f(x)$
  \task $\dfrac{f(x + h) - f(x)}{h} \quad h \neq 0$
\end{tasks}

\end{document}
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