LaTeX Making "tabs" in LaTeX for problem sets

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The discussion focuses on recreating a document in LaTeX, specifically aligning "Factor" and "Solution" after a numbered section (1.1.1). It explains that in an enumerated list, items are preceded by \item, and a blank line after an item starts a new paragraph aligned with the previous item. This alignment technique is confirmed as the method used in the original document. A user successfully implemented this by using \item[1.1.1]. The conversation then shifts to a question about matrices and the use of symbols for tilde alignment. Initially, attempts with \~ and \sim caused formatting issues, but the user ultimately resolved the problem by utilizing math mode.
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Trying to replicate a document in LaTeX. Not sure how they got the tab or alignment format.
I'm trying to recreate this document in LaTeX, but I'm not sure how they aligned "Factor" and "Solution" after 1.1.1.
Any ideas?
Screen Shot 2020-01-15 at 6.58.48 PM.png
 
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It looks like the paras with numbers like 1.1.1 are part of an enumerated list, between \begin{enumerate} and \end{enumerate}.

In such a list, numbered items must be preceded by the code \item. The default is to number them as 1, 2, 3 but settings can be changed to show legal style numbering such as is shown above.

If you put a blank line after a numbered item and then start a new para, without starting it with \item, latex will align the left side of the new para with the left side of text of the numbered item above, as you see in the OP.

I think that's what they've done.

Note that a blank line in latex code signifies a new para. It doesn't put a blank line in the output text.
 
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Excellent thank you andrew! That was it exactly. I just did the enumerate and \item[1.1.1]
 
Ok one more question if it's not too much trouble. This is with the matrices on the bottom. I've tried \~ as well as \sim to go where to the tilde is and neither works.
The former jumbles everything up and even makes a matrix disappear.
The latter looks good but it gets ride of the centering. Any ideas?
\
Screen Shot 2020-01-15 at 9.34.23 PM.png
Screen Shot 2020-01-15 at 9.35.09 PM.png
 
Actually just got it. Had to use math mode for some reason.
 

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