From 8f30c764c5916d0b69ecf46afd2bf6066284ce67 Mon Sep 17 00:00:00 2001
From: Dan Buch <daniel.buch@gmail.com>
Date: Mon, 2 Apr 2012 00:50:58 -0400
Subject: [PATCH] working through problems for "Solving for a variable"

---
 .../algebra/solving-for-a-variable.tex        | 54 +++++++++++++++++++
 1 file changed, 54 insertions(+)
 create mode 100644 math-replay/algebra/solving-for-a-variable.tex

diff --git a/math-replay/algebra/solving-for-a-variable.tex b/math-replay/algebra/solving-for-a-variable.tex
new file mode 100644
index 0000000..7875d95
--- /dev/null
+++ b/math-replay/algebra/solving-for-a-variable.tex
@@ -0,0 +1,54 @@
+\documentclass{article}
+\begin{document}
+
+\begin{eqnarray*}
+-2lmn + 8m - 3n + 9 & = & -5m + 3n - 7 \\
+-2lmn + 8m - 3n + 9 - 9 & = & -5m + 3n - 7 - 9 \\
+-2lmn + 8m - 3n & = & -5m + 3n - 16 \\
+-2lmn + 8m - 3n + 3n & = & -5m + 3n - 16 + 3n \\
+-2lmn + 8m & = & -5m + 3n - 16 + 3n \\
+-2lmn + 8m - 8m & = & -5m + 3n - 16 + 3n - 8m \\
+-2lmn & = & -5m + 3n - 16 + 3n - 8m \\
+\frac{-2lmn}{-2} & = & \frac{-5m + 3n - 16 + 3n - 8m}{-2} \\
+lmn & = & \frac{-5m + 3n - 16 + 3n - 8m}{-2} \\
+\frac{lmn}{mn} & = & \frac{\frac{-5m + 3n - 16 + 3n - 8m}{-2}}{mn} \\
+l & = & \frac{\frac{-5m + 3n - 16 + 3n - 8m}{-2}}{mn} \\
+l & = & \frac{\frac{-5m - 16 + 6n - 8m}{-2}}{mn} \\
+l & = & \frac{\frac{-16 + 6n - 13m}{-2}}{mn} \\
+l & = & \frac{8 - 3n - \frac{13m}{-2}}{mn} \\
+\end{eqnarray*}
+
+\begin{eqnarray*}
+-2lmn + 8m - 3n + 9 & = & -5m + 3n - 7 \\
+-2lmn + 8m - 3n + 9 - 9 & = & -5m + 3n - 7 - 9 \\
+-2lmn + 8m - 3n & = & -5m + 3n + 2 \\
+-2lmn + 8m - 3n + 3n & = & -5m + 3n + 2 + 3n \\
+-2lmn + 8m & = & -5m + 6n + 2 \\
+-2lmn + 8m - 8m & = & -5m + 6n + 2 - 8m \\
+-2lmn & = & -13m + 6n + 2 \\
+\frac{-2lmn}{-2} & = & \frac{-13m + 6n + 2}{-2} \\
+lmn & = & \frac{-13m}{-2} + \frac{6n}{-2} + \frac{2}{-2} \\
+lmn & = & \frac{-13m}{-2} + \frac{6n}{-2} - 1 \\
+lmn & = & \frac{-13m}{-2} + \frac{3n}{-1} - 1 \\
+lmn & = & \frac{-13m}{-2} - 3n - 1 \\
+\frac{lmn}{mn} & = & \frac{\frac{-13m}{-2} - 3n - 1}{mn} \\
+l & = & \frac{\frac{-13m}{-2} - 3n - 1}{mn} \\
+\end{eqnarray*}
+
+\begin{eqnarray*}
+-2lmn + 8m - 3n + 9 & = & -5m + 3n - 7 \\
+-9 + -2lmn + 8m - 3n + 9 & = & -9 + -5m + 3n - 7 \\
+-2lmn + 8m - 3n & = & -9 + -5m + 3n - 7 \\
+-2lmn + 8m - 3n & = & -5m + 3n - 7 - 9 \\
+-2lmn + 8m - 3n & = & -5m + 3n + -7 + -9 \\
+-2lmn + 8m - 3n & = & -5m + 3n + -16 \\
+-2lmn + 8m - 3n + 3n & = & -5m + 3n + -16 + 3n \\
+-2lmn + 8m & = & -5m + -16 + 6n \\
+-2lmn + 8m - 8m & = & -5m + -16 + 6n - 8m \\
+-2lmn & = & -13m + 6n + -16 \\
+\frac{-2lmn}{-2mn} & = & \frac{-13m + 6n + -16}{-2mn} \\
+l & = & \frac{-13m + 6n + -16}{-2mn} \\
+l & = & \frac{13m - 6n + 16}{2mn} \\
+\end{eqnarray*}
+
+\end{document}