more solutions

math-replay/algebra/solving-for-a-variable.haml

@@ -84,5 +84,66 @@
         -2xy - 5x & = & -6y - 12 - 5xz \\
         -2xy + 2xy - 5x & = & -6y - 12 - 5xz + 2xy \\
         -5x & = & -6y - 12 - 5xz + 2xy \\
+        -5x \over -5 & = & -6y - 12 - 5xz + 2xy \over -5x \\
+        x & = & -6y - 12 - 5xz + 2xy \over -5x \\
+        x & = & \frac{-6y}{-5x} - \frac{12}{-5x} - \frac{5xz}{-5x} + \frac{2xy}{-5x} \\
+        \end{eqnarray}
+        $$
+
+    #solve-for-x-02.solution
+      :escaped
+        $$
+        \begin{eqnarray}
+        -2xy + 5xz - 5x + 10 & = & -6y - 2 \\
+        -2xy + 5xz - 5x + 10 - 10 & = & -6y - 2 - 10 \\
+        -2xy + 5xz - 5x & = & -6y + -2 + -10 \\
+        -2xy + 5xz - 5x & = & -6y - 12 \\
+        -2xy + 5xz - 5x \over 5z & = & -6y - 12 \over 5z \\
+        -2xy + x - 5x & = & -6y - 12 \over 5z \\
+        -2xy + x + -5x & = & -6y - 12 \over 5z \\
+        -2xy + -4x & = & -6y - 12 \over 5z \\
+        -2xy - 4x & = & -6y - 12 \over 5z \\
+        -2xy - 4x \over -2y & = & -6y - 12 \over -2y + 5z \\
+        -x - 4x \over -2y & = & -6y - 12 \over -2y + 5z \\
+        -x + -4x & = & -6y - 12 \over -2y + 5z \\
+        -5x & = & -6y - 12 \over -2y + 5z \\
+        -5x \over -5 & = & -6y - 12 \over -2y + 5z - 5 \\
+        x & = & -6y - 12 \over -2y + 5z - 5 \\
+        x & = & 6y + 12 \over 2y - 5z + 5 \\
+        \end{eqnarray}
+        $$
+
+    #solve-for-x-03.solution
+      :escaped
+        $$
+        \begin{eqnarray}
+        -2xy + 5xz - 5x + 10 & = & -6y - 2 \\
+        -2xy + 5xz - 5x + 10 - 10 & = & -6y - 2 - 10 \\
+        -2xy + 5xz - 5x & = & -6y - 12 \\
+        x \cdot (-2y + 5z - 5) & = & -6y - 12 \\
+        x \cdot (-2y + 5z - 5) \over -2y + 5z - 5 & = & -6y - 12 \over -2y + 5z - 5 \\
+        x & = & -6y - 12 \over -2y + 5z - 5 \\
+        x & = & 6y + 12 \over 2y - 5z + 5 \\
+        \end{eqnarray}
+        $$
+
+    %h2 Solve for $m$:
+    #solve-for-m-01.solution
+      :escaped
+        $$
+        \begin{eqnarray}
+        -8m - 4n - 8p - 5 & = & -5n - p + 6 \\
+        -8m - 4n - 8p - 5 + 5 & = & -5n - p + 6 + 5 \\
+        -8m - 4n - 8p & = & -5n - p + 11 \\
+        -8m - 4n - 8p + 8p & = & -5n - p + 11 + 8p \\
+        -8m - 4n & = & -5n + -p + 11 + 8p \\
+        -8m - 4n & = & -5n + 11 + 7p \\
+        -8m - 4n + 4n & = & -5n + 11 + 7p + 4n \\
+        -8m & = & -n + 11 + 7p \\
+        -8m & = & -n + 11 + 7p \\
+        -8m \over -8 & = & -n + 11 + 7p \over -8 \\
+        m & = & -n + 11 + 7p \over -8 \\
+        m & = & n - 11 - 7p \over 8 \\
+        m & = & n - 7p - 11 \over 8 \\
         \end{eqnarray}
         $$

math-replay/algebra/solving-for-a-variable.tex

@@ -1,67 +0,0 @@
-\documentclass{article}
-\begin{document}
-
-Solve for $l$:
-\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*}
-
-Solve for $x$:
-\begin{eqnarray*}
--2xy + 5xz - 5x + 10 & = & -6y - 2 \\
--2xy + 5xz - 5x + 10 - 10 & = & -6y - 2 - 10 \\
--2xy + 5xz - 5x & = & -6y + -2 + -10 \\
--2xy + 5xz - 5x & = & -6y + -12 \\
--2xy + 5xz - 5xz - 5x & = & -6y - 12 - 5xz \\
--2xy - 5x & = & -6y - 12 - 5xz \\
--2xy + 2xy - 5x & = & -6y - 12 - 5xz + 2xy \\
--5x & = & -6y - 12 - 5xz + 2xy \\
-\end{eqnarray*}
-
-\end{document}