diff --git a/math-replay/algebra/solving-for-a-variable.haml b/math-replay/algebra/solving-for-a-variable.haml index 3562e03..7a12659 100644 --- a/math-replay/algebra/solving-for-a-variable.haml +++ b/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} $$ diff --git a/math-replay/algebra/solving-for-a-variable.tex b/math-replay/algebra/solving-for-a-variable.tex deleted file mode 100644 index 3f86b74..0000000 --- a/math-replay/algebra/solving-for-a-variable.tex +++ /dev/null @@ -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}