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@ -7,10 +7,7 @@
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%link{:rel => 'stylesheet', :type => 'text/css', :href => './style.css'}
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%link{:rel => 'stylesheet', :type => 'text/css', :href => './style.css'}
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%body
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%body
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%h2 Solve for $l$:
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%h2 Solve for $l$:
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#solve-for-l-01.solution
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:eqnarray
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:escaped
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$$
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\begin{eqnarray}
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-2lmn + 8m - 3n + 9 & = & -5m + 3n - 7 \\
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-2lmn + 8m - 3n + 9 & = & -5m + 3n - 7 \\
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-2lmn + 8m - 3n + 9 - 9 & = & -5m + 3n - 7 - 9 \\
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-2lmn + 8m - 3n + 9 - 9 & = & -5m + 3n - 7 - 9 \\
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-2lmn + 8m - 3n & = & -5m + 3n - 16 \\
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-2lmn + 8m - 3n & = & -5m + 3n - 16 \\
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@ -25,13 +22,8 @@
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l & = & \frac{\frac{-5m - 16 + 6n - 8m}{-2}}{mn} \\
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l & = & \frac{\frac{-5m - 16 + 6n - 8m}{-2}}{mn} \\
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l & = & \frac{\frac{-16 + 6n - 13m}{-2}}{mn} \\
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l & = & \frac{\frac{-16 + 6n - 13m}{-2}}{mn} \\
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l & = & \frac{8 - 3n - \frac{13m}{-2}}{mn} \\
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l & = & \frac{8 - 3n - \frac{13m}{-2}}{mn} \\
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\end{eqnarray}
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$$
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#solve-for-l-02.solution
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:eqnarray
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:escaped
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$$
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\begin{eqnarray}
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-2lmn + 8m - 3n + 9 & = & -5m + 3n - 7 \\
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-2lmn + 8m - 3n + 9 & = & -5m + 3n - 7 \\
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-2lmn + 8m - 3n + 9 - 9 & = & -5m + 3n - 7 - 9 \\
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-2lmn + 8m - 3n + 9 - 9 & = & -5m + 3n - 7 - 9 \\
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-2lmn + 8m - 3n & = & -5m + 3n + 2 \\
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-2lmn + 8m - 3n & = & -5m + 3n + 2 \\
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@ -46,13 +38,8 @@
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lmn & = & \frac{-13m}{-2} - 3n - 1 \\
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lmn & = & \frac{-13m}{-2} - 3n - 1 \\
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\frac{lmn}{mn} & = & \frac{\frac{-13m}{-2} - 3n - 1}{mn} \\
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\frac{lmn}{mn} & = & \frac{\frac{-13m}{-2} - 3n - 1}{mn} \\
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l & = & \frac{\frac{-13m}{-2} - 3n - 1}{mn} \\
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l & = & \frac{\frac{-13m}{-2} - 3n - 1}{mn} \\
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\end{eqnarray}
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$$
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#solve-for-l-03.solution
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:eqnarray
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:escaped
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$$
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\begin{eqnarray}
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-2lmn + 8m - 3n + 9 & = & -5m + 3n - 7 \\
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-2lmn + 8m - 3n + 9 & = & -5m + 3n - 7 \\
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-9 + -2lmn + 8m - 3n + 9 & = & -9 + -5m + 3n - 7 \\
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-9 + -2lmn + 8m - 3n + 9 & = & -9 + -5m + 3n - 7 \\
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-2lmn + 8m - 3n & = & -9 + -5m + 3n - 7 \\
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-2lmn + 8m - 3n & = & -9 + -5m + 3n - 7 \\
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@ -66,14 +53,9 @@
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\frac{-2lmn}{-2mn} & = & \frac{-13m + 6n + -16}{-2mn} \\
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\frac{-2lmn}{-2mn} & = & \frac{-13m + 6n + -16}{-2mn} \\
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l & = & \frac{-13m + 6n + -16}{-2mn} \\
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l & = & \frac{-13m + 6n + -16}{-2mn} \\
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l & = & \frac{13m - 6n + 16}{2mn} \\
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l & = & \frac{13m - 6n + 16}{2mn} \\
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\end{eqnarray}
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$$
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%h2 Solve for $x$:
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%h2 Solve for $x$:
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#solve-for-x-01.solution
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:eqnarray
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:escaped
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$$
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\begin{eqnarray}
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-2xy + 5xz - 5x + 10 & = & -6y - 2 \\
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-2xy + 5xz - 5x + 10 & = & -6y - 2 \\
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-2xy + 5xz - 5x + 10 - 10 & = & -6y - 2 - 10 \\
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-2xy + 5xz - 5x + 10 - 10 & = & -6y - 2 - 10 \\
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-2xy + 5xz - 5x & = & -6y + -2 + -10 \\
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-2xy + 5xz - 5x & = & -6y + -2 + -10 \\
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@ -85,13 +67,8 @@
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-5x \over -5 & = & -6y - 12 - 5xz + 2xy \over -5x \\
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-5x \over -5 & = & -6y - 12 - 5xz + 2xy \over -5x \\
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x & = & -6y - 12 - 5xz + 2xy \over -5x \\
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x & = & -6y - 12 - 5xz + 2xy \over -5x \\
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x & = & \frac{-6y}{-5x} - \frac{12}{-5x} - \frac{5xz}{-5x} + \frac{2xy}{-5x} \\
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x & = & \frac{-6y}{-5x} - \frac{12}{-5x} - \frac{5xz}{-5x} + \frac{2xy}{-5x} \\
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\end{eqnarray}
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$$
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#solve-for-x-02.solution
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:eqnarray
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:escaped
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$$
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\begin{eqnarray}
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-2xy + 5xz - 5x + 10 & = & -6y - 2 \\
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-2xy + 5xz - 5x + 10 & = & -6y - 2 \\
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-2xy + 5xz - 5x + 10 - 10 & = & -6y - 2 - 10 \\
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-2xy + 5xz - 5x + 10 - 10 & = & -6y - 2 - 10 \\
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-2xy + 5xz - 5x & = & -6y + -2 + -10 \\
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-2xy + 5xz - 5x & = & -6y + -2 + -10 \\
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@ -108,13 +85,8 @@
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-5x \over -5 & = & -6y - 12 \over -2y + 5z - 5 \\
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-5x \over -5 & = & -6y - 12 \over -2y + 5z - 5 \\
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x & = & -6y - 12 \over -2y + 5z - 5 \\
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x & = & -6y - 12 \over -2y + 5z - 5 \\
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x & = & 6y + 12 \over 2y - 5z + 5 \\
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x & = & 6y + 12 \over 2y - 5z + 5 \\
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\end{eqnarray}
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$$
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#solve-for-x-03.solution
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:eqnarray
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:escaped
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$$
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\begin{eqnarray}
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-2xy + 5xz - 5x + 10 & = & -6y - 2 \\
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-2xy + 5xz - 5x + 10 & = & -6y - 2 \\
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-2xy + 5xz - 5x + 10 - 10 & = & -6y - 2 - 10 \\
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-2xy + 5xz - 5x + 10 - 10 & = & -6y - 2 - 10 \\
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-2xy + 5xz - 5x & = & -6y - 12 \\
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-2xy + 5xz - 5x & = & -6y - 12 \\
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@ -122,14 +94,9 @@
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x \cdot (-2y + 5z - 5) \over -2y + 5z - 5 & = & -6y - 12 \over -2y + 5z - 5 \\
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x \cdot (-2y + 5z - 5) \over -2y + 5z - 5 & = & -6y - 12 \over -2y + 5z - 5 \\
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x & = & -6y - 12 \over -2y + 5z - 5 \\
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x & = & -6y - 12 \over -2y + 5z - 5 \\
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x & = & 6y + 12 \over 2y - 5z + 5 \\
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x & = & 6y + 12 \over 2y - 5z + 5 \\
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\end{eqnarray}
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$$
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%h2 Solve for $m$:
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%h2 Solve for $m$:
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#solve-for-m-01.solution
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:eqnarray
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:escaped
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$$
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\begin{eqnarray}
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-8m - 4n - 8p - 5 & = & -5n - p + 6 \\
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-8m - 4n - 8p - 5 & = & -5n - p + 6 \\
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-8m - 4n - 8p - 5 + 5 & = & -5n - p + 6 + 5 \\
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-8m - 4n - 8p - 5 + 5 & = & -5n - p + 6 + 5 \\
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-8m - 4n - 8p & = & -5n - p + 11 \\
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-8m - 4n - 8p & = & -5n - p + 11 \\
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@ -143,33 +110,21 @@
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m & = & -n + 11 + 7p \over -8 \\
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m & = & -n + 11 + 7p \over -8 \\
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m & = & n - 11 - 7p \over 8 \\
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m & = & n - 11 - 7p \over 8 \\
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m & = & n - 7p - 11 \over 8 \\
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m & = & n - 7p - 11 \over 8 \\
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\end{eqnarray}
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$$
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%h2 Solve for $x$ (again):
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%h2 Solve for $x$ (again):
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#solve-for-x2-01.solution
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:eqnarray
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:escaped
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$$
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\begin{eqnarray}
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7xy + 4xz + x + 1 & = & y + 6 \\
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7xy + 4xz + x + 1 & = & y + 6 \\
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7xy + 4xz + x + 1 - 1 & = & y + 6 - 1 \\
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7xy + 4xz + x + 1 - 1 & = & y + 6 - 1 \\
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7xy + 4xz + x & = & y + 5 \\
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7xy + 4xz + x & = & y + 5 \\
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x \cdot (7y + 4z + 1) & = & y + 5 \\
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x \cdot (7y + 4z + 1) & = & y + 5 \\
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x \cdot (7y + 4z + 1) \over 7y + 4z + 1 & = & y + 5 \over 7y + 4z + 1 \\
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x \cdot (7y + 4z + 1) \over 7y + 4z + 1 & = & y + 5 \over 7y + 4z + 1 \\
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x & = & y + 5 \over 7y + 4z + 1 \\
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x & = & y + 5 \over 7y + 4z + 1 \\
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\end{eqnarray}
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$$
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%h2 Solve for $v$:
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%h2 Solve for $v$:
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#solve-for-v-01.solution
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:eqnarray
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:escaped
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$$
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\begin{eqnarray}
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3vw - 2vx + 10v + 1 & = & w + 4 \\
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3vw - 2vx + 10v + 1 & = & w + 4 \\
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3vw - 2vx + 10v + 1 - 1 & = & w + 4 - 1 \\
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3vw - 2vx + 10v + 1 - 1 & = & w + 4 - 1 \\
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3vw - 2vx + 10v & = & w + 3 \\
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3vw - 2vx + 10v & = & w + 3 \\
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v \cdot (3w - 2x + 10) & = & w + 3 \\
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v \cdot (3w - 2x + 10) & = & w + 3 \\
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v \cdot (3w - 2x + 10) \over 3w - 2x + 10 & = & w + 3 \over 3w - 2x + 10 \\
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v \cdot (3w - 2x + 10) \over 3w - 2x + 10 & = & w + 3 \over 3w - 2x + 10 \\
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v & = & w + 3 \over 3w - 2x + 10 \\
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v & = & w + 3 \over 3w - 2x + 10 \\
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\end{eqnarray}
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$$
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