%% This document created by Scientific Notebook (R) Version 3.0


\documentclass[12pt,thmsa]{article}
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\usepackage{sw20jart}

%TCIDATA{TCIstyle=article/art4.lat,jart,sw20jart}

%TCIDATA{<META NAME="ViewSettings" CONTENT="17">}
%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Mon Feb 17 12:23:09 1997}
%TCIDATA{CSTFile=Exam.cst}
%TCIDATA{PageSetup=72,72,36,36,0}
%TCIDATA{AllPages=
%F=36,\PARA{038<p type="texpara" tag="Body Text" >\hfill \thepage}
%}


\input{tcilatex}
\begin{document}


\section{Exam}

\subsection{Text}

\section{Elementary Equations}

Your Name: 
%TCIMACRO{\HTML{<Input TYPE="Text" NAME="STUDENTNAME" VALUE=" " SIZE=0>}}
%BeginExpansion
%%
%EndExpansion

\vspace{1pt}

\subsection{Setup}

$\limfunc{num}=\limfunc{rand}(1,10)$ [$\limfunc{num}$ will generate
numerators for the fraction problems]

$\limfunc{den}=\limfunc{rand}(2,10)$ \ [$\limfunc{den}$ will generate
denominators]

Choice Space: 2

Choices:\ No Break, Radio Buttons, Permute

Question Space: 1

Title:Equations

\section{Question}

\subsection{Setup}

Select: 10

\section{Variant}

\subsection{Setup}

$a:=\limfunc{rand}(-10,10)$

$b:=\limfunc{rand}(-10,10)$

$x=-b/a$

Conditions: $\left( ab\neq 0\right) \wedge (a\neq b)\wedge \left( a\neq
-b\right) $

\subsection{Statement}

Solve the equation $%
%TCIMACRO{\FORMULA{aX+b}{aX+b}{evaluate}}
%BeginExpansion
aX+b%
%EndExpansion
=0$.

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{-1/x}{-\frac{1}{x}}{evaluate}}
%BeginExpansion
-\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{-x}{-x}{evaluate}}
%BeginExpansion
-x%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{1/x}{\frac{1}{x}}{evaluate}}
%BeginExpansion
\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{x}{x}{evaluate}}
%BeginExpansion
x%
%EndExpansion
\correctchoice{}$
\end{itemize}

\begin{description}
\item[Fixed]  None of the above
\end{description}

\section{Variant}

\subsection{Setup}

$a:=\limfunc{rand}(-10,10)$

$b:=\limfunc{rand}(-10,10)$

$x=b/a$

Conditions: $\left( ab\neq 0\right) \wedge (a\neq b)\wedge \left( a\neq
-b\right) $

\subsection{Statement}

Solve the equation $%
%TCIMACRO{\FORMULA{aX}{aX}{evaluate}}
%BeginExpansion
aX%
%EndExpansion
=%
%TCIMACRO{\FORMULA{b}{b}{evaluate}}
%BeginExpansion
b%
%EndExpansion
$.

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{-1/x}{-\frac{1}{x}}{evaluate}}
%BeginExpansion
-\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{-x}{-x}{evaluate}}
%BeginExpansion
-x%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{1/x}{\frac{1}{x}}{evaluate}}
%BeginExpansion
\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{x}{x}{evaluate}}
%BeginExpansion
x%
%EndExpansion
\correctchoice{}$
\end{itemize}

\begin{description}
\item[Fixed]  None of the above
\end{description}

\section{Variant}

\subsection{Setup}

$a:=\frac{\limfunc{num}}{\limfunc{den}}$

$b:=\frac{\limfunc{num}}{\limfunc{den}}$

$x=-b/a$

Conditions: $\left( ab\neq 0\right) \wedge (a\neq b)\wedge \left( a\neq
-b\right) $

\subsection{Statement}

Solve the equation $%
%TCIMACRO{\FORMULA{aX+b}{aX+b}{evaluate}}
%BeginExpansion
aX+b%
%EndExpansion
=0$.

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{1/x}{\frac{1}{x}}{evaluate}}
%BeginExpansion
\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{-x}{-x}{evaluate}}
%BeginExpansion
-x%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{x}{x}{evaluate}}
%BeginExpansion
x%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{-1/x}{-\frac{1}{x}}{evaluate}}
%BeginExpansion
-\frac{1}{x}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of the above
\end{description}

\section{Variant}

\subsection{Setup}

$a:=\frac{\limfunc{num}}{\limfunc{den}}$

$b:=\frac{\limfunc{num}}{\limfunc{den}}$

$x=b/a$

Conditions: $\left( ab\neq 0\right) \wedge (a\neq b)\wedge \left( a\neq
-b\right) $

\subsection{Statement}

Solve the equation $%
%TCIMACRO{\FORMULA{aX-b}{aX-b}{evaluate}}
%BeginExpansion
aX-b%
%EndExpansion
=0$.

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{-x}{-x}{evaluate}}
%BeginExpansion
-x%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{x}{x}{evaluate}}
%BeginExpansion
x%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{1/x}{\frac{1}{x}}{evaluate}}
%BeginExpansion
\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{-1/x}{-\frac{1}{x}}{evaluate}}
%BeginExpansion
-\frac{1}{x}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of the above
\end{description}

\section{Variant}

\subsection{Setup}

$a:=\frac{\limfunc{num}}{\limfunc{den}}$

$b:=\frac{\limfunc{num}}{\limfunc{den}}$

$x=b/a$

Conditions: $\left( ab\neq 0\right) \wedge (a\neq b)\wedge \left( a\neq
-b\right) $

\subsection{Statement}

Solve the equation $%
%TCIMACRO{\FORMULA{aX}{aX}{evaluate}}
%BeginExpansion
aX%
%EndExpansion
=%
%TCIMACRO{\FORMULA{b}{b}{evaluate}}
%BeginExpansion
b%
%EndExpansion
$.

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{-1/x}{-\frac{1}{x}}{evaluate}}
%BeginExpansion
-\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{-x}{-x}{evaluate}}
%BeginExpansion
-x%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{1/x}{\frac{1}{x}}{evaluate}}
%BeginExpansion
\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{x}{x}{evaluate}}
%BeginExpansion
x%
%EndExpansion
\correctchoice{}$
\end{itemize}

\begin{description}
\item[Fixed]  None of the above
\end{description}

\section{Variant}

\subsection{Setup}

$a:=\frac{\limfunc{num}}{\limfunc{den}}$

$b:=\frac{\limfunc{num}}{\limfunc{den}}$

$x=-b/a$

Conditions: $\left( ab\neq 0\right) \wedge (a\neq b)\wedge \left( a\neq
-b\right) $

\subsection{Statement}

Solve the equation $%
%TCIMACRO{\FORMULA{-aX}{-aX}{evaluate}}
%BeginExpansion
-aX%
%EndExpansion
=%
%TCIMACRO{\FORMULA{b}{b}{evaluate}}
%BeginExpansion
b%
%EndExpansion
$.

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{x}{x}{evaluate}}
%BeginExpansion
x%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{-x}{-x}{evaluate}}
%BeginExpansion
-x%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{1/x}{\frac{1}{x}}{evaluate}}
%BeginExpansion
\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{-1/x}{-\frac{1}{x}}{evaluate}}
%BeginExpansion
-\frac{1}{x}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of the above
\end{description}

\section{Variant}

\subsection{Setup}

$a:=\limfunc{rand}(-10,10)$

$b:=\limfunc{rand}(-10,10)$

$x=\left( 1-b\right) /a$

Conditions: $\left( a\left( b-1\right) \neq 0\right) \wedge (a\neq
b-1)\wedge \left( a\neq -b+1\right) $

\subsection{Statement}

Solve the equation $%
%TCIMACRO{\FORMULA{aX+b}{aX+b}{evaluate}}
%BeginExpansion
aX+b%
%EndExpansion
=1$.

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{1/x}{\frac{1}{x}}{evaluate}}
%BeginExpansion
\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{-x}{-x}{evaluate}}
%BeginExpansion
-x%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{x}{x}{evaluate}}
%BeginExpansion
x%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{-1/x}{-\frac{1}{x}}{evaluate}}
%BeginExpansion
-\frac{1}{x}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of the above
\end{description}

\section{Variant}

\subsection{Setup}

$a:=\frac{\limfunc{num}}{\limfunc{den}}$

$b:=\frac{\limfunc{num}}{\limfunc{den}}$

$x=\left( 1-b\right) /a$

Conditions: $\left( a\left( b-1\right) \neq 0\right) \wedge (a\neq
b-1)\wedge \left( a\neq -b+1\right) $

\subsection{Statement}

Solve the equation $%
%TCIMACRO{\FORMULA{aX+b}{aX+b}{evaluate}}
%BeginExpansion
aX+b%
%EndExpansion
=1$.

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{-x}{-x}{evaluate}}
%BeginExpansion
-x%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{x}{x}{evaluate}}
%BeginExpansion
x%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{1/x}{\frac{1}{x}}{evaluate}}
%BeginExpansion
\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{-1/x}{-\frac{1}{x}}{evaluate}}
%BeginExpansion
-\frac{1}{x}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of the above
\end{description}

\section{Variant}

\subsection{Setup}

$a:=\limfunc{rand}(-10,10)$

$b:=\limfunc{rand}(-10,10)$

$c:=\limfunc{rand}(-10,10)$

$x=\left( c-b\right) /a$

Conditions: $\left( a\left( b-c\right) \neq 0\right) \wedge (a\neq
b-c)\wedge \left( a\neq c-b\right) $

\subsection{Statement}

Solve the equation $%
%TCIMACRO{\FORMULA{aX+b}{aX+b}{evaluate}}
%BeginExpansion
aX+b%
%EndExpansion
=%
%TCIMACRO{\FORMULA{c}{c}{evaluate}}
%BeginExpansion
c%
%EndExpansion
$.

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{-1/x}{-\frac{1}{x}}{evaluate}}
%BeginExpansion
-\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{-x}{-x}{evaluate}}
%BeginExpansion
-x%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{1/x}{\frac{1}{x}}{evaluate}}
%BeginExpansion
\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{x}{x}{evaluate}}
%BeginExpansion
x%
%EndExpansion
\correctchoice{}$
\end{itemize}

\begin{description}
\item[Fixed]  None of the above
\end{description}

\section{Variant}

\subsection{Setup}

$a:=\frac{\limfunc{num}}{\limfunc{den}}$

$b:=\frac{\limfunc{num}}{\limfunc{den}}$

$c:=\frac{\limfunc{num}}{\limfunc{den}}$

$x=\left( c-b\right) /a$

Conditions: $\left( a\left( b-c\right) \neq 0\right) \wedge (a\neq
b-c)\wedge \left( a\neq c-b\right) $

\subsection{Statement}

Solve the equation $%
%TCIMACRO{\FORMULA{aX+b}{aX+b}{evaluate}}
%BeginExpansion
aX+b%
%EndExpansion
=%
%TCIMACRO{\FORMULA{c}{c}{evaluate}}
%BeginExpansion
c%
%EndExpansion
$.

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{1/x}{\frac{1}{x}}{evaluate}}
%BeginExpansion
\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{-x}{-x}{evaluate}}
%BeginExpansion
-x%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{x}{x}{evaluate}}
%BeginExpansion
x%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{-1/x}{-\frac{1}{x}}{evaluate}}
%BeginExpansion
-\frac{1}{x}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of the above
\end{description}

\section{Variant}

\subsection{Setup}

$a:=\limfunc{rand}(-10,10)$

$b:=\limfunc{rand}(-10,10)$

$x=a-2b$

Conditions: $\left( \left| x\right| \neq 1\right) \wedge (a\neq b)\wedge
\left( x\neq 0\right) $

\subsection{Statement}

Solve the equation $\frac{%
%TCIMACRO{\FORMULA{X+a}{X+a}{evaluate} }
%BeginExpansion
X+a%
%EndExpansion
}{%
%TCIMACRO{\FORMULA{X+b}{X+b}{evaluate} }
%BeginExpansion
X+b%
%EndExpansion
}=2$.

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{-x}{-x}{evaluate}}
%BeginExpansion
-x%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{x}{x}{evaluate}}
%BeginExpansion
x%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{1/x}{\frac{1}{x}}{evaluate}}
%BeginExpansion
\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{-1/x}{-\frac{1}{x}}{evaluate}}
%BeginExpansion
-\frac{1}{x}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of the above
\end{description}

\section{Variant}

\subsection{Setup}

$a:=\limfunc{rand}(-10,10)$

$b:=\limfunc{rand}(-10,10)$

$c:=\limfunc{rand}(3,10)$

$x=\left( a-cb\right) /\left( c-1\right) $

Conditions: $\left( \left( a-cb\right) \left( c-1\right) \neq 0\right)
\wedge \left( \left| \frac{a-cb}{c-1}\right| \neq 1\right) $

\subsection{Statement}

Solve the equation $\frac{%
%TCIMACRO{\FORMULA{X+a}{X+a}{evaluate} }
%BeginExpansion
X+a%
%EndExpansion
}{%
%TCIMACRO{\FORMULA{X+b}{X+b}{evaluate} }
%BeginExpansion
X+b%
%EndExpansion
}=%
%TCIMACRO{\FORMULA{c}{c}{evaluate}}
%BeginExpansion
c%
%EndExpansion
$.

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{1/x}{\frac{1}{x}}{evaluate}}
%BeginExpansion
\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{-x}{-x}{evaluate}}
%BeginExpansion
-x%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{x}{x}{evaluate}}
%BeginExpansion
x%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{-1/x}{-\frac{1}{x}}{evaluate}}
%BeginExpansion
-\frac{1}{x}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of the above
\end{description}

\section{Variant}

\subsection{Setup}

$a:=\limfunc{rand}(-10,10)$

$b:=\limfunc{rand}(-10,10)$

$x=-a$

Conditions: $\left( ab\neq 0\right) \wedge \left( a\neq b\right) $

\subsection{Statement}

Solve the equation $\frac{%
%TCIMACRO{\FORMULA{X+a}{X+a}{evaluate} }
%BeginExpansion
X+a%
%EndExpansion
}{%
%TCIMACRO{\FORMULA{X+b}{X+b}{evaluate} }
%BeginExpansion
X+b%
%EndExpansion
}=0$.

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{-1/x}{-\frac{1}{x}}{evaluate}}
%BeginExpansion
-\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{-x}{-x}{evaluate}}
%BeginExpansion
-x%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{1/x}{\frac{1}{x}}{evaluate}}
%BeginExpansion
\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{x}{x}{evaluate}}
%BeginExpansion
x%
%EndExpansion
\correctchoice{}$
\end{itemize}

\begin{description}
\item[Fixed]  None of the above
\end{description}

\section{Variant}

\subsection{Setup}

$a:=\limfunc{rand}(-10,10)$

$b:=\limfunc{rand}(-10,10)$

$c:=\limfunc{rand}(-10,-1)$

$x=\left( a-cb\right) /\left( c-1\right) $

Conditions: $\left( \left( a-cb\right) \left( c-1\right) \neq 0\right)
\wedge \left( \left| \frac{a-cb}{c-1}\right| \neq 1\right) \wedge \left(
a\neq b\right) $

\subsection{Statement}

Solve the equation $\frac{%
%TCIMACRO{\FORMULA{X+a}{X+a}{evaluate} }
%BeginExpansion
X+a%
%EndExpansion
}{%
%TCIMACRO{\FORMULA{X+b}{X+b}{evaluate} }
%BeginExpansion
X+b%
%EndExpansion
}=%
%TCIMACRO{\FORMULA{c}{c}{evaluate}}
%BeginExpansion
c%
%EndExpansion
$.

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{x}{x}{evaluate}}
%BeginExpansion
x%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{-x}{-x}{evaluate}}
%BeginExpansion
-x%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{1/x}{\frac{1}{x}}{evaluate}}
%BeginExpansion
\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{-1/x}{-\frac{1}{x}}{evaluate}}
%BeginExpansion
-\frac{1}{x}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of the above
\end{description}

\section{Variant}

\subsection{Setup}

$a:=\frac{\limfunc{num}}{\limfunc{den}}$

$b:=\frac{\limfunc{num}}{\limfunc{den}}$

$x=a-2b$

Conditions: $(a\neq 2b)\wedge \left( \left| a-2b\right| \neq 1\right) \wedge
\left( a\neq b\right) $

\subsection{Statement}

Solve the equation $\frac{%
%TCIMACRO{\FORMULA{X+a}{X+a}{evaluate} }
%BeginExpansion
X+a%
%EndExpansion
}{%
%TCIMACRO{\FORMULA{X+b}{X+b}{evaluate} }
%BeginExpansion
X+b%
%EndExpansion
}=2$.

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{1/x}{\frac{1}{x}}{evaluate}}
%BeginExpansion
\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{-x}{-x}{evaluate}}
%BeginExpansion
-x%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{x}{x}{evaluate}}
%BeginExpansion
x%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{-1/x}{-\frac{1}{x}}{evaluate}}
%BeginExpansion
-\frac{1}{x}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of the above
\end{description}

\section{Variant}

\subsection{Setup}

$a:=\frac{\limfunc{num}}{\limfunc{den}}$

$b:=\frac{\limfunc{num}}{\limfunc{den}}$

$c:=\frac{\limfunc{num}}{\limfunc{den}}$

$x=\left( a-cb\right) /\left( c-1\right) $

Conditions: $\left( a-cb\neq 0\right) \wedge \left( c>1\right) \wedge \left(
\left| \frac{a-cb}{c-1}\right| \neq 1\right) \wedge \left( a\neq b\right) $

\subsection{Statement}

Solve the equation $\frac{%
%TCIMACRO{\FORMULA{X+a}{X+a}{evaluate} }
%BeginExpansion
X+a%
%EndExpansion
}{%
%TCIMACRO{\FORMULA{X+b}{X+b}{evaluate} }
%BeginExpansion
X+b%
%EndExpansion
}=%
%TCIMACRO{\FORMULA{c}{c}{evaluate}}
%BeginExpansion
c%
%EndExpansion
$.

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{-x}{-x}{evaluate}}
%BeginExpansion
-x%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{x}{x}{evaluate}}
%BeginExpansion
x%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{1/x}{\frac{1}{x}}{evaluate}}
%BeginExpansion
\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{-1/x}{-\frac{1}{x}}{evaluate}}
%BeginExpansion
-\frac{1}{x}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of the above
\end{description}

\section{Variant}

\subsection{Setup}

$a:=\frac{\limfunc{num}}{\limfunc{den}}$

$b:=\frac{\limfunc{num}}{\limfunc{den}}$

$x:=-a$

Conditions: $\left( ab\neq 0\right) \wedge (a^{2}\neq 1)\wedge \left( a\neq
b\right) $

\subsection{Statement}

Solve the equation $\frac{%
%TCIMACRO{\FORMULA{X+a}{X+a}{evaluate} }
%BeginExpansion
X+a%
%EndExpansion
}{%
%TCIMACRO{\FORMULA{X+b}{X+b}{evaluate} }
%BeginExpansion
X+b%
%EndExpansion
}=0$.

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{1/x}{\frac{1}{x}}{evaluate}}
%BeginExpansion
\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{-x}{-x}{evaluate}}
%BeginExpansion
-x%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{x}{x}{evaluate}}
%BeginExpansion
x%
%EndExpansion
\correctchoice{}$

\item  $%
%TCIMACRO{\FORMULA{-1/x}{-\frac{1}{x}}{evaluate}}
%BeginExpansion
-\frac{1}{x}%
%EndExpansion
$
\end{itemize}

\begin{description}
\item[Fixed]  None of the above
\end{description}

\section{Variant}

\subsection{Setup}

$a:=\frac{\limfunc{num}}{\limfunc{den}}$

$b:=\frac{\limfunc{num}}{\limfunc{den}}$

$c:=-\frac{\limfunc{num}}{\limfunc{den}}$

$x=\left( a-cb\right) /\left( c-1\right) $

Conditions: $\left( \left( a-cb\right) \left( c-1\right) \neq 0\right)
\wedge \left( \left| x\right| \neq 1\right) \wedge \left( a\neq b\right) $

\subsection{Statement}

Solve the equation $\frac{%
%TCIMACRO{\FORMULA{X+a}{X+a}{evaluate} }
%BeginExpansion
X+a%
%EndExpansion
}{%
%TCIMACRO{\FORMULA{X+b}{X+b}{evaluate} }
%BeginExpansion
X+b%
%EndExpansion
}=%
%TCIMACRO{\FORMULA{c}{c}{evaluate}}
%BeginExpansion
c%
%EndExpansion
$.

\subsection{Choices}

\begin{itemize}
\item  $%
%TCIMACRO{\FORMULA{-1/x}{-\frac{1}{x}}{evaluate}}
%BeginExpansion
-\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{-x}{-x}{evaluate}}
%BeginExpansion
-x%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{1/x}{\frac{1}{x}}{evaluate}}
%BeginExpansion
\frac{1}{x}%
%EndExpansion
$

\item  $%
%TCIMACRO{\FORMULA{x}{x}{evaluate}}
%BeginExpansion
x%
%EndExpansion
\correctchoice{}$
\end{itemize}

\begin{description}
\item[Fixed]  None of the above
\end{description}

\end{document}
