\title{Simple fraction I}
\author{Gang Xiao}
\email{xiao@unice.fr}
\language{en}
\options{nofloat askresult}
\methods{ineq/addterm, ineq/mulexp, ineq/divexp, ineq/exsides}
\minsteps{3}

\text{x=random(a,b,c,d,p,q,r,s,t,u,v,x,y,z)}

\text{sh=shuffle(15)}
\integer{a=(item(1,\sh)+1)*random(-1,1)}
\integer{b=(item(2,\sh)+1)*random(-1,1)}
\integer{c=(item(3,\sh)+1)}
\integer{d=-(\b)}

\matrix{data=>,<,1
<,>,-1
}
\text{data=randomrow(\data)}
\text{s1=item(1,\data)}
\text{s2=item(2,\data)}
\integer{it=item(3,\data)}

\function{left=(\x + \a)/(\x + \b)}
\real{tester=(\a-(\b))*(\it)}
\integer{c=\tester>0?1+\c:1-\c}
\text{sign=random(<,>,<=,>=)}
\equivalence{\left \sign \c}
\context{\x \s1 \d}

\statement{
Solve the inequality \(\left \sign \c), under the condition
\(\x \s1 \d).
<p>
The goal of the exercise is to transform the given inequality into an
equivalent one whose left side is \x, and whos right side is a constant.
}

\text{cut=wims(translate internal <=> to , , in \equivalence)}
\text{newleft=item(1,\cut)}
\text{newright=item(2,\cut)}

\condition{\newleft issametext \x and \x notin \newright}

