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Diffstat (limited to 'macros/latex/contrib/profcollege/latex/PfCEquationSoustraction2.tex')
-rw-r--r--macros/latex/contrib/profcollege/latex/PfCEquationSoustraction2.tex247
1 files changed, 124 insertions, 123 deletions
 diff --git a/macros/latex/contrib/profcollege/latex/PfCEquationSoustraction2.tex b/macros/latex/contrib/profcollege/latex/PfCEquationSoustraction2.texindex a03f2d7442..5e64be9cf8 100644--- a/macros/latex/contrib/profcollege/latex/PfCEquationSoustraction2.tex+++ b/macros/latex/contrib/profcollege/latex/PfCEquationSoustraction2.tex@@ -6,7 +6,7 @@ \ifx\bla#2\bla%on teste si le paramètre #2 est vide: % si oui, on est dans le cas b=cx. Eh bien on échange :) % Mais attention si les deux paramètres a et c sont vides...- \EquaBase[#1]{#4}{}{}{#3}+ \EquaBase[#1]{#4}{0}{0}{#3} \else % si non, on est dans le cas ax=d \xintifboolexpr{#2==0}{%@@ -42,8 +42,9 @@ {\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{} } \end{align*}- \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2==1}{\useKV[ClesEquation]{Lettre}=\num{#5}}{\num{#2}\useKV[ClesEquation]{Lettre}=\num{#5}}$ a une unique solution : $\displaystyle\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\opdiv*{#5}{#2}{numequa}{resteequa}\opcmp{resteequa}{0}\ifopeq\opexport{numequa}{\numequa}\num{\numequa}\else\ifboolKV[ClesEquation]{Simplification}{\SSimplifie{#5}{#2}}{\frac{\num{#5}}{\num{#2}}}\fi$.%- }{}+ \xdef\Coeffb{#5}%+ \xdef\Coeffa{#2}%+ \ifboolKV[ClesEquation]{Solution}{\EcrireSolutionEquation{#2}{#3}{#4}{#5}}{}% } } \fi@@ -63,21 +64,21 @@ }% }{%ELSE \xintifboolexpr{#3==0}{%ax+b=d- \EquaBase[#1]{#2}{}{}{#5}%- }{%ax+b=d$Ici+ \EquaBase[#1]{#2}{0}{0}{#5}%+ }{%ax+b=d$ \begin{align*} \tikzmark{A-\theNbequa}\xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\num{#5}\tikzmark{E-\theNbequa}\\ \ifboolKV[ClesEquation]{Decomposition}{% \xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}&=\num{#5}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\\ }{}% \tikzmark{C-\theNbequa}\xdef\Coeffa{#2}\xdef\Coeffb{\fpeval{#5-#3}}\xintifboolexpr{\Coeffa==1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}- \ifboolKV[ClesEquation]{Decomposition}{\\\xintifboolexpr{\Coeffa==1}{}{\frac{\num{\Coeffa}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}}}{}+ \ifboolKV[ClesEquation]{Decomposition}{\xintifboolexpr{\Coeffa==1}{}{\\\frac{\num{\Coeffa}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}}}{} \xintifboolexpr{\Coeffa==1}{}{\\} \ifboolKV[ClesEquation]{Fleches}{% \leftcomment{A-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% \rightcomment{E-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}% }{}- \xintifboolexpr{\Coeffa==1}{% + \xintifboolexpr{\Coeffa==1}{% }{%\ifnum\cmtd>1 \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\ \ifboolKV[ClesEquation]{Fleches}{%@@ -103,133 +104,132 @@ }{} \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} \end{align*}- \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\num{#5}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.- }{}+ \ifboolKV[ClesEquation]{Solution}{\EcrireSolutionEquation{#2}{#3}{#4}{#5}}{}% } } \fi } -\newcommand{\EquaTroisSoustraction}[5][]{%ax+b=cx ou ax=cx+d+\newcommand\EquaTroisSoustraction[5][]{%ax+b=cx ou ax=cx+d \useKVdefault[ClesEquation]% \setKV[ClesEquation]{#1}% \ifx\bla#3\bla%on inverse en faisant attention à la boucle #3<->#5 \ifx\bla#5\bla% %% paramètre oublié \else- \EquaTroisSoustraction[#1]{#4}{#5}{#2}{}%+ \EquaTroisSoustraction[#1]{#4}{#5}{#2}{0}% \fi \else \xintifboolexpr{#2==0}{%b=cx- \EquaBase[#1]{#4}{}{}{#3}+ \EquaBase[#1]{#4}{0}{0}{#3} }{% \xintifboolexpr{#4==0}{%ax+b=0- \EquaDeuxSoustraction[#1]{#2}{#3}{}{0}- }{%ax+b=cx- \xintifboolexpr{#2==#4}{%- \xintifboolexpr{#3==0}{%ax=ax- L'équation $\xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}=\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ a une infinité de solutions.}%- {%ax+b=ax- L'équation $\xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ n'a aucune solution.%- }%- }{%% Cas délicat- \xintifboolexpr{#2>#4}{%ax+b=cx avec a>c- \begin{align*}- \tikzmark{A-\theNbequa}\xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\tikzmark{E-\theNbequa}\\- \ifboolKV[ClesEquation]{Decomposition}{%- \xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\\- }{}- \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa==1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=0\tikzmark{F-\theNbequa}\\- \ifboolKV[ClesEquation]{Decomposition}{%- \xintifboolexpr{\Coeffa==1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}&=0\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\tikzmark{F-\theNbequa}\\- }{}%- \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{\Coeffa==1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\- %eric- \ifboolKV[ClesEquation]{Decomposition}{\\\xintifboolexpr{\Coeffa==1}{}{\frac{\num{\Coeffa}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}}}{}- % eric- \xintifboolexpr{\Coeffa==1}{}{\\}- \ifboolKV[ClesEquation]{Fleches}{%- \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}- \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}- \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%- \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%- }{}- \xintifboolexpr{\Coeffa==1}{}{%\ifnum\cmtd>1- \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\- \ifboolKV[ClesEquation]{Fleches}{%- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{- \ifboolKV[ClesEquation]{FlecheDiv}{%- \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%- \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{}- }- %% decimal- \ifboolKV[ClesEquation]{Decimal}{%- \\\useKV[ClesEquation]{Lettre}&=\num{\fpeval{\Coeffb/\Coeffa}}%- }{}%- % %%% - \ifboolKV[ClesEquation]{Entier}{%- \SSimpliTest{\Coeffb}{\Coeffa}%- \ifboolKV[ClesEquation]{Simplification}{%- \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\- }{}- }{}- }- \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}- \end{align*}- \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.}{}- }{%ax+b=cx+d avec a0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\tikzmark{E-\theNbequa}\\- \ifboolKV[ClesEquation]{Decomposition}{%- \xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\\- }{}- \tikzmark{B-\theNbequa}\xdef\Coeffb{#3}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa==1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\tikzmark{F-\theNbequa}- \xintifboolexpr{\Coeffa==1}{}{\\}- \ifboolKV[ClesEquation]{Fleches}{%- \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}- \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}- }{}- % eric- \ifboolKV[ClesEquation]{Decomposition}{\\\xintifboolexpr{\Coeffa==1}{}{\frac{\num{\Coeffb}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}&=\frac{\num{\Coeffa}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}}}{}- % eric- \xintifboolexpr{\Coeffa==1}{}{%\ifnum\cmtd>1- \tikzmark{D-\theNbequa}\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}\tikzmark{H-\theNbequa}%\\- \ifboolKV[ClesEquation]{Fleches}{%- \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%- \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{- \ifboolKV[ClesEquation]{FlecheDiv}{%- \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%- \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% - }{}- }- %% decimal- \ifboolKV[ClesEquation]{Decimal}{%- \\\num{\fpeval{\Coeffb/\Coeffa}}&=\useKV[ClesEquation]{Lettre}%- }{}%- % %%% - \ifboolKV[ClesEquation]{Entier}{%- \SSimpliTest{\Coeffb}{\Coeffa}%- \ifboolKV[ClesEquation]{Simplification}{%- \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\- }{}- }{}- }- \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}- \end{align*}- \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.}{}%- }%- }%+ \EquaDeuxSoustraction[#1]{#2}{#3}{0}{0}+ }{%ax+b=cx+ \xintifboolexpr{#2==#4}{%+ \xintifboolexpr{#3==0}{%ax=ax+ L'équation $\xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}=\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ a une infinité de solutions.}%+ {%ax+b=ax+ L'équation $\xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}$ n'a aucune solution.%+ }%+ }{%% Cas délicat+ \xintifboolexpr{#2>#4}{%ax+b=cx avec a>c+ \begin{align*}+ \tikzmark{A-\theNbequa}\xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\tikzmark{E-\theNbequa}\\+ \ifboolKV[ClesEquation]{Decomposition}{%+ \xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#4>0}{-\num{#4}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#4}}\useKV[ClesEquation]{Lettre}}}\\+ }{}+ \tikzmark{B-\theNbequa}\xdef\Coeffa{\fpeval{#2-#4}}\xintifboolexpr{\Coeffa==1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=0\tikzmark{F-\theNbequa}\\+ \ifboolKV[ClesEquation]{Decomposition}{%+ \xintifboolexpr{\Coeffa==1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}&=0\mathcolor{Cdecomp}{\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}}\tikzmark{F-\theNbequa}\\+ }{}%+ \tikzmark{C-\theNbequa}\xdef\Coeffb{\fpeval{0-#3}}\xintifboolexpr{\Coeffa==1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}&=\num{\Coeffb}\tikzmark{G-\theNbequa}%\\+ % eric+ \ifboolKV[ClesEquation]{Decomposition}{\\\xintifboolexpr{\Coeffa==1}{}{\frac{\num{\Coeffa}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}}}{}%\\+ % eric+ \xintifboolexpr{\Coeffa==1}{}{\\}+ \ifboolKV[ClesEquation]{Fleches}{%+ \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}+ \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#4>0}{-\num{#4}}{+\num{\fpeval{0-#4}}}\useKV[ClesEquation]{Lettre}$}+ \leftcomment{B-\theNbequa}{C-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%+ \rightcomment{F-\theNbequa}{G-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#3>0}{-\num{#3}}{+\num{\fpeval{0-#3}}}$}%+ }{}%+ \xintifboolexpr{\Coeffa==1}{}{%\ifnum\cmtd>1+ \tikzmark{D-\theNbequa}\useKV[ClesEquation]{Lettre}&=\frac{\num{\Coeffb}}{\num{\Coeffa}}\tikzmark{H-\theNbequa}%\\+ \ifboolKV[ClesEquation]{Fleches}{%+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{%+ \ifboolKV[ClesEquation]{FlecheDiv}{%+ \leftcomment{C-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%+ \rightcomment{G-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{}+ }+ %% decimal+ \ifboolKV[ClesEquation]{Decimal}{%+ \\\useKV[ClesEquation]{Lettre}&=\num{\fpeval{\Coeffb/\Coeffa}}%\\+ }{}%+ %+ \ifboolKV[ClesEquation]{Entier}{%+ \SSimpliTest{\Coeffb}{\Coeffa}%+ \ifboolKV[ClesEquation]{Simplification}{%+ \ifthenelse{\boolean{Simplification}}{\\\useKV[ClesEquation]{Lettre}&=\SSimplifie{\Coeffb}{\Coeffa}}{}%\\+ }{}+ }{}+ }+ \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}+ \end{align*}+ % \ifboolKV[ClesEquation]{Solution}{L'équation \AffichageEqua{#2}{#3}{#4}{#5} a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.}{}+ }{%ax+b=cx+d avec a0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\tikzmark{E-\theNbequa}\\+ \ifboolKV[ClesEquation]{Decomposition}{%+ \xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\mathcolor{Cdecomp}{\xintifboolexpr{#2>0}{-\num{#2}\useKV[ClesEquation]{Lettre}}{+\num{\fpeval{0-#2}}\useKV[ClesEquation]{Lettre}}}\\+ }{}+ \tikzmark{B-\theNbequa}\xdef\Coeffb{#3}\xdef\Coeffa{\fpeval{#4-#2}}\xintifboolexpr{#3>0}{\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{\Coeffa==1}{}{\num{\Coeffa}}\useKV[ClesEquation]{Lettre}\tikzmark{F-\theNbequa}%\\+ \xintifboolexpr{\Coeffa==1}{}{\\}+ \ifboolKV[ClesEquation]{Fleches}{%+ \leftcomment{A-\theNbequa}{B-\theNbequa}{A-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}+ \rightcomment{E-\theNbequa}{F-\theNbequa}{E-\theNbequa}{$\xintifboolexpr{#2>0}{-\num{#2}}{+\num{\fpeval{0-#2}}}\useKV[ClesEquation]{Lettre}$}+ }{}%\\+ %% eric+ \ifboolKV[ClesEquation]{Decomposition}{\xintifboolexpr{\Coeffa==1}{}{\frac{\num{\Coeffb}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}&=\frac{\num{\Coeffa}}{\mathcolor{Cdecomp}{\num{\Coeffa}}}\useKV[ClesEquation]{Lettre}}\\}{}%\\+ % eric+ \xintifboolexpr{\Coeffa==1}{}{%\ifnum\cmtd>1+ \tikzmark{D-\theNbequa}\frac{\num{\Coeffb}}{\num{\Coeffa}}&=\useKV[ClesEquation]{Lettre}\tikzmark{H-\theNbequa}%\\+ \ifboolKV[ClesEquation]{Fleches}{%+ \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%+ \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{+ \ifboolKV[ClesEquation]{FlecheDiv}{%+ \leftcomment{B-\theNbequa}{D-\theNbequa}{A-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}%+ \rightcomment{F-\theNbequa}{H-\theNbequa}{E-\theNbequa}{$\div\xintifboolexpr{\Coeffa<0}{(\num{\Coeffa})}{\num{\Coeffa}}$}% + }{}+ }+ %% decimal+ \ifboolKV[ClesEquation]{Decimal}{%+ \\\num{\fpeval{\Coeffb/\Coeffa}}&=\useKV[ClesEquation]{Lettre}%\\+ }{}%+ %+ \ifboolKV[ClesEquation]{Entier}{%+ \SSimpliTest{\Coeffb}{\Coeffa}%+ \ifboolKV[ClesEquation]{Simplification}{%+ \ifthenelse{\boolean{Simplification}}{\\\SSimplifie{\Coeffb}{\Coeffa}&=\useKV[ClesEquation]{Lettre}}{}%\\+ }{}+ }{}+ }+ \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}}+ \end{align*}+ % \ifboolKV[ClesEquation]{Solution}{L'équation \AffichageEqua{#2}{#3}{#4}{#5} a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.}{}% }% }%- \fi+ \ifboolKV[ClesEquation]{Solution}{\EcrireSolutionEquation{#2}{#3}{#4}{#5}}{}%+ }% }%+ \fi+}% --\newcommand{\ResolEquationSoustraction}[5][]{%+\newcommand\ResolEquationSoustraction[5][]{% \useKVdefault[ClesEquation]% \setKV[ClesEquation]{#1}% \xintifboolexpr{#2==0}{%@@ -241,23 +241,23 @@ }% }% {%0x+b=cx+d$- \EquaDeuxSoustraction[#1]{#4}{#5}{}{#3}%+ \EquaDeuxSoustraction[#1]{#4}{#5}{0}{#3}% }% }{% \xintifboolexpr{#4==0}{%ax+b=0x+d- \EquaDeuxSoustraction[#1]{#2}{#3}{}{#5}%+ \EquaDeuxSoustraction[#1]{#2}{#3}{0}{#5}% } {%ax+b=cx+d$ \xintifboolexpr{#3==0}{% \xintifboolexpr{#5==0}{%ax=cx- \EquaTroisSoustraction[#1]{#2}{0}{#4}{}%+ \EquaTroisSoustraction[#1]{#2}{0}{#4}{0}% }% {%ax=cx+d- \EquaTroisSoustraction[#1]{#4}{#5}{#2}{}%+ \EquaTroisSoustraction[#1]{#4}{#5}{#2}{0}% }% }% {\xintifboolexpr{#5==0}{%ax+b=cx- \EquaTroisSoustraction[#1]{#2}{#3}{#4}{}%+ \EquaTroisSoustraction[#1]{#2}{#3}{#4}{0}% }% {%ax+b=cx+d -- ici \xintifboolexpr{#2==#4}{%@@ -314,8 +314,8 @@ } \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} \end{align*}- \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.%- }{}+ %\ifboolKV[ClesEquation]{Solution}{L'équation \AffichageEqua{#2}{#3}{#4}{#5} une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.%+ %}{} }{%ax+b=cx+d avec a0}{+\num{#3}}{-\num{\fpeval{0-#3}}}&=\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}\tikzmark{E-\theNbequa}\\@@ -362,9 +362,10 @@ } \ifboolKV[ClesEquation]{Fleches}{\stepcounter{Nbequa}}{\ifboolKV[ClesEquation]{FlecheDiv}{\stepcounter{Nbequa}}{}} \end{align*}- \ifboolKV[ClesEquation]{Solution}{L'équation $\xintifboolexpr{#2==1}{}{\num{#2}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#3>0}{+\num{#3}}{-\num{\fpeval{0-#3}}}=\xintifboolexpr{#4==1}{}{\num{#4}}\useKV[ClesEquation]{Lettre}\xintifboolexpr{#5>0}{+\num{#5}}{-\num{\fpeval{0-#5}}}$ a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.%- }{}%+ %\ifboolKV[ClesEquation]{Solution}{L'équation \AffichageEqua{#2}{#3}{#4}{#5} a une unique solution : \opdiv*{\Coeffb}{\Coeffa}{solution}{resteequa}\opcmp{resteequa}{0}$\ifboolKV[ClesEquation]{LettreSol}{\useKV[ClesEquation]{Lettre}=}{}\displaystyle\ifopeq\opexport{solution}{\solution}\num{\solution}\else\ifboolKV[ClesEquation]{Entier}{\SSimplifie{\Coeffb}{\Coeffa}}{\frac{\num{\Coeffb}}{\num{\Coeffa}}}\fi$.%+ %}{}% }%+ \ifboolKV[ClesEquation]{Solution}{\EcrireSolutionEquation{#2}{#3}{#4}{#5}}{}% }% }% }%