lehrkraefte:blc:miniaufgaben:kw46-2025 [https://fginfo.ksbg.ch Fachgruppe Informatik der KSBG]

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  miniaufgabe.js
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===== Montag 17. November 2025 =====
==== Aufgabe 1 ====
Lösen Sie die Gleichung nach $x$ auf.<JS>miniAufgabe("#exolinGleichGanzzahlen","#sollinGleichGanzzahlen",
[["$\\displaystyle 3\\left(5x -6\\right) = \\frac{5x-6}{-4}$", "\\begin{align*}3\\left(5x -6\\right) & = \\frac{5x-6}{-4} && | \\cdot -4\\\\\n-12\\left(5x -6\\right) & = 5x-6 && | \\text{TU}\\\\\n -60x+72 & =  5x-6 && | -5x-72\\\\\n -65x & = -78&& | :-65\\\\\nx & = \\frac{6}{5}\\\\\n\\end{align*}\n"], ["$\\displaystyle 3\\left(-5x +2\\right) = \\frac{6x-3}{-3}$", "\\begin{align*}3\\left(-5x +2\\right) & = \\frac{6x-3}{-3} && | \\cdot -3\\\\\n-9\\left(-5x +2\\right) & = 6x-3 && | \\text{TU}\\\\\n 45x-18 & =  6x-3 && | -6x+18\\\\\n 39x & = 15&& | :39\\\\\nx & = \\frac{5}{13}\\\\\n\\end{align*}\n"], ["$\\displaystyle -3\\left(-4x +2\\right) = \\frac{-4x+6}{3}$", "\\begin{align*}-3\\left(-4x +2\\right) & = \\frac{-4x+6}{3} && | \\cdot 3\\\\\n-9\\left(-4x +2\\right) & = -4x+6 && | \\text{TU}\\\\\n 36x-18 & =  -4x+6 && | 4x+18\\\\\n 40x & = 24&& | :40\\\\\nx & = \\frac{3}{5}\\\\\n\\end{align*}\n"], ["$\\displaystyle 3\\left(6x -3\\right) = \\frac{-4x+6}{-2}$", "\\begin{align*}3\\left(6x -3\\right) & = \\frac{-4x+6}{-2} && | \\cdot -2\\\\\n-6\\left(6x -3\\right) & = -4x+6 && | \\text{TU}\\\\\n -36x+18 & =  -4x+6 && | 4x-18\\\\\n -32x & = -12&& | :-32\\\\\nx & = \\frac{3}{8}\\\\\n\\end{align*}\n"], ["$\\displaystyle -2\\left(-4x +3\\right) = \\frac{6x-2}{5}$", "\\begin{align*}-2\\left(-4x +3\\right) & = \\frac{6x-2}{5} && | \\cdot 5\\\\\n-10\\left(-4x +3\\right) & = 6x-2 && | \\text{TU}\\\\\n 40x-30 & =  6x-2 && | -6x+30\\\\\n 34x & = 28&& | :34\\\\\nx & = \\frac{14}{17}\\\\\n\\end{align*}\n"], ["$\\displaystyle -5\\left(-2x +4\\right) = \\frac{5x-3}{4}$", "\\begin{align*}-5\\left(-2x +4\\right) & = \\frac{5x-3}{4} && | \\cdot 4\\\\\n-20\\left(-2x +4\\right) & = 5x-3 && | \\text{TU}\\\\\n 40x-80 & =  5x-3 && | -5x+80\\\\\n 35x & = 77&& | :35\\\\\nx & = \\frac{11}{5}\\\\\n\\end{align*}\n"], ["$\\displaystyle -6\\left(2x -5\\right) = \\frac{4x-2}{3}$", "\\begin{align*}-6\\left(2x -5\\right) & = \\frac{4x-2}{3} && | \\cdot 3\\\\\n-18\\left(2x -5\\right) & = 4x-2 && | \\text{TU}\\\\\n -36x+90 & =  4x-2 && | -4x-90\\\\\n -40x & = -92&& | :-40\\\\\nx & = \\frac{23}{10}\\\\\n\\end{align*}\n"], ["$\\displaystyle -3\\left(6x -4\\right) = \\frac{-6x+3}{2}$", "\\begin{align*}-3\\left(6x -4\\right) & = \\frac{-6x+3}{2} && | \\cdot 2\\\\\n-6\\left(6x -4\\right) & = -6x+3 && | \\text{TU}\\\\\n -36x+24 & =  -6x+3 && | 6x-24\\\\\n -30x & = -21&& | :-30\\\\\nx & = \\frac{7}{10}\\\\\n\\end{align*}\n"], ["$\\displaystyle 3\\left(3x -4\\right) = \\frac{3x-6}{-5}$", "\\begin{align*}3\\left(3x -4\\right) & = \\frac{3x-6}{-5} && | \\cdot -5\\\\\n-15\\left(3x -4\\right) & = 3x-6 && | \\text{TU}\\\\\n -45x+60 & =  3x-6 && | -3x-60\\\\\n -48x & = -66&& | :-48\\\\\nx & = \\frac{11}{8}\\\\\n\\end{align*}\n"], ["$\\displaystyle -3\\left(-3x +5\\right) = \\frac{3x-6}{3}$", "\\begin{align*}-3\\left(-3x +5\\right) & = \\frac{3x-6}{3} && | \\cdot 3\\\\\n-9\\left(-3x +5\\right) & = 3x-6 && | \\text{TU}\\\\\n 27x-45 & =  3x-6 && | -3x+45\\\\\n 24x & = 39&& | :24\\\\\nx & = \\frac{13}{8}\\\\\n\\end{align*}\n"]],
" <hr> ", " <hr> ");
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<div id="sollinGleichGanzzahlen"></div>
<div style='font-size:12px;color:gray;'>ruby linearegleichungen.rb 4</div>
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==== Aufgabe 2 ====
Lösen Sie die Gleichung nach $x$ auf.<JS>miniAufgabe("#exolinGleich","#sollinGleich",
[["$$-\\frac{5}{4}x = \\frac{2}{9}-\\frac{4}{3}x$$", "\\begin{align*}\n-\\frac{5}{4}x = & \\frac{2}{9}-\\frac{4}{3}x & & | +\\frac{4}{3}x\\\\\n\\frac{1}{12}x  = & \\frac{2}{9} & & | : \\frac{1}{12}\\\\\nx  = & \\frac{8}{3}\n\\end{align*}"], ["$$-\\frac{13}{9}x = -\\frac{5}{6}-\\frac{17}{9}x$$", "\\begin{align*}\n-\\frac{13}{9}x = & -\\frac{5}{6}-\\frac{17}{9}x & & | +\\frac{17}{9}x\\\\\n\\frac{4}{9}x  = & -\\frac{5}{6} & & | : \\frac{4}{9}\\\\\nx  = & -\\frac{15}{8}\n\\end{align*}"], ["$$-\\frac{7}{4}x = \\frac{7}{5}-\\frac{7}{8}x$$", "\\begin{align*}\n-\\frac{7}{4}x = & \\frac{7}{5}-\\frac{7}{8}x & & | +\\frac{7}{8}x\\\\\n-\\frac{7}{8}x  = & \\frac{7}{5} & & | : -\\frac{7}{8}\\\\\nx  = & -\\frac{8}{5}\n\\end{align*}"], ["$$-\\frac{17}{6}x = \\frac{7}{3}-\\frac{7}{6}x$$", "\\begin{align*}\n-\\frac{17}{6}x = & \\frac{7}{3}-\\frac{7}{6}x & & | +\\frac{7}{6}x\\\\\n-\\frac{5}{3}x  = & \\frac{7}{3} & & | : -\\frac{5}{3}\\\\\nx  = & -\\frac{7}{5}\n\\end{align*}"], ["$$-\\frac{9}{4}x = -\\frac{3}{2}-\\frac{19}{6}x$$", "\\begin{align*}\n-\\frac{9}{4}x = & -\\frac{3}{2}-\\frac{19}{6}x & & | +\\frac{19}{6}x\\\\\n\\frac{11}{12}x  = & -\\frac{3}{2} & & | : \\frac{11}{12}\\\\\nx  = & -\\frac{18}{11}\n\\end{align*}"], ["$$-\\frac{10}{9}x = \\frac{10}{9}+\\frac{4}{3}x$$", "\\begin{align*}\n-\\frac{10}{9}x = & \\frac{10}{9}+\\frac{4}{3}x & & | -\\frac{4}{3}x\\\\\n-\\frac{22}{9}x  = & \\frac{10}{9} & & | : -\\frac{22}{9}\\\\\nx  = & -\\frac{5}{11}\n\\end{align*}"], ["$$-\\frac{17}{8}x = -\\frac{3}{8}-\\frac{23}{16}x$$", "\\begin{align*}\n-\\frac{17}{8}x = & -\\frac{3}{8}-\\frac{23}{16}x & & | +\\frac{23}{16}x\\\\\n-\\frac{11}{16}x  = & -\\frac{3}{8} & & | : -\\frac{11}{16}\\\\\nx  = & \\frac{6}{11}\n\\end{align*}"], ["$$\\frac{9}{5}x = -\\frac{3}{4}+\\frac{12}{5}x$$", "\\begin{align*}\n\\frac{9}{5}x = & -\\frac{3}{4}+\\frac{12}{5}x & & | -\\frac{12}{5}x\\\\\n-\\frac{3}{5}x  = & -\\frac{3}{4} & & | : -\\frac{3}{5}\\\\\nx  = & \\frac{5}{4}\n\\end{align*}"], ["$$\\frac{3}{5}x = \\frac{4}{5}+\\frac{17}{10}x$$", "\\begin{align*}\n\\frac{3}{5}x = & \\frac{4}{5}+\\frac{17}{10}x & & | -\\frac{17}{10}x\\\\\n-\\frac{11}{10}x  = & \\frac{4}{5} & & | : -\\frac{11}{10}\\\\\nx  = & -\\frac{8}{11}\n\\end{align*}"], ["$$\\frac{11}{8}x = \\frac{3}{10}+\\frac{3}{2}x$$", "\\begin{align*}\n\\frac{11}{8}x = & \\frac{3}{10}+\\frac{3}{2}x & & | -\\frac{3}{2}x\\\\\n-\\frac{1}{8}x  = & \\frac{3}{10} & & | : -\\frac{1}{8}\\\\\nx  = & -\\frac{12}{5}\n\\end{align*}"]],
" <hr> ", " <hr> ");
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<HTML>
<div id="exolinGleich"></div>

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<hidden Lösungen>

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<div id="sollinGleich"></div>
<div style='font-size:12px;color:gray;'>ruby linearegleichungen.rb 1</div>
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