miniaufgabe.js
==== 23. August 2021 bis 27. August 2021 ====
=== Donnerstag 26. August 2021 ===
Lösen Sie die Gleichung nach $x$ auf.miniAufgabe("#exolinGleich","#sollinGleich",
[["$$-\\frac{6}{7}x = -\\frac{10}{3}+\\frac{4}{7}x$$", "\\begin{align*}\n-\\frac{6}{7}x = & -\\frac{10}{3}+\\frac{4}{7}x & & | -\\frac{4}{7}x\\\\\n-\\frac{10}{7}x = & -\\frac{10}{3} & & | : -\\frac{10}{7}\\\\\nx = & \\frac{7}{3}\n\\end{align*}"], ["$$-\\frac{5}{11}x = \\frac{7}{3}+\\frac{16}{11}x$$", "\\begin{align*}\n-\\frac{5}{11}x = & \\frac{7}{3}+\\frac{16}{11}x & & | -\\frac{16}{11}x\\\\\n-\\frac{21}{11}x = & \\frac{7}{3} & & | : -\\frac{21}{11}\\\\\nx = & -\\frac{11}{9}\n\\end{align*}"], ["$$\\frac{3}{5}x = -\\frac{3}{2}-\\frac{3}{5}x$$", "\\begin{align*}\n\\frac{3}{5}x = & -\\frac{3}{2}-\\frac{3}{5}x & & | +\\frac{3}{5}x\\\\\n\\frac{6}{5}x = & -\\frac{3}{2} & & | : \\frac{6}{5}\\\\\nx = & -\\frac{5}{4}\n\\end{align*}"], ["$$-\\frac{7}{3}x = -\\frac{3}{2}+\\frac{1}{6}x$$", "\\begin{align*}\n-\\frac{7}{3}x = & -\\frac{3}{2}+\\frac{1}{6}x & & | -\\frac{1}{6}x\\\\\n-\\frac{5}{2}x = & -\\frac{3}{2} & & | : -\\frac{5}{2}\\\\\nx = & \\frac{3}{5}\n\\end{align*}"], ["$$-\\frac{5}{7}x = -\\frac{4}{7}-\\frac{1}{2}x$$", "\\begin{align*}\n-\\frac{5}{7}x = & -\\frac{4}{7}-\\frac{1}{2}x & & | +\\frac{1}{2}x\\\\\n-\\frac{3}{14}x = & -\\frac{4}{7} & & | : -\\frac{3}{14}\\\\\nx = & \\frac{8}{3}\n\\end{align*}"], ["$$\\frac{5}{3}x = \\frac{2}{3}+\\frac{17}{15}x$$", "\\begin{align*}\n\\frac{5}{3}x = & \\frac{2}{3}+\\frac{17}{15}x & & | -\\frac{17}{15}x\\\\\n\\frac{8}{15}x = & \\frac{2}{3} & & | : \\frac{8}{15}\\\\\nx = & \\frac{5}{4}\n\\end{align*}"], ["$$-\\frac{15}{8}x = \\frac{5}{3}-\\frac{15}{16}x$$", "\\begin{align*}\n-\\frac{15}{8}x = & \\frac{5}{3}-\\frac{15}{16}x & & | +\\frac{15}{16}x\\\\\n-\\frac{15}{16}x = & \\frac{5}{3} & & | : -\\frac{15}{16}\\\\\nx = & -\\frac{16}{9}\n\\end{align*}"], ["$$-\\frac{10}{11}x = \\frac{5}{3}+\\frac{5}{11}x$$", "\\begin{align*}\n-\\frac{10}{11}x = & \\frac{5}{3}+\\frac{5}{11}x & & | -\\frac{5}{11}x\\\\\n-\\frac{15}{11}x = & \\frac{5}{3} & & | : -\\frac{15}{11}\\\\\nx = & -\\frac{11}{9}\n\\end{align*}"], ["$$\\frac{5}{6}x = \\frac{5}{2}-\\frac{11}{3}x$$", "\\begin{align*}\n\\frac{5}{6}x = & \\frac{5}{2}-\\frac{11}{3}x & & | +\\frac{11}{3}x\\\\\n\\frac{9}{2}x = & \\frac{5}{2} & & | : \\frac{9}{2}\\\\\nx = & \\frac{5}{9}\n\\end{align*}"], ["$$\\frac{7}{5}x = -\\frac{1}{2}+\\frac{19}{15}x$$", "\\begin{align*}\n\\frac{7}{5}x = & -\\frac{1}{2}+\\frac{19}{15}x & & | -\\frac{19}{15}x\\\\\n\\frac{2}{15}x = & -\\frac{1}{2} & & | : \\frac{2}{15}\\\\\nx = & -\\frac{15}{4}\n\\end{align*}"]],
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Hinweis: Die Lösungen sind automatisch generiert. In vielen Fällen könnte es sich lohnen, die Gleichung erst mit dem gemeinsamen Nenner der Koeffizienten von $x$ zu multiplizieren.
=== Freitag 27. August 2021 ===
Fassen Sie zusammen:miniAufgabe("#exomulOnly","#solmulOnly",
[["$ \\left(-\\frac{5}{11}a^{2}k^{5}m^{2}\\right) \\cdot \\left(-\\frac{4}{5}a^{5}\\right) \\cdot \\frac{11}{6}k^{3}m^{3}$", "$ \\frac{2}{3}a^{7}k^{8}m^{5}$"], ["$ \\frac{7}{6}m^{4}n^{5}t \\cdot \\frac{2}{7}n^{2} \\cdot \\left(-\\frac{3}{2}m^{5}n^{5}t\\right)$", "$ -\\frac{1}{2}m^{9}n^{12}t^{2}$"], ["$ \\left(-\\frac{8}{5}gw^{4}\\right) \\cdot \\left(-\\frac{5}{2}p^{5}w^{4}\\right) \\cdot \\frac{3}{8}g^{2}p^{5}w^{3}$", "$ \\frac{3}{2}g^{3}p^{10}w^{11}$"], ["$ \\left(-\\frac{9}{8}du^{5}w^{5}\\right) \\cdot \\left(-\\frac{10}{3}d^{3}u\\right) \\cdot \\frac{4}{9}u^{5}$", "$ \\frac{5}{3}d^{4}u^{11}w^{5}$"], ["$ \\frac{7}{5}b^{5}d^{5}e^{4} \\cdot \\left(-\\frac{3}{5}d^{5}\\right) \\cdot \\frac{15}{7}b^{3}$", "$ -\\frac{9}{5}b^{8}d^{10}e^{4}$"], ["$ \\left(-\\frac{4}{3}w^{2}\\right) \\cdot \\left(-\\frac{1}{4}wy^{5}\\right) \\cdot \\frac{10}{3}w$", "$ \\frac{10}{9}w^{4}y^{5}$"], ["$ \\frac{11}{10}e^{2}m^{2}t^{3} \\cdot \\left(-\\frac{7}{11}em^{4}t^{5}\\right) \\cdot \\frac{5}{7}em^{4}t$", "$ -\\frac{1}{2}e^{4}m^{10}t^{9}$"], ["$ \\left(-\\frac{10}{9}w^{3}x^{3}\\right) \\cdot \\left(-\\frac{2}{5}d^{3}x\\right) \\cdot \\left(-\\frac{9}{16}w^{5}\\right)$", "$ -\\frac{1}{4}d^{3}w^{8}x^{4}$"], ["$ \\left(-\\frac{1}{3}f^{4}\\right) \\cdot \\left(-\\frac{5}{4}f^{2}p^{3}t^{4}\\right) \\cdot \\frac{9}{5}f^{3}t$", "$ \\frac{3}{4}f^{9}p^{3}t^{5}$"], ["$ \\frac{1}{3}e^{4}p^{3}t^{2} \\cdot \\left(-\\frac{5}{4}e^{3}pt\\right) \\cdot \\frac{18}{5}e$", "$ -\\frac{3}{2}e^{8}p^{4}t^{3}$"]],
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