lehrkraefte:blc:miniaufgaben:kw11-2026 [https://fginfo.ksbg.ch Fachgruppe Informatik der KSBG]

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  miniaufgabe.js
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==== Montag 16. März 2026 ====
=== Aufgabe 1 ===
Lösen Sie nach $x$ auf. Lösung vollständig gekürzt.<JS>miniAufgabe("#exolineare-gleichungen-mit-erweitern-und-zusammenfassen","#sollineare-gleichungen-mit-erweitern-und-zusammenfassen",
[['$\\displaystyle \\frac{6+4x}{8}-\\frac{3+6x}{6} = 3+9x$', '\\begin{align*}\n\\frac{6+4x}{8}-\\frac{3+6x}{6} & = 3+9x && |\\cdot 24 \\\\\n3 \\cdot \\left(6+4x\\right)-4 \\cdot \\left(3+6x\\right) & = 24 \\cdot \\left(3+9x\\right) && |\\text{TU} \\\\\n18+12x-\\left(12+24x\\right) & = 72+216x && |\\text{TU} \\\\\n18+12x-12-24x & = 72+216x && |\\text{TU} \\\\\n-12x+6 & = 216x+72 && |+12x \\\\\n6 & = 228x+72 && |-72 \\\\\n-66 & = 228x && |:228 \\\\\n-\\frac{11}{38} & = x\\\\\n\\end{align*}'], ['$\\displaystyle \\frac{10+8x}{4}-\\frac{5+10x}{6} = 2+7x$', '\\begin{align*}\n\\frac{10+8x}{4}-\\frac{5+10x}{6} & = 2+7x && |\\cdot 12 \\\\\n3 \\cdot \\left(10+8x\\right)-2 \\cdot \\left(5+10x\\right) & = 12 \\cdot \\left(2+7x\\right) && |\\text{TU} \\\\\n30+24x-\\left(10+20x\\right) & = 24+84x && |\\text{TU} \\\\\n30+24x-10-20x & = 24+84x && |\\text{TU} \\\\\n4x+20 & = 84x+24 && |-4x \\\\\n20 & = 80x+24 && |-24 \\\\\n-4 & = 80x && |:80 \\\\\n-\\frac{1}{20} & = x\\\\\n\\end{align*}'], ['$\\displaystyle \\frac{6+9x}{10}-\\frac{10+9x}{6} = 4+5x$', '\\begin{align*}\n\\frac{6+9x}{10}-\\frac{10+9x}{6} & = 4+5x && |\\cdot 30 \\\\\n3 \\cdot \\left(6+9x\\right)-5 \\cdot \\left(10+9x\\right) & = 30 \\cdot \\left(4+5x\\right) && |\\text{TU} \\\\\n18+27x-\\left(50+45x\\right) & = 120+150x && |\\text{TU} \\\\\n18+27x-50-45x & = 120+150x && |\\text{TU} \\\\\n-18x-32 & = 150x+120 && |+18x \\\\\n-32 & = 168x+120 && |-120 \\\\\n-152 & = 168x && |:168 \\\\\n-\\frac{19}{21} & = x\\\\\n\\end{align*}'], ['$\\displaystyle \\frac{11+2x}{6}-\\frac{10+4x}{4} = 3+2x$', '\\begin{align*}\n\\frac{11+2x}{6}-\\frac{10+4x}{4} & = 3+2x && |\\cdot 12 \\\\\n2 \\cdot \\left(11+2x\\right)-3 \\cdot \\left(10+4x\\right) & = 12 \\cdot \\left(3+2x\\right) && |\\text{TU} \\\\\n22+4x-\\left(30+12x\\right) & = 36+24x && |\\text{TU} \\\\\n22+4x-30-12x & = 36+24x && |\\text{TU} \\\\\n-8x-8 & = 24x+36 && |+8x \\\\\n-8 & = 32x+36 && |-36 \\\\\n-44 & = 32x && |:32 \\\\\n-\\frac{11}{8} & = x\\\\\n\\end{align*}'], ['$\\displaystyle \\frac{6+4x}{4}-\\frac{10+8x}{6} = 3+8x$', '\\begin{align*}\n\\frac{6+4x}{4}-\\frac{10+8x}{6} & = 3+8x && |\\cdot 12 \\\\\n3 \\cdot \\left(6+4x\\right)-2 \\cdot \\left(10+8x\\right) & = 12 \\cdot \\left(3+8x\\right) && |\\text{TU} \\\\\n18+12x-\\left(20+16x\\right) & = 36+96x && |\\text{TU} \\\\\n18+12x-20-16x & = 36+96x && |\\text{TU} \\\\\n-4x-2 & = 96x+36 && |+4x \\\\\n-2 & = 100x+36 && |-36 \\\\\n-38 & = 100x && |:100 \\\\\n-\\frac{19}{50} & = x\\\\\n\\end{align*}'], ['$\\displaystyle \\frac{9+9x}{9}-\\frac{7+5x}{6} = 9+8x$', '\\begin{align*}\n\\frac{9+9x}{9}-\\frac{7+5x}{6} & = 9+8x && |\\cdot 18 \\\\\n2 \\cdot \\left(9+9x\\right)-3 \\cdot \\left(7+5x\\right) & = 18 \\cdot \\left(9+8x\\right) && |\\text{TU} \\\\\n18+18x-\\left(21+15x\\right) & = 162+144x && |\\text{TU} \\\\\n18+18x-21-15x & = 162+144x && |\\text{TU} \\\\\n3x-3 & = 144x+162 && |-3x \\\\\n-3 & = 141x+162 && |-162 \\\\\n-165 & = 141x && |:141 \\\\\n-\\frac{55}{47} & = x\\\\\n\\end{align*}'], ['$\\displaystyle \\frac{6+6x}{6}-\\frac{3+2x}{4} = 8+8x$', '\\begin{align*}\n\\frac{6+6x}{6}-\\frac{3+2x}{4} & = 8+8x && |\\cdot 12 \\\\\n2 \\cdot \\left(6+6x\\right)-3 \\cdot \\left(3+2x\\right) & = 12 \\cdot \\left(8+8x\\right) && |\\text{TU} \\\\\n12+12x-\\left(9+6x\\right) & = 96+96x && |\\text{TU} \\\\\n12+12x-9-6x & = 96+96x && |\\text{TU} \\\\\n6x+3 & = 96x+96 && |-6x \\\\\n3 & = 90x+96 && |-96 \\\\\n-93 & = 90x && |:90 \\\\\n-\\frac{31}{30} & = x\\\\\n\\end{align*}'], ['$\\displaystyle \\frac{10+8x}{10}-\\frac{6+6x}{4} = 3+2x$', '\\begin{align*}\n\\frac{10+8x}{10}-\\frac{6+6x}{4} & = 3+2x && |\\cdot 20 \\\\\n2 \\cdot \\left(10+8x\\right)-5 \\cdot \\left(6+6x\\right) & = 20 \\cdot \\left(3+2x\\right) && |\\text{TU} \\\\\n20+16x-\\left(30+30x\\right) & = 60+40x && |\\text{TU} \\\\\n20+16x-30-30x & = 60+40x && |\\text{TU} \\\\\n-14x-10 & = 40x+60 && |+14x \\\\\n-10 & = 54x+60 && |-60 \\\\\n-70 & = 54x && |:54 \\\\\n-\\frac{35}{27} & = x\\\\\n\\end{align*}'], ['$\\displaystyle \\frac{7+9x}{9}-\\frac{6+10x}{6} = 7+6x$', '\\begin{align*}\n\\frac{7+9x}{9}-\\frac{6+10x}{6} & = 7+6x && |\\cdot 18 \\\\\n2 \\cdot \\left(7+9x\\right)-3 \\cdot \\left(6+10x\\right) & = 18 \\cdot \\left(7+6x\\right) && |\\text{TU} \\\\\n14+18x-\\left(18+30x\\right) & = 126+108x && |\\text{TU} \\\\\n14+18x-18-30x & = 126+108x && |\\text{TU} \\\\\n-12x-4 & = 108x+126 && |+12x \\\\\n-4 & = 120x+126 && |-126 \\\\\n-130 & = 120x && |:120 \\\\\n-\\frac{13}{12} & = x\\\\\n\\end{align*}'], ['$\\displaystyle \\frac{5+9x}{6}-\\frac{8+2x}{4} = 6+9x$', '\\begin{align*}\n\\frac{5+9x}{6}-\\frac{8+2x}{4} & = 6+9x && |\\cdot 12 \\\\\n2 \\cdot \\left(5+9x\\right)-3 \\cdot \\left(8+2x\\right) & = 12 \\cdot \\left(6+9x\\right) && |\\text{TU} \\\\\n10+18x-\\left(24+6x\\right) & = 72+108x && |\\text{TU} \\\\\n10+18x-24-6x & = 72+108x && |\\text{TU} \\\\\n12x-14 & = 108x+72 && |-12x \\\\\n-14 & = 96x+72 && |-72 \\\\\n-86 & = 96x && |:96 \\\\\n-\\frac{43}{48} & = x\\\\\n\\end{align*}']],
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<div id="sollineare-gleichungen-mit-erweitern-und-zusammenfassen"></div>
<div style='font-size:12px;color:gray;'>python /home/ivo/burggraben/git/ivo/math/miniaufgaben/headerfooter.py lineare-gleichungen.py</div>
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=== Aufgabe 2 ===
Lösen Sie nach $x$ auf und vereinfachen Sie das Resultat.<JS>miniAufgabe("#exogleichung-mit-parametern-binomische-formel","#solgleichung-mit-parametern-binomische-formel",
[['$\\displaystyle 3k \\cdot \\left(x-16am\\right)-2a \\cdot \\left(16am-x\\right) = 4m \\cdot \\left(3k+2a\\right) \\cdot \\left(3k-2a\\right)$', '\\begin{align*}\n3k \\cdot \\left(x-16am\\right)-2a \\cdot \\left(16am-x\\right) & = 4m \\cdot \\left(3k+2a\\right) \\cdot \\left(3k-2a\\right) && |\\text{TU} \\\\\n3kx-48akm-32a^{2}m+2ax & = 4m \\cdot \\left(9k^{2}-4a^{2}\\right) && |\\text{TU} \\\\\n3kx-48akm-32a^{2}m+2ax & = 36k^{2}m-16a^{2}m && |+48akm+32a^{2}m \\\\\n2ax+3kx & = 16a^{2}m+48akm+36k^{2}m && |\\text{TU} \\\\\nx \\cdot \\left(3k+2a\\right) & = 4m \\cdot \\left(9k^{2}+12ak+4a^{2}\\right) && |\\text{TU} \\\\\nx \\cdot \\left(3k+2a\\right) & = 4m \\cdot \\left(3k+2a\\right)^{2} && |:\\left(3k+2a\\right) \\\\\nx & = 4m \\cdot \\left(3k+2a\\right) \\\\\n\\end{align*}'], ['$\\displaystyle 3d \\cdot \\left(x-16ce\\right)-2e \\cdot \\left(16ce-x\\right) = 4c \\cdot \\left(3d+2e\\right) \\cdot \\left(3d-2e\\right)$', '\\begin{align*}\n3d \\cdot \\left(x-16ce\\right)-2e \\cdot \\left(16ce-x\\right) & = 4c \\cdot \\left(3d+2e\\right) \\cdot \\left(3d-2e\\right) && |\\text{TU} \\\\\n3dx-48cde-32ce^{2}+2ex & = 4c \\cdot \\left(9d^{2}-4e^{2}\\right) && |\\text{TU} \\\\\n3dx-48cde-32ce^{2}+2ex & = 36cd^{2}-16ce^{2} && |+48cde+32ce^{2} \\\\\n3dx+2ex & = 36cd^{2}+48cde+16ce^{2} && |\\text{TU} \\\\\nx \\cdot \\left(3d+2e\\right) & = 4c \\cdot \\left(9d^{2}+12de+4e^{2}\\right) && |\\text{TU} \\\\\nx \\cdot \\left(3d+2e\\right) & = 4c \\cdot \\left(3d+2e\\right)^{2} && |:\\left(3d+2e\\right) \\\\\nx & = 4c \\cdot \\left(3d+2e\\right) \\\\\n\\end{align*}'], ['$\\displaystyle 2d \\cdot \\left(x-24ck\\right)-4c \\cdot \\left(24ck-x\\right) = 3k \\cdot \\left(2d+4c\\right) \\cdot \\left(2d-4c\\right)$', '\\begin{align*}\n2d \\cdot \\left(x-24ck\\right)-4c \\cdot \\left(24ck-x\\right) & = 3k \\cdot \\left(2d+4c\\right) \\cdot \\left(2d-4c\\right) && |\\text{TU} \\\\\n2dx-48cdk-96c^{2}k+4cx & = 3k \\cdot \\left(4d^{2}-16c^{2}\\right) && |\\text{TU} \\\\\n2dx-48cdk-96c^{2}k+4cx & = 12d^{2}k-48c^{2}k && |+48cdk+96c^{2}k \\\\\n4cx+2dx & = 48c^{2}k+48cdk+12d^{2}k && |\\text{TU} \\\\\nx \\cdot \\left(2d+4c\\right) & = 3k \\cdot \\left(4d^{2}+16cd+16c^{2}\\right) && |\\text{TU} \\\\\nx \\cdot \\left(2d+4c\\right) & = 3k \\cdot \\left(2d+4c\\right)^{2} && |:\\left(2d+4c\\right) \\\\\nx & = 3k \\cdot \\left(2d+4c\\right) \\\\\n\\end{align*}'], ['$\\displaystyle 3n \\cdot \\left(x-16ew\\right)-4w \\cdot \\left(16ew-x\\right) = 2e \\cdot \\left(3n+4w\\right) \\cdot \\left(3n-4w\\right)$', '\\begin{align*}\n3n \\cdot \\left(x-16ew\\right)-4w \\cdot \\left(16ew-x\\right) & = 2e \\cdot \\left(3n+4w\\right) \\cdot \\left(3n-4w\\right) && |\\text{TU} \\\\\n3nx-48enw-64ew^{2}+4wx & = 2e \\cdot \\left(9n^{2}-16w^{2}\\right) && |\\text{TU} \\\\\n3nx-48enw-64ew^{2}+4wx & = 18en^{2}-32ew^{2} && |+48enw+64ew^{2} \\\\\n3nx+4wx & = 18en^{2}+48enw+32ew^{2} && |\\text{TU} \\\\\nx \\cdot \\left(3n+4w\\right) & = 2e \\cdot \\left(9n^{2}+24nw+16w^{2}\\right) && |\\text{TU} \\\\\nx \\cdot \\left(3n+4w\\right) & = 2e \\cdot \\left(3n+4w\\right)^{2} && |:\\left(3n+4w\\right) \\\\\nx & = 2e \\cdot \\left(3n+4w\\right) \\\\\n\\end{align*}'], ['$\\displaystyle 4k \\cdot \\left(x-12fw\\right)-3f \\cdot \\left(12fw-x\\right) = 2w \\cdot \\left(4k+3f\\right) \\cdot \\left(4k-3f\\right)$', '\\begin{align*}\n4k \\cdot \\left(x-12fw\\right)-3f \\cdot \\left(12fw-x\\right) & = 2w \\cdot \\left(4k+3f\\right) \\cdot \\left(4k-3f\\right) && |\\text{TU} \\\\\n4kx-48fkw-36f^{2}w+3fx & = 2w \\cdot \\left(16k^{2}-9f^{2}\\right) && |\\text{TU} \\\\\n4kx-48fkw-36f^{2}w+3fx & = 32k^{2}w-18f^{2}w && |+48fkw+36f^{2}w \\\\\n3fx+4kx & = 18f^{2}w+48fkw+32k^{2}w && |\\text{TU} \\\\\nx \\cdot \\left(4k+3f\\right) & = 2w \\cdot \\left(16k^{2}+24fk+9f^{2}\\right) && |\\text{TU} \\\\\nx \\cdot \\left(4k+3f\\right) & = 2w \\cdot \\left(4k+3f\\right)^{2} && |:\\left(4k+3f\\right) \\\\\nx & = 2w \\cdot \\left(4k+3f\\right) \\\\\n\\end{align*}'], ['$\\displaystyle 4h \\cdot \\left(x-12em\\right)-2m \\cdot \\left(12em-x\\right) = 3e \\cdot \\left(4h+2m\\right) \\cdot \\left(4h-2m\\right)$', '\\begin{align*}\n4h \\cdot \\left(x-12em\\right)-2m \\cdot \\left(12em-x\\right) & = 3e \\cdot \\left(4h+2m\\right) \\cdot \\left(4h-2m\\right) && |\\text{TU} \\\\\n4hx-48ehm-24em^{2}+2mx & = 3e \\cdot \\left(16h^{2}-4m^{2}\\right) && |\\text{TU} \\\\\n4hx-48ehm-24em^{2}+2mx & = 48eh^{2}-12em^{2} && |+48ehm+24em^{2} \\\\\n4hx+2mx & = 48eh^{2}+48ehm+12em^{2} && |\\text{TU} \\\\\nx \\cdot \\left(4h+2m\\right) & = 3e \\cdot \\left(16h^{2}+16hm+4m^{2}\\right) && |\\text{TU} \\\\\nx \\cdot \\left(4h+2m\\right) & = 3e \\cdot \\left(4h+2m\\right)^{2} && |:\\left(4h+2m\\right) \\\\\nx & = 3e \\cdot \\left(4h+2m\\right) \\\\\n\\end{align*}'], ['$\\displaystyle 2a \\cdot \\left(x-24kw\\right)-3k \\cdot \\left(24kw-x\\right) = 4w \\cdot \\left(2a+3k\\right) \\cdot \\left(2a-3k\\right)$', '\\begin{align*}\n2a \\cdot \\left(x-24kw\\right)-3k \\cdot \\left(24kw-x\\right) & = 4w \\cdot \\left(2a+3k\\right) \\cdot \\left(2a-3k\\right) && |\\text{TU} \\\\\n2ax-48akw-72k^{2}w+3kx & = 4w \\cdot \\left(4a^{2}-9k^{2}\\right) && |\\text{TU} \\\\\n2ax-48akw-72k^{2}w+3kx & = 16a^{2}w-36k^{2}w && |+48akw+72k^{2}w \\\\\n2ax+3kx & = 16a^{2}w+48akw+36k^{2}w && |\\text{TU} \\\\\nx \\cdot \\left(2a+3k\\right) & = 4w \\cdot \\left(4a^{2}+12ak+9k^{2}\\right) && |\\text{TU} \\\\\nx \\cdot \\left(2a+3k\\right) & = 4w \\cdot \\left(2a+3k\\right)^{2} && |:\\left(2a+3k\\right) \\\\\nx & = 4w \\cdot \\left(2a+3k\\right) \\\\\n\\end{align*}'], ['$\\displaystyle 2k \\cdot \\left(x-24cn\\right)-4c \\cdot \\left(24cn-x\\right) = 3n \\cdot \\left(2k+4c\\right) \\cdot \\left(2k-4c\\right)$', '\\begin{align*}\n2k \\cdot \\left(x-24cn\\right)-4c \\cdot \\left(24cn-x\\right) & = 3n \\cdot \\left(2k+4c\\right) \\cdot \\left(2k-4c\\right) && |\\text{TU} \\\\\n2kx-48ckn-96c^{2}n+4cx & = 3n \\cdot \\left(4k^{2}-16c^{2}\\right) && |\\text{TU} \\\\\n2kx-48ckn-96c^{2}n+4cx & = 12k^{2}n-48c^{2}n && |+48ckn+96c^{2}n \\\\\n4cx+2kx & = 48c^{2}n+48ckn+12k^{2}n && |\\text{TU} \\\\\nx \\cdot \\left(2k+4c\\right) & = 3n \\cdot \\left(4k^{2}+16ck+16c^{2}\\right) && |\\text{TU} \\\\\nx \\cdot \\left(2k+4c\\right) & = 3n \\cdot \\left(2k+4c\\right)^{2} && |:\\left(2k+4c\\right) \\\\\nx & = 3n \\cdot \\left(2k+4c\\right) \\\\\n\\end{align*}'], ['$\\displaystyle 4k \\cdot \\left(x-12dh\\right)-3h \\cdot \\left(12dh-x\\right) = 2d \\cdot \\left(4k+3h\\right) \\cdot \\left(4k-3h\\right)$', '\\begin{align*}\n4k \\cdot \\left(x-12dh\\right)-3h \\cdot \\left(12dh-x\\right) & = 2d \\cdot \\left(4k+3h\\right) \\cdot \\left(4k-3h\\right) && |\\text{TU} \\\\\n4kx-48dhk-36dh^{2}+3hx & = 2d \\cdot \\left(16k^{2}-9h^{2}\\right) && |\\text{TU} \\\\\n4kx-48dhk-36dh^{2}+3hx & = 32dk^{2}-18dh^{2} && |+48dhk+36dh^{2} \\\\\n3hx+4kx & = 18dh^{2}+48dhk+32dk^{2} && |\\text{TU} \\\\\nx \\cdot \\left(4k+3h\\right) & = 2d \\cdot \\left(16k^{2}+24hk+9h^{2}\\right) && |\\text{TU} \\\\\nx \\cdot \\left(4k+3h\\right) & = 2d \\cdot \\left(4k+3h\\right)^{2} && |:\\left(4k+3h\\right) \\\\\nx & = 2d \\cdot \\left(4k+3h\\right) \\\\\n\\end{align*}'], ['$\\displaystyle 4c \\cdot \\left(x-12ep\\right)-3p \\cdot \\left(12ep-x\\right) = 2e \\cdot \\left(4c+3p\\right) \\cdot \\left(4c-3p\\right)$', '\\begin{align*}\n4c \\cdot \\left(x-12ep\\right)-3p \\cdot \\left(12ep-x\\right) & = 2e \\cdot \\left(4c+3p\\right) \\cdot \\left(4c-3p\\right) && |\\text{TU} \\\\\n4cx-48cep-36ep^{2}+3px & = 2e \\cdot \\left(16c^{2}-9p^{2}\\right) && |\\text{TU} \\\\\n4cx-48cep-36ep^{2}+3px & = 32c^{2}e-18ep^{2} && |+48cep+36ep^{2} \\\\\n4cx+3px & = 32c^{2}e+48cep+18ep^{2} && |\\text{TU} \\\\\nx \\cdot \\left(4c+3p\\right) & = 2e \\cdot \\left(16c^{2}+24cp+9p^{2}\\right) && |\\text{TU} \\\\\nx \\cdot \\left(4c+3p\\right) & = 2e \\cdot \\left(4c+3p\\right)^{2} && |:\\left(4c+3p\\right) \\\\\nx & = 2e \\cdot \\left(4c+3p\\right) \\\\\n\\end{align*}']],
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<div style='font-size:12px;color:gray;'>python /home/ivo/burggraben/git/ivo/math/miniaufgaben/headerfooter.py /home/ivo/burggraben/git/ivo/math/miniaufgaben/gleichungen-mit-parametern-und-binomischer-formel.py</div>
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