lehrkraefte:blc:miniaufgaben:kw17-2026 [https://fginfo.ksbg.ch Fachgruppe Informatik der KSBG]

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==== Montag 27. April 2026 ====
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[["$\\displaystyle \\left(x+2\\right)^{2}-\\frac{14}{5}-6x \\leq \\left(x-\\frac{4}{5}\\right) \\cdot \\left(x+\\frac{4}{5}\\right)$", "$\\begin{align} \\left(x+2\\right)^{2}-\\frac{14}{5}-6x  & \\leq \\left(x-\\frac{4}{5}\\right) \\cdot \\left(x+\\frac{4}{5}\\right)&&|\\text{TU}\\\\\nx^{2}+4x-6x+4-\\frac{14}{5}  & \\leq x^{2}-\\frac{16}{25}&&|\\text{TU}\\\\\nx^{2}-2x+\\frac{6}{5}  & \\leq x^{2}-\\frac{16}{25}&&|-x^{2} \\\\\n-2x+\\frac{6}{5}  & \\leq -\\frac{16}{25}&&|-\\frac{6}{5}\\\\\n-2x  & \\leq -\\frac{46}{25}&&|\\text{TU}\\\\\nx \\cdot -2  & \\leq -\\frac{46}{25}&&|: -2\\\\\nx  & \\geq \\frac{-\\frac{46}{25}}{-2}&&|\\text{TU}\\\\\nx  & \\geq \\frac{23}{25}\\\\\n \\end{align}$"], ["$\\displaystyle \\left(x-\\frac{5}{2}\\right)^{2}+\\frac{15}{4}-5x < \\left(x+5\\right) \\cdot \\left(x-5\\right)$", "$\\begin{align} \\left(x-\\frac{5}{2}\\right)^{2}+\\frac{15}{4}-5x  & < \\left(x+5\\right) \\cdot \\left(x-5\\right)&&|\\text{TU}\\\\\nx^{2}-5x-5x+\\frac{25}{4}+\\frac{15}{4}  & < x^{2}-25&&|\\text{TU}\\\\\nx^{2}-10x+10  & < x^{2}-25&&|-x^{2} \\\\\n-10x+10  & < -25&&|-10\\\\\n-10x  & < -35&&|\\text{TU}\\\\\nx \\cdot -10  & < -35&&|: -10\\\\\nx  & > \\frac{-35}{-10}&&|\\text{TU}\\\\\nx  & > \\frac{7}{2}\\\\\n \\end{align}$"], ["$\\displaystyle \\left(x-2\\right)^{2}-\\frac{10}{3}-4x \\leq \\left(x+4\\right) \\cdot \\left(x-4\\right)$", "$\\begin{align} \\left(x-2\\right)^{2}-\\frac{10}{3}-4x  & \\leq \\left(x+4\\right) \\cdot \\left(x-4\\right)&&|\\text{TU}\\\\\nx^{2}-4x-4x+4-\\frac{10}{3}  & \\leq x^{2}-16&&|\\text{TU}\\\\\nx^{2}-8x+\\frac{2}{3}  & \\leq x^{2}-16&&|-x^{2} \\\\\n-8x+\\frac{2}{3}  & \\leq -16&&|-\\frac{2}{3}\\\\\n-8x  & \\leq -\\frac{50}{3}&&|\\text{TU}\\\\\nx \\cdot -8  & \\leq -\\frac{50}{3}&&|: -8\\\\\nx  & \\geq \\frac{-\\frac{50}{3}}{-8}&&|\\text{TU}\\\\\nx  & \\geq \\frac{25}{12}\\\\\n \\end{align}$"], ["$\\displaystyle \\left(x-\\frac{5}{2}\\right)^{2}-\\frac{35}{4}+3x \\leq \\left(x+5\\right) \\cdot \\left(x-5\\right)$", "$\\begin{align} \\left(x-\\frac{5}{2}\\right)^{2}-\\frac{35}{4}+3x  & \\leq \\left(x+5\\right) \\cdot \\left(x-5\\right)&&|\\text{TU}\\\\\nx^{2}+3x-5x+\\frac{25}{4}-\\frac{35}{4}  & \\leq x^{2}-25&&|\\text{TU}\\\\\nx^{2}-2x-\\frac{5}{2}  & \\leq x^{2}-25&&|-x^{2} \\\\\n-2x-\\frac{5}{2}  & \\leq -25&&|+\\frac{5}{2}\\\\\n-2x  & \\leq -\\frac{45}{2}&&|\\text{TU}\\\\\nx \\cdot -2  & \\leq -\\frac{45}{2}&&|: -2\\\\\nx  & \\geq \\frac{-\\frac{45}{2}}{-2}&&|\\text{TU}\\\\\nx  & \\geq \\frac{45}{4}\\\\\n \\end{align}$"], ["$\\displaystyle \\left(x+\\frac{4}{3}\\right)^{2}-\\frac{10}{3}-7x \\geq \\left(x+2\\right) \\cdot \\left(x-2\\right)$", "$\\begin{align} \\left(x+\\frac{4}{3}\\right)^{2}-\\frac{10}{3}-7x  & \\geq \\left(x+2\\right) \\cdot \\left(x-2\\right)&&|\\text{TU}\\\\\nx^{2}+\\frac{8}{3}x-7x+\\frac{16}{9}-\\frac{10}{3}  & \\geq x^{2}-4&&|\\text{TU}\\\\\nx^{2}-\\frac{13}{3}x-\\frac{14}{9}  & \\geq x^{2}-4&&|-x^{2} \\\\\n-\\frac{13}{3}x-\\frac{14}{9}  & \\geq -4&&|+\\frac{14}{9}\\\\\n-\\frac{13}{3}x  & \\geq -\\frac{22}{9}&&|\\text{TU}\\\\\nx \\cdot -\\frac{13}{3}  & \\geq -\\frac{22}{9}&&|: -\\frac{13}{3}\\\\\nx  & \\leq \\frac{-\\frac{22}{9}}{-\\frac{13}{3}}&&|\\text{TU}\\\\\nx  & \\leq \\frac{22}{39}\\\\\n \\end{align}$"], ["$\\displaystyle \\left(x-2\\right)^{2}-\\frac{14}{3}-5x > \\left(x+\\frac{4}{3}\\right) \\cdot \\left(x-\\frac{4}{3}\\right)$", "$\\begin{align} \\left(x-2\\right)^{2}-\\frac{14}{3}-5x  & > \\left(x+\\frac{4}{3}\\right) \\cdot \\left(x-\\frac{4}{3}\\right)&&|\\text{TU}\\\\\nx^{2}-4x-5x+4-\\frac{14}{3}  & > x^{2}-\\frac{16}{9}&&|\\text{TU}\\\\\nx^{2}-9x-\\frac{2}{3}  & > x^{2}-\\frac{16}{9}&&|-x^{2} \\\\\n-9x-\\frac{2}{3}  & > -\\frac{16}{9}&&|+\\frac{2}{3}\\\\\n-9x  & > -\\frac{10}{9}&&|\\text{TU}\\\\\nx \\cdot -9  & > -\\frac{10}{9}&&|: -9\\\\\nx  & < \\frac{-\\frac{10}{9}}{-9}&&|\\text{TU}\\\\\nx  & < \\frac{10}{81}\\\\\n \\end{align}$"], ["$\\displaystyle \\left(x-\\frac{4}{3}\\right)^{2}-\\frac{10}{3}-7x < \\left(x+2\\right) \\cdot \\left(x-2\\right)$", "$\\begin{align} \\left(x-\\frac{4}{3}\\right)^{2}-\\frac{10}{3}-7x  & < \\left(x+2\\right) \\cdot \\left(x-2\\right)&&|\\text{TU}\\\\\nx^{2}-\\frac{8}{3}x-7x+\\frac{16}{9}-\\frac{10}{3}  & < x^{2}-4&&|\\text{TU}\\\\\nx^{2}-\\frac{29}{3}x-\\frac{14}{9}  & < x^{2}-4&&|-x^{2} \\\\\n-\\frac{29}{3}x-\\frac{14}{9}  & < -4&&|+\\frac{14}{9}\\\\\n-\\frac{29}{3}x  & < -\\frac{22}{9}&&|\\text{TU}\\\\\nx \\cdot -\\frac{29}{3}  & < -\\frac{22}{9}&&|: -\\frac{29}{3}\\\\\nx  & > \\frac{-\\frac{22}{9}}{-\\frac{29}{3}}&&|\\text{TU}\\\\\nx  & > \\frac{22}{87}\\\\\n \\end{align}$"], ["$\\displaystyle \\left(x+\\frac{4}{5}\\right)^{2}-2-4x \\leq \\left(x+\\frac{6}{5}\\right) \\cdot \\left(x-\\frac{6}{5}\\right)$", "$\\begin{align} \\left(x+\\frac{4}{5}\\right)^{2}-2-4x  & \\leq \\left(x+\\frac{6}{5}\\right) \\cdot \\left(x-\\frac{6}{5}\\right)&&|\\text{TU}\\\\\nx^{2}+\\frac{8}{5}x-4x+\\frac{16}{25}-2  & \\leq x^{2}-\\frac{36}{25}&&|\\text{TU}\\\\\nx^{2}-\\frac{12}{5}x-\\frac{34}{25}  & \\leq x^{2}-\\frac{36}{25}&&|-x^{2} \\\\\n-\\frac{12}{5}x-\\frac{34}{25}  & \\leq -\\frac{36}{25}&&|+\\frac{34}{25}\\\\\n-\\frac{12}{5}x  & \\leq -\\frac{2}{25}&&|\\text{TU}\\\\\nx \\cdot -\\frac{12}{5}  & \\leq -\\frac{2}{25}&&|: -\\frac{12}{5}\\\\\nx  & \\geq \\frac{-\\frac{2}{25}}{-\\frac{12}{5}}&&|\\text{TU}\\\\\nx  & \\geq \\frac{1}{30}\\\\\n \\end{align}$"], ["$\\displaystyle \\left(x+3\\right)^{2}-\\frac{9}{2}-7x \\geq \\left(x+\\frac{3}{2}\\right) \\cdot \\left(x-\\frac{3}{2}\\right)$", "$\\begin{align} \\left(x+3\\right)^{2}-\\frac{9}{2}-7x  & \\geq \\left(x+\\frac{3}{2}\\right) \\cdot \\left(x-\\frac{3}{2}\\right)&&|\\text{TU}\\\\\nx^{2}+6x-7x+9-\\frac{9}{2}  & \\geq x^{2}-\\frac{9}{4}&&|\\text{TU}\\\\\nx^{2}-x+\\frac{9}{2}  & \\geq x^{2}-\\frac{9}{4}&&|-x^{2} \\\\\n-x+\\frac{9}{2}  & \\geq -\\frac{9}{4}&&|-\\frac{9}{2}\\\\\n-x  & \\geq -\\frac{27}{4}&&|\\text{TU}\\\\\nx \\cdot -1  & \\geq -\\frac{27}{4}&&|: -1\\\\\nx  & \\leq \\frac{-\\frac{27}{4}}{-1}&&|\\text{TU}\\\\\nx  & \\leq \\frac{27}{4}\\\\\n \\end{align}$"], ["$\\displaystyle \\left(x-4\\right)^{2}-\\frac{14}{3}+4x < \\left(x+2\\right) \\cdot \\left(x-2\\right)$", "$\\begin{align} \\left(x-4\\right)^{2}-\\frac{14}{3}+4x  & < \\left(x+2\\right) \\cdot \\left(x-2\\right)&&|\\text{TU}\\\\\nx^{2}+4x-8x+16-\\frac{14}{3}  & < x^{2}-4&&|\\text{TU}\\\\\nx^{2}-4x+\\frac{34}{3}  & < x^{2}-4&&|-x^{2} \\\\\n-4x+\\frac{34}{3}  & < -4&&|-\\frac{34}{3}\\\\\n-4x  & < -\\frac{46}{3}&&|\\text{TU}\\\\\nx \\cdot -4  & < -\\frac{46}{3}&&|: -4\\\\\nx  & > \\frac{-\\frac{46}{3}}{-4}&&|\\text{TU}\\\\\nx  & > \\frac{23}{6}\\\\\n \\end{align}$"]],
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