Vgln. eerste graad (reeks 4)

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Reeks met breuken waarbij we ervoor kiezen om de breuken weg te werken. Neem je ZRM!

  1. \(\frac{x}{2}-\frac{3}{13}=\frac{5}{3}x+3\)
  2. \(\frac{x}{2}-\frac{5}{14}=\frac{2}{5}x-7\)
  3. \(\frac{x}{7}+\frac{2}{15}=\frac{5}{6}x+4\)
  4. \(\frac{x}{4}-\frac{5}{14}=\frac{4}{7}x+3\)
  5. \(\frac{x}{6}-\frac{3}{7}=\frac{-6}{7}x-3\)
  6. \(\frac{x}{2}-\frac{4}{17}=\frac{7}{3}x-3\)
  7. \(\frac{x}{6}-\frac{4}{13}=\frac{-2}{5}x+7\)
  8. \(\frac{x}{4}-\frac{5}{13}=\frac{4}{3}x-2\)
  9. \(\frac{x}{2}-\frac{2}{17}=\frac{-6}{7}x+4\)
  10. \(\frac{x}{5}-\frac{4}{9}=\frac{3}{4}x-4\)
  11. \(\frac{x}{6}+\frac{4}{7}=\frac{-6}{7}x-8\)
  12. \(\frac{x}{4}-\frac{3}{10}=\frac{8}{5}x-6\)

Reeks met breuken waarbij we ervoor kiezen om de breuken weg te werken. Neem je ZRM!

Verbetersleutel

  1. \(\text{78 is het kleinste gemene veelvoud van 2, 13 en 3} \\ \begin{align} & \color{blue}{78.} (\frac{x}{2}-\frac{3}{13})& = & (\frac{5}{3}x+3) \color{blue}{.78} \\\Leftrightarrow & 39x-18& = & 130x+234 \\\Leftrightarrow & 39x \color{red}{-18} \color{blue}{+18} \color{blue}{-130x} & = & \color{red}{130x} +234 \color{blue}{-130x} \color{blue}{+18} \\\Leftrightarrow & -91x& = & 252 \\\Leftrightarrow & \frac{-91x}{ \color{red}{-91} }& = & \frac{252}{-91} \\\Leftrightarrow & x = \frac{-36}{13} & & \\ & V = \left\{ \frac{-36}{13} \right\} & \\\end{align}\)
  2. \(\text{70 is het kleinste gemene veelvoud van 2, 14 en 5} \\ \begin{align} & \color{blue}{70.} (\frac{x}{2}-\frac{5}{14})& = & (\frac{2}{5}x-7) \color{blue}{.70} \\\Leftrightarrow & 35x-25& = & 28x-490 \\\Leftrightarrow & 35x \color{red}{-25} \color{blue}{+25} \color{blue}{-28x} & = & \color{red}{28x} -490 \color{blue}{-28x} \color{blue}{+25} \\\Leftrightarrow & 7x& = & -465 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = & \frac{-465}{7} \\\Leftrightarrow & x = \frac{-465}{7} & & \\ & V = \left\{ \frac{-465}{7} \right\} & \\\end{align}\)
  3. \(\text{210 is het kleinste gemene veelvoud van 7, 15 en 6} \\ \begin{align} & \color{blue}{210.} (\frac{x}{7}+\frac{2}{15})& = & (\frac{5}{6}x+4) \color{blue}{.210} \\\Leftrightarrow & 30x+28& = & 175x+840 \\\Leftrightarrow & 30x \color{red}{+28} \color{blue}{-28} \color{blue}{-175x} & = & \color{red}{175x} +840 \color{blue}{-175x} \color{blue}{-28} \\\Leftrightarrow & -145x& = & 812 \\\Leftrightarrow & \frac{-145x}{ \color{red}{-145} }& = & \frac{812}{-145} \\\Leftrightarrow & x = \frac{-28}{5} & & \\ & V = \left\{ \frac{-28}{5} \right\} & \\\end{align}\)
  4. \(\text{28 is het kleinste gemene veelvoud van 4, 14 en 7} \\ \begin{align} & \color{blue}{28.} (\frac{x}{4}-\frac{5}{14})& = & (\frac{4}{7}x+3) \color{blue}{.28} \\\Leftrightarrow & 7x-10& = & 16x+84 \\\Leftrightarrow & 7x \color{red}{-10} \color{blue}{+10} \color{blue}{-16x} & = & \color{red}{16x} +84 \color{blue}{-16x} \color{blue}{+10} \\\Leftrightarrow & -9x& = & 94 \\\Leftrightarrow & \frac{-9x}{ \color{red}{-9} }& = & \frac{94}{-9} \\\Leftrightarrow & x = \frac{-94}{9} & & \\ & V = \left\{ \frac{-94}{9} \right\} & \\\end{align}\)
  5. \(\text{42 is het kleinste gemene veelvoud van 6, 7 en 7} \\ \begin{align} & \color{blue}{42.} (\frac{x}{6}-\frac{3}{7})& = & (\frac{-6}{7}x-3) \color{blue}{.42} \\\Leftrightarrow & 7x-18& = & -36x-126 \\\Leftrightarrow & 7x \color{red}{-18} \color{blue}{+18} \color{blue}{+36x} & = & \color{red}{-36x} -126 \color{blue}{+36x} \color{blue}{+18} \\\Leftrightarrow & 43x& = & -108 \\\Leftrightarrow & \frac{43x}{ \color{red}{43} }& = & \frac{-108}{43} \\\Leftrightarrow & x = \frac{-108}{43} & & \\ & V = \left\{ \frac{-108}{43} \right\} & \\\end{align}\)
  6. \(\text{102 is het kleinste gemene veelvoud van 2, 17 en 3} \\ \begin{align} & \color{blue}{102.} (\frac{x}{2}-\frac{4}{17})& = & (\frac{7}{3}x-3) \color{blue}{.102} \\\Leftrightarrow & 51x-24& = & 238x-306 \\\Leftrightarrow & 51x \color{red}{-24} \color{blue}{+24} \color{blue}{-238x} & = & \color{red}{238x} -306 \color{blue}{-238x} \color{blue}{+24} \\\Leftrightarrow & -187x& = & -282 \\\Leftrightarrow & \frac{-187x}{ \color{red}{-187} }& = & \frac{-282}{-187} \\\Leftrightarrow & x = \frac{282}{187} & & \\ & V = \left\{ \frac{282}{187} \right\} & \\\end{align}\)
  7. \(\text{390 is het kleinste gemene veelvoud van 6, 13 en 5} \\ \begin{align} & \color{blue}{390.} (\frac{x}{6}-\frac{4}{13})& = & (\frac{-2}{5}x+7) \color{blue}{.390} \\\Leftrightarrow & 65x-120& = & -156x+2730 \\\Leftrightarrow & 65x \color{red}{-120} \color{blue}{+120} \color{blue}{+156x} & = & \color{red}{-156x} +2730 \color{blue}{+156x} \color{blue}{+120} \\\Leftrightarrow & 221x& = & 2850 \\\Leftrightarrow & \frac{221x}{ \color{red}{221} }& = & \frac{2850}{221} \\\Leftrightarrow & x = \frac{2850}{221} & & \\ & V = \left\{ \frac{2850}{221} \right\} & \\\end{align}\)
  8. \(\text{156 is het kleinste gemene veelvoud van 4, 13 en 3} \\ \begin{align} & \color{blue}{156.} (\frac{x}{4}-\frac{5}{13})& = & (\frac{4}{3}x-2) \color{blue}{.156} \\\Leftrightarrow & 39x-60& = & 208x-312 \\\Leftrightarrow & 39x \color{red}{-60} \color{blue}{+60} \color{blue}{-208x} & = & \color{red}{208x} -312 \color{blue}{-208x} \color{blue}{+60} \\\Leftrightarrow & -169x& = & -252 \\\Leftrightarrow & \frac{-169x}{ \color{red}{-169} }& = & \frac{-252}{-169} \\\Leftrightarrow & x = \frac{252}{169} & & \\ & V = \left\{ \frac{252}{169} \right\} & \\\end{align}\)
  9. \(\text{238 is het kleinste gemene veelvoud van 2, 17 en 7} \\ \begin{align} & \color{blue}{238.} (\frac{x}{2}-\frac{2}{17})& = & (\frac{-6}{7}x+4) \color{blue}{.238} \\\Leftrightarrow & 119x-28& = & -204x+952 \\\Leftrightarrow & 119x \color{red}{-28} \color{blue}{+28} \color{blue}{+204x} & = & \color{red}{-204x} +952 \color{blue}{+204x} \color{blue}{+28} \\\Leftrightarrow & 323x& = & 980 \\\Leftrightarrow & \frac{323x}{ \color{red}{323} }& = & \frac{980}{323} \\\Leftrightarrow & x = \frac{980}{323} & & \\ & V = \left\{ \frac{980}{323} \right\} & \\\end{align}\)
  10. \(\text{180 is het kleinste gemene veelvoud van 5, 9 en 4} \\ \begin{align} & \color{blue}{180.} (\frac{x}{5}-\frac{4}{9})& = & (\frac{3}{4}x-4) \color{blue}{.180} \\\Leftrightarrow & 36x-80& = & 135x-720 \\\Leftrightarrow & 36x \color{red}{-80} \color{blue}{+80} \color{blue}{-135x} & = & \color{red}{135x} -720 \color{blue}{-135x} \color{blue}{+80} \\\Leftrightarrow & -99x& = & -640 \\\Leftrightarrow & \frac{-99x}{ \color{red}{-99} }& = & \frac{-640}{-99} \\\Leftrightarrow & x = \frac{640}{99} & & \\ & V = \left\{ \frac{640}{99} \right\} & \\\end{align}\)
  11. \(\text{42 is het kleinste gemene veelvoud van 6, 7 en 7} \\ \begin{align} & \color{blue}{42.} (\frac{x}{6}+\frac{4}{7})& = & (\frac{-6}{7}x-8) \color{blue}{.42} \\\Leftrightarrow & 7x+24& = & -36x-336 \\\Leftrightarrow & 7x \color{red}{+24} \color{blue}{-24} \color{blue}{+36x} & = & \color{red}{-36x} -336 \color{blue}{+36x} \color{blue}{-24} \\\Leftrightarrow & 43x& = & -360 \\\Leftrightarrow & \frac{43x}{ \color{red}{43} }& = & \frac{-360}{43} \\\Leftrightarrow & x = \frac{-360}{43} & & \\ & V = \left\{ \frac{-360}{43} \right\} & \\\end{align}\)
  12. \(\text{20 is het kleinste gemene veelvoud van 4, 10 en 5} \\ \begin{align} & \color{blue}{20.} (\frac{x}{4}-\frac{3}{10})& = & (\frac{8}{5}x-6) \color{blue}{.20} \\\Leftrightarrow & 5x-6& = & 32x-120 \\\Leftrightarrow & 5x \color{red}{-6} \color{blue}{+6} \color{blue}{-32x} & = & \color{red}{32x} -120 \color{blue}{-32x} \color{blue}{+6} \\\Leftrightarrow & -27x& = & -114 \\\Leftrightarrow & \frac{-27x}{ \color{red}{-27} }& = & \frac{-114}{-27} \\\Leftrightarrow & x = \frac{38}{9} & & \\ & V = \left\{ \frac{38}{9} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-04-24 01:38:31