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

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

Verbetersleutel

  1. \(\text{70 is het kleinste gemene veelvoud van 2, 14 en 5} \\ \begin{align} & \color{blue}{70.} (\frac{x}{2}-\frac{5}{14})& = & (\frac{6}{5}x-4) \color{blue}{.70} \\\Leftrightarrow & 35x-25& = & 84x-280 \\\Leftrightarrow & 35x \color{red}{-25} \color{blue}{+25} \color{blue}{-84x} & = & \color{red}{84x} -280 \color{blue}{-84x} \color{blue}{+25} \\\Leftrightarrow & -49x& = & -255 \\\Leftrightarrow & \frac{-49x}{ \color{red}{-49} }& = & \frac{-255}{-49} \\\Leftrightarrow & x = \frac{255}{49} & & \\ & V = \left\{ \frac{255}{49} \right\} & \\\end{align}\)
  2. \(\text{252 is het kleinste gemene veelvoud van 4, 9 en 7} \\ \begin{align} & \color{blue}{252.} (\frac{x}{4}+\frac{2}{9})& = & (\frac{-6}{7}x+5) \color{blue}{.252} \\\Leftrightarrow & 63x+56& = & -216x+1260 \\\Leftrightarrow & 63x \color{red}{+56} \color{blue}{-56} \color{blue}{+216x} & = & \color{red}{-216x} +1260 \color{blue}{+216x} \color{blue}{-56} \\\Leftrightarrow & 279x& = & 1204 \\\Leftrightarrow & \frac{279x}{ \color{red}{279} }& = & \frac{1204}{279} \\\Leftrightarrow & x = \frac{1204}{279} & & \\ & V = \left\{ \frac{1204}{279} \right\} & \\\end{align}\)
  3. \(\text{156 is het kleinste gemene veelvoud van 4, 13 en 3} \\ \begin{align} & \color{blue}{156.} (\frac{x}{4}+\frac{3}{13})& = & (\frac{7}{3}x-3) \color{blue}{.156} \\\Leftrightarrow & 39x+36& = & 364x-468 \\\Leftrightarrow & 39x \color{red}{+36} \color{blue}{-36} \color{blue}{-364x} & = & \color{red}{364x} -468 \color{blue}{-364x} \color{blue}{-36} \\\Leftrightarrow & -325x& = & -504 \\\Leftrightarrow & \frac{-325x}{ \color{red}{-325} }& = & \frac{-504}{-325} \\\Leftrightarrow & x = \frac{504}{325} & & \\ & V = \left\{ \frac{504}{325} \right\} & \\\end{align}\)
  4. \(\text{252 is het kleinste gemene veelvoud van 7, 9 en 4} \\ \begin{align} & \color{blue}{252.} (\frac{x}{7}-\frac{2}{9})& = & (\frac{1}{4}x+6) \color{blue}{.252} \\\Leftrightarrow & 36x-56& = & 63x+1512 \\\Leftrightarrow & 36x \color{red}{-56} \color{blue}{+56} \color{blue}{-63x} & = & \color{red}{63x} +1512 \color{blue}{-63x} \color{blue}{+56} \\\Leftrightarrow & -27x& = & 1568 \\\Leftrightarrow & \frac{-27x}{ \color{red}{-27} }& = & \frac{1568}{-27} \\\Leftrightarrow & x = \frac{-1568}{27} & & \\ & V = \left\{ \frac{-1568}{27} \right\} & \\\end{align}\)
  5. \(\text{260 is het kleinste gemene veelvoud van 5, 13 en 4} \\ \begin{align} & \color{blue}{260.} (\frac{x}{5}+\frac{4}{13})& = & (\frac{7}{4}x-1) \color{blue}{.260} \\\Leftrightarrow & 52x+80& = & 455x-260 \\\Leftrightarrow & 52x \color{red}{+80} \color{blue}{-80} \color{blue}{-455x} & = & \color{red}{455x} -260 \color{blue}{-455x} \color{blue}{-80} \\\Leftrightarrow & -403x& = & -340 \\\Leftrightarrow & \frac{-403x}{ \color{red}{-403} }& = & \frac{-340}{-403} \\\Leftrightarrow & x = \frac{340}{403} & & \\ & V = \left\{ \frac{340}{403} \right\} & \\\end{align}\)
  6. \(\text{40 is het kleinste gemene veelvoud van 2, 8 en 5} \\ \begin{align} & \color{blue}{40.} (\frac{x}{2}+\frac{3}{8})& = & (\frac{-7}{5}x-5) \color{blue}{.40} \\\Leftrightarrow & 20x+15& = & -56x-200 \\\Leftrightarrow & 20x \color{red}{+15} \color{blue}{-15} \color{blue}{+56x} & = & \color{red}{-56x} -200 \color{blue}{+56x} \color{blue}{-15} \\\Leftrightarrow & 76x& = & -215 \\\Leftrightarrow & \frac{76x}{ \color{red}{76} }& = & \frac{-215}{76} \\\Leftrightarrow & x = \frac{-215}{76} & & \\ & V = \left\{ \frac{-215}{76} \right\} & \\\end{align}\)
  7. \(\text{84 is het kleinste gemene veelvoud van 4, 7 en 3} \\ \begin{align} & \color{blue}{84.} (\frac{x}{4}+\frac{2}{7})& = & (\frac{2}{3}x+6) \color{blue}{.84} \\\Leftrightarrow & 21x+24& = & 56x+504 \\\Leftrightarrow & 21x \color{red}{+24} \color{blue}{-24} \color{blue}{-56x} & = & \color{red}{56x} +504 \color{blue}{-56x} \color{blue}{-24} \\\Leftrightarrow & -35x& = & 480 \\\Leftrightarrow & \frac{-35x}{ \color{red}{-35} }& = & \frac{480}{-35} \\\Leftrightarrow & x = \frac{-96}{7} & & \\ & V = \left\{ \frac{-96}{7} \right\} & \\\end{align}\)
  8. \(\text{210 is het kleinste gemene veelvoud van 5, 14 en 3} \\ \begin{align} & \color{blue}{210.} (\frac{x}{5}+\frac{5}{14})& = & (\frac{7}{3}x-1) \color{blue}{.210} \\\Leftrightarrow & 42x+75& = & 490x-210 \\\Leftrightarrow & 42x \color{red}{+75} \color{blue}{-75} \color{blue}{-490x} & = & \color{red}{490x} -210 \color{blue}{-490x} \color{blue}{-75} \\\Leftrightarrow & -448x& = & -285 \\\Leftrightarrow & \frac{-448x}{ \color{red}{-448} }& = & \frac{-285}{-448} \\\Leftrightarrow & x = \frac{285}{448} & & \\ & V = \left\{ \frac{285}{448} \right\} & \\\end{align}\)
  9. \(\text{126 is het kleinste gemene veelvoud van 7, 9 en 6} \\ \begin{align} & \color{blue}{126.} (\frac{x}{7}+\frac{4}{9})& = & (\frac{-5}{6}x+8) \color{blue}{.126} \\\Leftrightarrow & 18x+56& = & -105x+1008 \\\Leftrightarrow & 18x \color{red}{+56} \color{blue}{-56} \color{blue}{+105x} & = & \color{red}{-105x} +1008 \color{blue}{+105x} \color{blue}{-56} \\\Leftrightarrow & 123x& = & 952 \\\Leftrightarrow & \frac{123x}{ \color{red}{123} }& = & \frac{952}{123} \\\Leftrightarrow & x = \frac{952}{123} & & \\ & V = \left\{ \frac{952}{123} \right\} & \\\end{align}\)
  10. \(\text{70 is het kleinste gemene veelvoud van 7, 10 en 5} \\ \begin{align} & \color{blue}{70.} (\frac{x}{7}-\frac{3}{10})& = & (\frac{-7}{5}x-2) \color{blue}{.70} \\\Leftrightarrow & 10x-21& = & -98x-140 \\\Leftrightarrow & 10x \color{red}{-21} \color{blue}{+21} \color{blue}{+98x} & = & \color{red}{-98x} -140 \color{blue}{+98x} \color{blue}{+21} \\\Leftrightarrow & 108x& = & -119 \\\Leftrightarrow & \frac{108x}{ \color{red}{108} }& = & \frac{-119}{108} \\\Leftrightarrow & x = \frac{-119}{108} & & \\ & V = \left\{ \frac{-119}{108} \right\} & \\\end{align}\)
  11. \(\text{90 is het kleinste gemene veelvoud van 6, 9 en 5} \\ \begin{align} & \color{blue}{90.} (\frac{x}{6}+\frac{4}{9})& = & (\frac{2}{5}x+6) \color{blue}{.90} \\\Leftrightarrow & 15x+40& = & 36x+540 \\\Leftrightarrow & 15x \color{red}{+40} \color{blue}{-40} \color{blue}{-36x} & = & \color{red}{36x} +540 \color{blue}{-36x} \color{blue}{-40} \\\Leftrightarrow & -21x& = & 500 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = & \frac{500}{-21} \\\Leftrightarrow & x = \frac{-500}{21} & & \\ & V = \left\{ \frac{-500}{21} \right\} & \\\end{align}\)
  12. \(\text{60 is het kleinste gemene veelvoud van 4, 15 en 3} \\ \begin{align} & \color{blue}{60.} (\frac{x}{4}+\frac{2}{15})& = & (\frac{1}{3}x+4) \color{blue}{.60} \\\Leftrightarrow & 15x+8& = & 20x+240 \\\Leftrightarrow & 15x \color{red}{+8} \color{blue}{-8} \color{blue}{-20x} & = & \color{red}{20x} +240 \color{blue}{-20x} \color{blue}{-8} \\\Leftrightarrow & -5x& = & 232 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = & \frac{232}{-5} \\\Leftrightarrow & x = \frac{-232}{5} & & \\ & V = \left\{ \frac{-232}{5} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-05-07 14:39:28