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. \(\frac{x}{7}+\frac{2}{17}=\frac{-7}{5}x-5\)
2. \(\frac{x}{7}+\frac{3}{13}=\frac{-5}{6}x+8\)
3. \(\frac{x}{6}-\frac{2}{11}=\frac{6}{7}x-8\)
4. \(\frac{x}{3}-\frac{3}{16}=\frac{4}{7}x-4\)
5. \(\frac{x}{6}+\frac{2}{13}=\frac{3}{7}x+7\)
6. \(\frac{x}{2}-\frac{4}{17}=\frac{-4}{5}x+3\)
7. \(\frac{x}{3}-\frac{4}{9}=\frac{7}{4}x+3\)
8. \(\frac{x}{7}+\frac{2}{11}=\frac{8}{3}x-6\)
9. \(\frac{x}{2}+\frac{4}{7}=\frac{-7}{5}x-6\)
10. \(\frac{x}{4}+\frac{2}{13}=\frac{6}{5}x-2\)
11. \(\frac{x}{7}-\frac{3}{17}=\frac{5}{2}x-1\)
12. \(\frac{x}{2}+\frac{2}{7}=\frac{7}{5}x+7\)

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

Verbetersleutel

1. \(\text{595 is het kleinste gemene veelvoud van 7, 17 en 5} \\ \begin{align} & \color{blue}{595.} (\frac{x}{7}+\frac{2}{17})& = & (\frac{-7}{5}x-5) \color{blue}{.595} \\\Leftrightarrow & 85x+70& = & -833x-2975 \\\Leftrightarrow & 85x \color{red}{+70} \color{blue}{-70} \color{blue}{+833x} & = & \color{red}{-833x} -2975 \color{blue}{+833x} \color{blue}{-70} \\\Leftrightarrow & 918x& = & -3045 \\\Leftrightarrow & \frac{918x}{ \color{red}{918} }& = & \frac{-3045}{918} \\\Leftrightarrow & x = \frac{-1015}{306} & & \\ & V = \left\{ \frac{-1015}{306} \right\} & \\\end{align}\)
2. \(\text{546 is het kleinste gemene veelvoud van 7, 13 en 6} \\ \begin{align} & \color{blue}{546.} (\frac{x}{7}+\frac{3}{13})& = & (\frac{-5}{6}x+8) \color{blue}{.546} \\\Leftrightarrow & 78x+126& = & -455x+4368 \\\Leftrightarrow & 78x \color{red}{+126} \color{blue}{-126} \color{blue}{+455x} & = & \color{red}{-455x} +4368 \color{blue}{+455x} \color{blue}{-126} \\\Leftrightarrow & 533x& = & 4242 \\\Leftrightarrow & \frac{533x}{ \color{red}{533} }& = & \frac{4242}{533} \\\Leftrightarrow & x = \frac{4242}{533} & & \\ & V = \left\{ \frac{4242}{533} \right\} & \\\end{align}\)
3. \(\text{462 is het kleinste gemene veelvoud van 6, 11 en 7} \\ \begin{align} & \color{blue}{462.} (\frac{x}{6}-\frac{2}{11})& = & (\frac{6}{7}x-8) \color{blue}{.462} \\\Leftrightarrow & 77x-84& = & 396x-3696 \\\Leftrightarrow & 77x \color{red}{-84} \color{blue}{+84} \color{blue}{-396x} & = & \color{red}{396x} -3696 \color{blue}{-396x} \color{blue}{+84} \\\Leftrightarrow & -319x& = & -3612 \\\Leftrightarrow & \frac{-319x}{ \color{red}{-319} }& = & \frac{-3612}{-319} \\\Leftrightarrow & x = \frac{3612}{319} & & \\ & V = \left\{ \frac{3612}{319} \right\} & \\\end{align}\)
4. \(\text{336 is het kleinste gemene veelvoud van 3, 16 en 7} \\ \begin{align} & \color{blue}{336.} (\frac{x}{3}-\frac{3}{16})& = & (\frac{4}{7}x-4) \color{blue}{.336} \\\Leftrightarrow & 112x-63& = & 192x-1344 \\\Leftrightarrow & 112x \color{red}{-63} \color{blue}{+63} \color{blue}{-192x} & = & \color{red}{192x} -1344 \color{blue}{-192x} \color{blue}{+63} \\\Leftrightarrow & -80x& = & -1281 \\\Leftrightarrow & \frac{-80x}{ \color{red}{-80} }& = & \frac{-1281}{-80} \\\Leftrightarrow & x = \frac{1281}{80} & & \\ & V = \left\{ \frac{1281}{80} \right\} & \\\end{align}\)
5. \(\text{546 is het kleinste gemene veelvoud van 6, 13 en 7} \\ \begin{align} & \color{blue}{546.} (\frac{x}{6}+\frac{2}{13})& = & (\frac{3}{7}x+7) \color{blue}{.546} \\\Leftrightarrow & 91x+84& = & 234x+3822 \\\Leftrightarrow & 91x \color{red}{+84} \color{blue}{-84} \color{blue}{-234x} & = & \color{red}{234x} +3822 \color{blue}{-234x} \color{blue}{-84} \\\Leftrightarrow & -143x& = & 3738 \\\Leftrightarrow & \frac{-143x}{ \color{red}{-143} }& = & \frac{3738}{-143} \\\Leftrightarrow & x = \frac{-3738}{143} & & \\ & V = \left\{ \frac{-3738}{143} \right\} & \\\end{align}\)
6. \(\text{170 is het kleinste gemene veelvoud van 2, 17 en 5} \\ \begin{align} & \color{blue}{170.} (\frac{x}{2}-\frac{4}{17})& = & (\frac{-4}{5}x+3) \color{blue}{.170} \\\Leftrightarrow & 85x-40& = & -136x+510 \\\Leftrightarrow & 85x \color{red}{-40} \color{blue}{+40} \color{blue}{+136x} & = & \color{red}{-136x} +510 \color{blue}{+136x} \color{blue}{+40} \\\Leftrightarrow & 221x& = & 550 \\\Leftrightarrow & \frac{221x}{ \color{red}{221} }& = & \frac{550}{221} \\\Leftrightarrow & x = \frac{550}{221} & & \\ & V = \left\{ \frac{550}{221} \right\} & \\\end{align}\)
7. \(\text{36 is het kleinste gemene veelvoud van 3, 9 en 4} \\ \begin{align} & \color{blue}{36.} (\frac{x}{3}-\frac{4}{9})& = & (\frac{7}{4}x+3) \color{blue}{.36} \\\Leftrightarrow & 12x-16& = & 63x+108 \\\Leftrightarrow & 12x \color{red}{-16} \color{blue}{+16} \color{blue}{-63x} & = & \color{red}{63x} +108 \color{blue}{-63x} \color{blue}{+16} \\\Leftrightarrow & -51x& = & 124 \\\Leftrightarrow & \frac{-51x}{ \color{red}{-51} }& = & \frac{124}{-51} \\\Leftrightarrow & x = \frac{-124}{51} & & \\ & V = \left\{ \frac{-124}{51} \right\} & \\\end{align}\)
8. \(\text{231 is het kleinste gemene veelvoud van 7, 11 en 3} \\ \begin{align} & \color{blue}{231.} (\frac{x}{7}+\frac{2}{11})& = & (\frac{8}{3}x-6) \color{blue}{.231} \\\Leftrightarrow & 33x+42& = & 616x-1386 \\\Leftrightarrow & 33x \color{red}{+42} \color{blue}{-42} \color{blue}{-616x} & = & \color{red}{616x} -1386 \color{blue}{-616x} \color{blue}{-42} \\\Leftrightarrow & -583x& = & -1428 \\\Leftrightarrow & \frac{-583x}{ \color{red}{-583} }& = & \frac{-1428}{-583} \\\Leftrightarrow & x = \frac{1428}{583} & & \\ & V = \left\{ \frac{1428}{583} \right\} & \\\end{align}\)
9. \(\text{70 is het kleinste gemene veelvoud van 2, 7 en 5} \\ \begin{align} & \color{blue}{70.} (\frac{x}{2}+\frac{4}{7})& = & (\frac{-7}{5}x-6) \color{blue}{.70} \\\Leftrightarrow & 35x+40& = & -98x-420 \\\Leftrightarrow & 35x \color{red}{+40} \color{blue}{-40} \color{blue}{+98x} & = & \color{red}{-98x} -420 \color{blue}{+98x} \color{blue}{-40} \\\Leftrightarrow & 133x& = & -460 \\\Leftrightarrow & \frac{133x}{ \color{red}{133} }& = & \frac{-460}{133} \\\Leftrightarrow & x = \frac{-460}{133} & & \\ & V = \left\{ \frac{-460}{133} \right\} & \\\end{align}\)
10. \(\text{260 is het kleinste gemene veelvoud van 4, 13 en 5} \\ \begin{align} & \color{blue}{260.} (\frac{x}{4}+\frac{2}{13})& = & (\frac{6}{5}x-2) \color{blue}{.260} \\\Leftrightarrow & 65x+40& = & 312x-520 \\\Leftrightarrow & 65x \color{red}{+40} \color{blue}{-40} \color{blue}{-312x} & = & \color{red}{312x} -520 \color{blue}{-312x} \color{blue}{-40} \\\Leftrightarrow & -247x& = & -560 \\\Leftrightarrow & \frac{-247x}{ \color{red}{-247} }& = & \frac{-560}{-247} \\\Leftrightarrow & x = \frac{560}{247} & & \\ & V = \left\{ \frac{560}{247} \right\} & \\\end{align}\)
11. \(\text{238 is het kleinste gemene veelvoud van 7, 17 en 2} \\ \begin{align} & \color{blue}{238.} (\frac{x}{7}-\frac{3}{17})& = & (\frac{5}{2}x-1) \color{blue}{.238} \\\Leftrightarrow & 34x-42& = & 595x-238 \\\Leftrightarrow & 34x \color{red}{-42} \color{blue}{+42} \color{blue}{-595x} & = & \color{red}{595x} -238 \color{blue}{-595x} \color{blue}{+42} \\\Leftrightarrow & -561x& = & -196 \\\Leftrightarrow & \frac{-561x}{ \color{red}{-561} }& = & \frac{-196}{-561} \\\Leftrightarrow & x = \frac{196}{561} & & \\ & V = \left\{ \frac{196}{561} \right\} & \\\end{align}\)
12. \(\text{70 is het kleinste gemene veelvoud van 2, 7 en 5} \\ \begin{align} & \color{blue}{70.} (\frac{x}{2}+\frac{2}{7})& = & (\frac{7}{5}x+7) \color{blue}{.70} \\\Leftrightarrow & 35x+20& = & 98x+490 \\\Leftrightarrow & 35x \color{red}{+20} \color{blue}{-20} \color{blue}{-98x} & = & \color{red}{98x} +490 \color{blue}{-98x} \color{blue}{-20} \\\Leftrightarrow & -63x& = & 470 \\\Leftrightarrow & \frac{-63x}{ \color{red}{-63} }& = & \frac{470}{-63} \\\Leftrightarrow & x = \frac{-470}{63} & & \\ & V = \left\{ \frac{-470}{63} \right\} & \\\end{align}\)