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

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

Verbetersleutel

  1. \(\text{130 is het kleinste gemene veelvoud van 2, 13 en 5} \\ \begin{align} & \color{blue}{130.} (\frac{x}{2}+\frac{3}{13})& = & (\frac{3}{5}x+6) \color{blue}{.130} \\\Leftrightarrow & 65x+30& = & 78x+780 \\\Leftrightarrow & 65x \color{red}{+30} \color{blue}{-30} \color{blue}{-78x} & = & \color{red}{78x} +780 \color{blue}{-78x} \color{blue}{-30} \\\Leftrightarrow & -13x& = & 750 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = & \frac{750}{-13} \\\Leftrightarrow & x = \frac{-750}{13} & & \\ & V = \left\{ \frac{-750}{13} \right\} & \\\end{align}\)
  2. \(\text{390 is het kleinste gemene veelvoud van 6, 13 en 5} \\ \begin{align} & \color{blue}{390.} (\frac{x}{6}+\frac{4}{13})& = & (\frac{6}{5}x-3) \color{blue}{.390} \\\Leftrightarrow & 65x+120& = & 468x-1170 \\\Leftrightarrow & 65x \color{red}{+120} \color{blue}{-120} \color{blue}{-468x} & = & \color{red}{468x} -1170 \color{blue}{-468x} \color{blue}{-120} \\\Leftrightarrow & -403x& = & -1290 \\\Leftrightarrow & \frac{-403x}{ \color{red}{-403} }& = & \frac{-1290}{-403} \\\Leftrightarrow & x = \frac{1290}{403} & & \\ & V = \left\{ \frac{1290}{403} \right\} & \\\end{align}\)
  3. \(\text{340 is het kleinste gemene veelvoud van 5, 17 en 4} \\ \begin{align} & \color{blue}{340.} (\frac{x}{5}-\frac{4}{17})& = & (\frac{7}{4}x-7) \color{blue}{.340} \\\Leftrightarrow & 68x-80& = & 595x-2380 \\\Leftrightarrow & 68x \color{red}{-80} \color{blue}{+80} \color{blue}{-595x} & = & \color{red}{595x} -2380 \color{blue}{-595x} \color{blue}{+80} \\\Leftrightarrow & -527x& = & -2300 \\\Leftrightarrow & \frac{-527x}{ \color{red}{-527} }& = & \frac{-2300}{-527} \\\Leftrightarrow & x = \frac{2300}{527} & & \\ & V = \left\{ \frac{2300}{527} \right\} & \\\end{align}\)
  4. \(\text{105 is het kleinste gemene veelvoud van 3, 15 en 7} \\ \begin{align} & \color{blue}{105.} (\frac{x}{3}+\frac{4}{15})& = & (\frac{-3}{7}x+2) \color{blue}{.105} \\\Leftrightarrow & 35x+28& = & -45x+210 \\\Leftrightarrow & 35x \color{red}{+28} \color{blue}{-28} \color{blue}{+45x} & = & \color{red}{-45x} +210 \color{blue}{+45x} \color{blue}{-28} \\\Leftrightarrow & 80x& = & 182 \\\Leftrightarrow & \frac{80x}{ \color{red}{80} }& = & \frac{182}{80} \\\Leftrightarrow & x = \frac{91}{40} & & \\ & V = \left\{ \frac{91}{40} \right\} & \\\end{align}\)
  5. \(\text{231 is het kleinste gemene veelvoud van 7, 11 en 3} \\ \begin{align} & \color{blue}{231.} (\frac{x}{7}-\frac{5}{11})& = & (\frac{4}{3}x-6) \color{blue}{.231} \\\Leftrightarrow & 33x-105& = & 308x-1386 \\\Leftrightarrow & 33x \color{red}{-105} \color{blue}{+105} \color{blue}{-308x} & = & \color{red}{308x} -1386 \color{blue}{-308x} \color{blue}{+105} \\\Leftrightarrow & -275x& = & -1281 \\\Leftrightarrow & \frac{-275x}{ \color{red}{-275} }& = & \frac{-1281}{-275} \\\Leftrightarrow & x = \frac{1281}{275} & & \\ & V = \left\{ \frac{1281}{275} \right\} & \\\end{align}\)
  6. \(\text{170 is het kleinste gemene veelvoud van 5, 17 en 2} \\ \begin{align} & \color{blue}{170.} (\frac{x}{5}-\frac{2}{17})& = & (\frac{1}{2}x+5) \color{blue}{.170} \\\Leftrightarrow & 34x-20& = & 85x+850 \\\Leftrightarrow & 34x \color{red}{-20} \color{blue}{+20} \color{blue}{-85x} & = & \color{red}{85x} +850 \color{blue}{-85x} \color{blue}{+20} \\\Leftrightarrow & -51x& = & 870 \\\Leftrightarrow & \frac{-51x}{ \color{red}{-51} }& = & \frac{870}{-51} \\\Leftrightarrow & x = \frac{-290}{17} & & \\ & V = \left\{ \frac{-290}{17} \right\} & \\\end{align}\)
  7. \(\text{24 is het kleinste gemene veelvoud van 2, 8 en 3} \\ \begin{align} & \color{blue}{24.} (\frac{x}{2}+\frac{3}{8})& = & (\frac{7}{3}x+6) \color{blue}{.24} \\\Leftrightarrow & 12x+9& = & 56x+144 \\\Leftrightarrow & 12x \color{red}{+9} \color{blue}{-9} \color{blue}{-56x} & = & \color{red}{56x} +144 \color{blue}{-56x} \color{blue}{-9} \\\Leftrightarrow & -44x& = & 135 \\\Leftrightarrow & \frac{-44x}{ \color{red}{-44} }& = & \frac{135}{-44} \\\Leftrightarrow & x = \frac{-135}{44} & & \\ & V = \left\{ \frac{-135}{44} \right\} & \\\end{align}\)
  8. \(\text{84 is het kleinste gemene veelvoud van 4, 14 en 3} \\ \begin{align} & \color{blue}{84.} (\frac{x}{4}-\frac{5}{14})& = & (\frac{8}{3}x+7) \color{blue}{.84} \\\Leftrightarrow & 21x-30& = & 224x+588 \\\Leftrightarrow & 21x \color{red}{-30} \color{blue}{+30} \color{blue}{-224x} & = & \color{red}{224x} +588 \color{blue}{-224x} \color{blue}{+30} \\\Leftrightarrow & -203x& = & 618 \\\Leftrightarrow & \frac{-203x}{ \color{red}{-203} }& = & \frac{618}{-203} \\\Leftrightarrow & x = \frac{-618}{203} & & \\ & V = \left\{ \frac{-618}{203} \right\} & \\\end{align}\)
  9. \(\text{42 is het kleinste gemene veelvoud van 6, 6 en 7} \\ \begin{align} & \color{blue}{42.} (\frac{x}{6}-\frac{5}{6})& = & (\frac{6}{7}x-4) \color{blue}{.42} \\\Leftrightarrow & 7x-35& = & 36x-168 \\\Leftrightarrow & 7x \color{red}{-35} \color{blue}{+35} \color{blue}{-36x} & = & \color{red}{36x} -168 \color{blue}{-36x} \color{blue}{+35} \\\Leftrightarrow & -29x& = & -133 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = & \frac{-133}{-29} \\\Leftrightarrow & x = \frac{133}{29} & & \\ & V = \left\{ \frac{133}{29} \right\} & \\\end{align}\)
  10. \(\text{420 is het kleinste gemene veelvoud van 7, 15 en 4} \\ \begin{align} & \color{blue}{420.} (\frac{x}{7}-\frac{2}{15})& = & (\frac{1}{4}x-3) \color{blue}{.420} \\\Leftrightarrow & 60x-56& = & 105x-1260 \\\Leftrightarrow & 60x \color{red}{-56} \color{blue}{+56} \color{blue}{-105x} & = & \color{red}{105x} -1260 \color{blue}{-105x} \color{blue}{+56} \\\Leftrightarrow & -45x& = & -1204 \\\Leftrightarrow & \frac{-45x}{ \color{red}{-45} }& = & \frac{-1204}{-45} \\\Leftrightarrow & x = \frac{1204}{45} & & \\ & V = \left\{ \frac{1204}{45} \right\} & \\\end{align}\)
  11. \(\text{273 is het kleinste gemene veelvoud van 7, 13 en 3} \\ \begin{align} & \color{blue}{273.} (\frac{x}{7}+\frac{3}{13})& = & (\frac{2}{3}x-8) \color{blue}{.273} \\\Leftrightarrow & 39x+63& = & 182x-2184 \\\Leftrightarrow & 39x \color{red}{+63} \color{blue}{-63} \color{blue}{-182x} & = & \color{red}{182x} -2184 \color{blue}{-182x} \color{blue}{-63} \\\Leftrightarrow & -143x& = & -2247 \\\Leftrightarrow & \frac{-143x}{ \color{red}{-143} }& = & \frac{-2247}{-143} \\\Leftrightarrow & x = \frac{2247}{143} & & \\ & V = \left\{ \frac{2247}{143} \right\} & \\\end{align}\)
  12. \(\text{510 is het kleinste gemene veelvoud van 6, 17 en 5} \\ \begin{align} & \color{blue}{510.} (\frac{x}{6}-\frac{5}{17})& = & (\frac{3}{5}x+6) \color{blue}{.510} \\\Leftrightarrow & 85x-150& = & 306x+3060 \\\Leftrightarrow & 85x \color{red}{-150} \color{blue}{+150} \color{blue}{-306x} & = & \color{red}{306x} +3060 \color{blue}{-306x} \color{blue}{+150} \\\Leftrightarrow & -221x& = & 3210 \\\Leftrightarrow & \frac{-221x}{ \color{red}{-221} }& = & \frac{3210}{-221} \\\Leftrightarrow & x = \frac{-3210}{221} & & \\ & V = \left\{ \frac{-3210}{221} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-04-03 04:13:41