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. \(\frac{x}{7}+\frac{5}{8}=\frac{7}{4}x+8\)
  2. \(\frac{x}{2}+\frac{4}{11}=\frac{6}{7}x-4\)
  3. \(\frac{x}{2}-\frac{5}{6}=\frac{-6}{7}x-6\)
  4. \(\frac{x}{5}-\frac{3}{17}=\frac{5}{6}x+3\)
  5. \(\frac{x}{3}-\frac{2}{9}=\frac{3}{2}x-4\)
  6. \(\frac{x}{6}-\frac{3}{10}=\frac{3}{7}x+7\)
  7. \(\frac{x}{4}-\frac{3}{17}=\frac{-2}{3}x-8\)
  8. \(\frac{x}{3}+\frac{4}{9}=\frac{3}{4}x+3\)
  9. \(\frac{x}{2}+\frac{4}{9}=\frac{2}{7}x+2\)
  10. \(\frac{x}{5}-\frac{4}{15}=\frac{1}{6}x+5\)
  11. \(\frac{x}{5}+\frac{5}{16}=\frac{7}{3}x+3\)
  12. \(\frac{x}{5}+\frac{5}{8}=\frac{5}{6}x-4\)

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

Verbetersleutel

  1. \(\text{56 is het kleinste gemene veelvoud van 7, 8 en 4} \\ \begin{align} & \color{blue}{56.} (\frac{x}{7}+\frac{5}{8})& = & (\frac{7}{4}x+8) \color{blue}{.56} \\\Leftrightarrow & 8x+35& = & 98x+448 \\\Leftrightarrow & 8x \color{red}{+35} \color{blue}{-35} \color{blue}{-98x} & = & \color{red}{98x} +448 \color{blue}{-98x} \color{blue}{-35} \\\Leftrightarrow & -90x& = & 413 \\\Leftrightarrow & \frac{-90x}{ \color{red}{-90} }& = & \frac{413}{-90} \\\Leftrightarrow & x = \frac{-413}{90} & & \\ & V = \left\{ \frac{-413}{90} \right\} & \\\end{align}\)
  2. \(\text{154 is het kleinste gemene veelvoud van 2, 11 en 7} \\ \begin{align} & \color{blue}{154.} (\frac{x}{2}+\frac{4}{11})& = & (\frac{6}{7}x-4) \color{blue}{.154} \\\Leftrightarrow & 77x+56& = & 132x-616 \\\Leftrightarrow & 77x \color{red}{+56} \color{blue}{-56} \color{blue}{-132x} & = & \color{red}{132x} -616 \color{blue}{-132x} \color{blue}{-56} \\\Leftrightarrow & -55x& = & -672 \\\Leftrightarrow & \frac{-55x}{ \color{red}{-55} }& = & \frac{-672}{-55} \\\Leftrightarrow & x = \frac{672}{55} & & \\ & V = \left\{ \frac{672}{55} \right\} & \\\end{align}\)
  3. \(\text{42 is het kleinste gemene veelvoud van 2, 6 en 7} \\ \begin{align} & \color{blue}{42.} (\frac{x}{2}-\frac{5}{6})& = & (\frac{-6}{7}x-6) \color{blue}{.42} \\\Leftrightarrow & 21x-35& = & -36x-252 \\\Leftrightarrow & 21x \color{red}{-35} \color{blue}{+35} \color{blue}{+36x} & = & \color{red}{-36x} -252 \color{blue}{+36x} \color{blue}{+35} \\\Leftrightarrow & 57x& = & -217 \\\Leftrightarrow & \frac{57x}{ \color{red}{57} }& = & \frac{-217}{57} \\\Leftrightarrow & x = \frac{-217}{57} & & \\ & V = \left\{ \frac{-217}{57} \right\} & \\\end{align}\)
  4. \(\text{510 is het kleinste gemene veelvoud van 5, 17 en 6} \\ \begin{align} & \color{blue}{510.} (\frac{x}{5}-\frac{3}{17})& = & (\frac{5}{6}x+3) \color{blue}{.510} \\\Leftrightarrow & 102x-90& = & 425x+1530 \\\Leftrightarrow & 102x \color{red}{-90} \color{blue}{+90} \color{blue}{-425x} & = & \color{red}{425x} +1530 \color{blue}{-425x} \color{blue}{+90} \\\Leftrightarrow & -323x& = & 1620 \\\Leftrightarrow & \frac{-323x}{ \color{red}{-323} }& = & \frac{1620}{-323} \\\Leftrightarrow & x = \frac{-1620}{323} & & \\ & V = \left\{ \frac{-1620}{323} \right\} & \\\end{align}\)
  5. \(\text{18 is het kleinste gemene veelvoud van 3, 9 en 2} \\ \begin{align} & \color{blue}{18.} (\frac{x}{3}-\frac{2}{9})& = & (\frac{3}{2}x-4) \color{blue}{.18} \\\Leftrightarrow & 6x-4& = & 27x-72 \\\Leftrightarrow & 6x \color{red}{-4} \color{blue}{+4} \color{blue}{-27x} & = & \color{red}{27x} -72 \color{blue}{-27x} \color{blue}{+4} \\\Leftrightarrow & -21x& = & -68 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = & \frac{-68}{-21} \\\Leftrightarrow & x = \frac{68}{21} & & \\ & V = \left\{ \frac{68}{21} \right\} & \\\end{align}\)
  6. \(\text{210 is het kleinste gemene veelvoud van 6, 10 en 7} \\ \begin{align} & \color{blue}{210.} (\frac{x}{6}-\frac{3}{10})& = & (\frac{3}{7}x+7) \color{blue}{.210} \\\Leftrightarrow & 35x-63& = & 90x+1470 \\\Leftrightarrow & 35x \color{red}{-63} \color{blue}{+63} \color{blue}{-90x} & = & \color{red}{90x} +1470 \color{blue}{-90x} \color{blue}{+63} \\\Leftrightarrow & -55x& = & 1533 \\\Leftrightarrow & \frac{-55x}{ \color{red}{-55} }& = & \frac{1533}{-55} \\\Leftrightarrow & x = \frac{-1533}{55} & & \\ & V = \left\{ \frac{-1533}{55} \right\} & \\\end{align}\)
  7. \(\text{204 is het kleinste gemene veelvoud van 4, 17 en 3} \\ \begin{align} & \color{blue}{204.} (\frac{x}{4}-\frac{3}{17})& = & (\frac{-2}{3}x-8) \color{blue}{.204} \\\Leftrightarrow & 51x-36& = & -136x-1632 \\\Leftrightarrow & 51x \color{red}{-36} \color{blue}{+36} \color{blue}{+136x} & = & \color{red}{-136x} -1632 \color{blue}{+136x} \color{blue}{+36} \\\Leftrightarrow & 187x& = & -1596 \\\Leftrightarrow & \frac{187x}{ \color{red}{187} }& = & \frac{-1596}{187} \\\Leftrightarrow & x = \frac{-1596}{187} & & \\ & V = \left\{ \frac{-1596}{187} \right\} & \\\end{align}\)
  8. \(\text{36 is het kleinste gemene veelvoud van 3, 9 en 4} \\ \begin{align} & \color{blue}{36.} (\frac{x}{3}+\frac{4}{9})& = & (\frac{3}{4}x+3) \color{blue}{.36} \\\Leftrightarrow & 12x+16& = & 27x+108 \\\Leftrightarrow & 12x \color{red}{+16} \color{blue}{-16} \color{blue}{-27x} & = & \color{red}{27x} +108 \color{blue}{-27x} \color{blue}{-16} \\\Leftrightarrow & -15x& = & 92 \\\Leftrightarrow & \frac{-15x}{ \color{red}{-15} }& = & \frac{92}{-15} \\\Leftrightarrow & x = \frac{-92}{15} & & \\ & V = \left\{ \frac{-92}{15} \right\} & \\\end{align}\)
  9. \(\text{126 is het kleinste gemene veelvoud van 2, 9 en 7} \\ \begin{align} & \color{blue}{126.} (\frac{x}{2}+\frac{4}{9})& = & (\frac{2}{7}x+2) \color{blue}{.126} \\\Leftrightarrow & 63x+56& = & 36x+252 \\\Leftrightarrow & 63x \color{red}{+56} \color{blue}{-56} \color{blue}{-36x} & = & \color{red}{36x} +252 \color{blue}{-36x} \color{blue}{-56} \\\Leftrightarrow & 27x& = & 196 \\\Leftrightarrow & \frac{27x}{ \color{red}{27} }& = & \frac{196}{27} \\\Leftrightarrow & x = \frac{196}{27} & & \\ & V = \left\{ \frac{196}{27} \right\} & \\\end{align}\)
  10. \(\text{30 is het kleinste gemene veelvoud van 5, 15 en 6} \\ \begin{align} & \color{blue}{30.} (\frac{x}{5}-\frac{4}{15})& = & (\frac{1}{6}x+5) \color{blue}{.30} \\\Leftrightarrow & 6x-8& = & 5x+150 \\\Leftrightarrow & 6x \color{red}{-8} \color{blue}{+8} \color{blue}{-5x} & = & \color{red}{5x} +150 \color{blue}{-5x} \color{blue}{+8} \\\Leftrightarrow & x& = & 158 \\ & V = \left\{ 158 \right\} & \\\end{align}\)
  11. \(\text{240 is het kleinste gemene veelvoud van 5, 16 en 3} \\ \begin{align} & \color{blue}{240.} (\frac{x}{5}+\frac{5}{16})& = & (\frac{7}{3}x+3) \color{blue}{.240} \\\Leftrightarrow & 48x+75& = & 560x+720 \\\Leftrightarrow & 48x \color{red}{+75} \color{blue}{-75} \color{blue}{-560x} & = & \color{red}{560x} +720 \color{blue}{-560x} \color{blue}{-75} \\\Leftrightarrow & -512x& = & 645 \\\Leftrightarrow & \frac{-512x}{ \color{red}{-512} }& = & \frac{645}{-512} \\\Leftrightarrow & x = \frac{-645}{512} & & \\ & V = \left\{ \frac{-645}{512} \right\} & \\\end{align}\)
  12. \(\text{120 is het kleinste gemene veelvoud van 5, 8 en 6} \\ \begin{align} & \color{blue}{120.} (\frac{x}{5}+\frac{5}{8})& = & (\frac{5}{6}x-4) \color{blue}{.120} \\\Leftrightarrow & 24x+75& = & 100x-480 \\\Leftrightarrow & 24x \color{red}{+75} \color{blue}{-75} \color{blue}{-100x} & = & \color{red}{100x} -480 \color{blue}{-100x} \color{blue}{-75} \\\Leftrightarrow & -76x& = & -555 \\\Leftrightarrow & \frac{-76x}{ \color{red}{-76} }& = & \frac{-555}{-76} \\\Leftrightarrow & x = \frac{555}{76} & & \\ & V = \left\{ \frac{555}{76} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-05-30 04:31:29