Vgln. eerste graad (reeks 4)

Hoofdmenu Eentje per keer 

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

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

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

Verbetersleutel

  1. \(\text{42 is het kleinste gemene veelvoud van 7, 7 en 6} \\ \begin{align} & \color{blue}{42.} (\frac{x}{7}+\frac{3}{7})& = & (\frac{5}{6}x-8) \color{blue}{.42} \\\Leftrightarrow & 6x+18& = & 35x-336 \\\Leftrightarrow & 6x \color{red}{+18} \color{blue}{-18} \color{blue}{-35x} & = & \color{red}{35x} -336 \color{blue}{-35x} \color{blue}{-18} \\\Leftrightarrow & -29x& = & -354 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = & \frac{-354}{-29} \\\Leftrightarrow & x = \frac{354}{29} & & \\ & V = \left\{ \frac{354}{29} \right\} & \\\end{align}\)
  2. \(\text{255 is het kleinste gemene veelvoud van 3, 17 en 5} \\ \begin{align} & \color{blue}{255.} (\frac{x}{3}-\frac{2}{17})& = & (\frac{-4}{5}x-3) \color{blue}{.255} \\\Leftrightarrow & 85x-30& = & -204x-765 \\\Leftrightarrow & 85x \color{red}{-30} \color{blue}{+30} \color{blue}{+204x} & = & \color{red}{-204x} -765 \color{blue}{+204x} \color{blue}{+30} \\\Leftrightarrow & 289x& = & -735 \\\Leftrightarrow & \frac{289x}{ \color{red}{289} }& = & \frac{-735}{289} \\\Leftrightarrow & x = \frac{-735}{289} & & \\ & V = \left\{ \frac{-735}{289} \right\} & \\\end{align}\)
  3. \(\text{6 is het kleinste gemene veelvoud van 3, 6 en 2} \\ \begin{align} & \color{blue}{6.} (\frac{x}{3}-\frac{5}{6})& = & (\frac{7}{2}x-3) \color{blue}{.6} \\\Leftrightarrow & 2x-5& = & 21x-18 \\\Leftrightarrow & 2x \color{red}{-5} \color{blue}{+5} \color{blue}{-21x} & = & \color{red}{21x} -18 \color{blue}{-21x} \color{blue}{+5} \\\Leftrightarrow & -19x& = & -13 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = & \frac{-13}{-19} \\\Leftrightarrow & x = \frac{13}{19} & & \\ & V = \left\{ \frac{13}{19} \right\} & \\\end{align}\)
  4. \(\text{42 is het kleinste gemene veelvoud van 7, 14 en 6} \\ \begin{align} & \color{blue}{42.} (\frac{x}{7}+\frac{5}{14})& = & (\frac{5}{6}x+8) \color{blue}{.42} \\\Leftrightarrow & 6x+15& = & 35x+336 \\\Leftrightarrow & 6x \color{red}{+15} \color{blue}{-15} \color{blue}{-35x} & = & \color{red}{35x} +336 \color{blue}{-35x} \color{blue}{-15} \\\Leftrightarrow & -29x& = & 321 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = & \frac{321}{-29} \\\Leftrightarrow & x = \frac{-321}{29} & & \\ & V = \left\{ \frac{-321}{29} \right\} & \\\end{align}\)
  5. \(\text{140 is het kleinste gemene veelvoud van 4, 7 en 5} \\ \begin{align} & \color{blue}{140.} (\frac{x}{4}-\frac{3}{7})& = & (\frac{-4}{5}x-2) \color{blue}{.140} \\\Leftrightarrow & 35x-60& = & -112x-280 \\\Leftrightarrow & 35x \color{red}{-60} \color{blue}{+60} \color{blue}{+112x} & = & \color{red}{-112x} -280 \color{blue}{+112x} \color{blue}{+60} \\\Leftrightarrow & 147x& = & -220 \\\Leftrightarrow & \frac{147x}{ \color{red}{147} }& = & \frac{-220}{147} \\\Leftrightarrow & x = \frac{-220}{147} & & \\ & V = \left\{ \frac{-220}{147} \right\} & \\\end{align}\)
  6. \(\text{168 is het kleinste gemene veelvoud van 6, 8 en 7} \\ \begin{align} & \color{blue}{168.} (\frac{x}{6}-\frac{3}{8})& = & (\frac{1}{7}x+4) \color{blue}{.168} \\\Leftrightarrow & 28x-63& = & 24x+672 \\\Leftrightarrow & 28x \color{red}{-63} \color{blue}{+63} \color{blue}{-24x} & = & \color{red}{24x} +672 \color{blue}{-24x} \color{blue}{+63} \\\Leftrightarrow & 4x& = & 735 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = & \frac{735}{4} \\\Leftrightarrow & x = \frac{735}{4} & & \\ & V = \left\{ \frac{735}{4} \right\} & \\\end{align}\)
  7. \(\text{21 is het kleinste gemene veelvoud van 3, 7 en 7} \\ \begin{align} & \color{blue}{21.} (\frac{x}{3}-\frac{4}{7})& = & (\frac{2}{7}x-6) \color{blue}{.21} \\\Leftrightarrow & 7x-12& = & 6x-126 \\\Leftrightarrow & 7x \color{red}{-12} \color{blue}{+12} \color{blue}{-6x} & = & \color{red}{6x} -126 \color{blue}{-6x} \color{blue}{+12} \\\Leftrightarrow & x& = & -114 \\ & V = \left\{ -114 \right\} & \\\end{align}\)
  8. \(\text{45 is het kleinste gemene veelvoud van 5, 9 en 3} \\ \begin{align} & \color{blue}{45.} (\frac{x}{5}-\frac{4}{9})& = & (\frac{1}{3}x-4) \color{blue}{.45} \\\Leftrightarrow & 9x-20& = & 15x-180 \\\Leftrightarrow & 9x \color{red}{-20} \color{blue}{+20} \color{blue}{-15x} & = & \color{red}{15x} -180 \color{blue}{-15x} \color{blue}{+20} \\\Leftrightarrow & -6x& = & -160 \\\Leftrightarrow & \frac{-6x}{ \color{red}{-6} }& = & \frac{-160}{-6} \\\Leftrightarrow & x = \frac{80}{3} & & \\ & V = \left\{ \frac{80}{3} \right\} & \\\end{align}\)
  9. \(\text{45 is het kleinste gemene veelvoud van 3, 9 en 5} \\ \begin{align} & \color{blue}{45.} (\frac{x}{3}-\frac{2}{9})& = & (\frac{-4}{5}x-3) \color{blue}{.45} \\\Leftrightarrow & 15x-10& = & -36x-135 \\\Leftrightarrow & 15x \color{red}{-10} \color{blue}{+10} \color{blue}{+36x} & = & \color{red}{-36x} -135 \color{blue}{+36x} \color{blue}{+10} \\\Leftrightarrow & 51x& = & -125 \\\Leftrightarrow & \frac{51x}{ \color{red}{51} }& = & \frac{-125}{51} \\\Leftrightarrow & x = \frac{-125}{51} & & \\ & V = \left\{ \frac{-125}{51} \right\} & \\\end{align}\)
  10. \(\text{455 is het kleinste gemene veelvoud van 5, 13 en 7} \\ \begin{align} & \color{blue}{455.} (\frac{x}{5}-\frac{2}{13})& = & (\frac{2}{7}x-3) \color{blue}{.455} \\\Leftrightarrow & 91x-70& = & 130x-1365 \\\Leftrightarrow & 91x \color{red}{-70} \color{blue}{+70} \color{blue}{-130x} & = & \color{red}{130x} -1365 \color{blue}{-130x} \color{blue}{+70} \\\Leftrightarrow & -39x& = & -1295 \\\Leftrightarrow & \frac{-39x}{ \color{red}{-39} }& = & \frac{-1295}{-39} \\\Leftrightarrow & x = \frac{1295}{39} & & \\ & V = \left\{ \frac{1295}{39} \right\} & \\\end{align}\)
  11. \(\text{60 is het kleinste gemene veelvoud van 4, 15 en 5} \\ \begin{align} & \color{blue}{60.} (\frac{x}{4}+\frac{2}{15})& = & (\frac{8}{5}x+3) \color{blue}{.60} \\\Leftrightarrow & 15x+8& = & 96x+180 \\\Leftrightarrow & 15x \color{red}{+8} \color{blue}{-8} \color{blue}{-96x} & = & \color{red}{96x} +180 \color{blue}{-96x} \color{blue}{-8} \\\Leftrightarrow & -81x& = & 172 \\\Leftrightarrow & \frac{-81x}{ \color{red}{-81} }& = & \frac{172}{-81} \\\Leftrightarrow & x = \frac{-172}{81} & & \\ & V = \left\{ \frac{-172}{81} \right\} & \\\end{align}\)
  12. \(\text{66 is het kleinste gemene veelvoud van 3, 11 en 2} \\ \begin{align} & \color{blue}{66.} (\frac{x}{3}+\frac{2}{11})& = & (\frac{1}{2}x+5) \color{blue}{.66} \\\Leftrightarrow & 22x+12& = & 33x+330 \\\Leftrightarrow & 22x \color{red}{+12} \color{blue}{-12} \color{blue}{-33x} & = & \color{red}{33x} +330 \color{blue}{-33x} \color{blue}{-12} \\\Leftrightarrow & -11x& = & 318 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = & \frac{318}{-11} \\\Leftrightarrow & x = \frac{-318}{11} & & \\ & V = \left\{ \frac{-318}{11} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-04-03 12:07:40