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. \(\frac{x}{3}+\frac{2}{15}=\frac{6}{7}x-8\)
  2. \(\frac{x}{3}-\frac{5}{8}=\frac{3}{2}x+4\)
  3. \(\frac{x}{5}+\frac{2}{7}=\frac{7}{4}x+4\)
  4. \(\frac{x}{4}-\frac{4}{7}=\frac{3}{5}x+7\)
  5. \(\frac{x}{6}-\frac{4}{13}=\frac{1}{7}x+7\)
  6. \(\frac{x}{5}+\frac{2}{11}=\frac{6}{7}x+3\)
  7. \(\frac{x}{7}+\frac{3}{11}=\frac{3}{2}x-2\)
  8. \(\frac{x}{3}+\frac{4}{15}=\frac{5}{7}x+2\)
  9. \(\frac{x}{7}+\frac{5}{12}=\frac{3}{2}x-5\)
  10. \(\frac{x}{3}+\frac{3}{16}=\frac{6}{7}x+3\)
  11. \(\frac{x}{4}+\frac{4}{15}=\frac{5}{3}x-4\)
  12. \(\frac{x}{7}-\frac{3}{7}=\frac{-3}{4}x+2\)

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

Verbetersleutel

  1. \(\text{105 is het kleinste gemene veelvoud van 3, 15 en 7} \\ \begin{align} & \color{blue}{105.} (\frac{x}{3}+\frac{2}{15})& = & (\frac{6}{7}x-8) \color{blue}{.105} \\\Leftrightarrow & 35x+14& = & 90x-840 \\\Leftrightarrow & 35x \color{red}{+14} \color{blue}{-14} \color{blue}{-90x} & = & \color{red}{90x} -840 \color{blue}{-90x} \color{blue}{-14} \\\Leftrightarrow & -55x& = & -854 \\\Leftrightarrow & \frac{-55x}{ \color{red}{-55} }& = & \frac{-854}{-55} \\\Leftrightarrow & x = \frac{854}{55} & & \\ & V = \left\{ \frac{854}{55} \right\} & \\\end{align}\)
  2. \(\text{24 is het kleinste gemene veelvoud van 3, 8 en 2} \\ \begin{align} & \color{blue}{24.} (\frac{x}{3}-\frac{5}{8})& = & (\frac{3}{2}x+4) \color{blue}{.24} \\\Leftrightarrow & 8x-15& = & 36x+96 \\\Leftrightarrow & 8x \color{red}{-15} \color{blue}{+15} \color{blue}{-36x} & = & \color{red}{36x} +96 \color{blue}{-36x} \color{blue}{+15} \\\Leftrightarrow & -28x& = & 111 \\\Leftrightarrow & \frac{-28x}{ \color{red}{-28} }& = & \frac{111}{-28} \\\Leftrightarrow & x = \frac{-111}{28} & & \\ & V = \left\{ \frac{-111}{28} \right\} & \\\end{align}\)
  3. \(\text{140 is het kleinste gemene veelvoud van 5, 7 en 4} \\ \begin{align} & \color{blue}{140.} (\frac{x}{5}+\frac{2}{7})& = & (\frac{7}{4}x+4) \color{blue}{.140} \\\Leftrightarrow & 28x+40& = & 245x+560 \\\Leftrightarrow & 28x \color{red}{+40} \color{blue}{-40} \color{blue}{-245x} & = & \color{red}{245x} +560 \color{blue}{-245x} \color{blue}{-40} \\\Leftrightarrow & -217x& = & 520 \\\Leftrightarrow & \frac{-217x}{ \color{red}{-217} }& = & \frac{520}{-217} \\\Leftrightarrow & x = \frac{-520}{217} & & \\ & V = \left\{ \frac{-520}{217} \right\} & \\\end{align}\)
  4. \(\text{140 is het kleinste gemene veelvoud van 4, 7 en 5} \\ \begin{align} & \color{blue}{140.} (\frac{x}{4}-\frac{4}{7})& = & (\frac{3}{5}x+7) \color{blue}{.140} \\\Leftrightarrow & 35x-80& = & 84x+980 \\\Leftrightarrow & 35x \color{red}{-80} \color{blue}{+80} \color{blue}{-84x} & = & \color{red}{84x} +980 \color{blue}{-84x} \color{blue}{+80} \\\Leftrightarrow & -49x& = & 1060 \\\Leftrightarrow & \frac{-49x}{ \color{red}{-49} }& = & \frac{1060}{-49} \\\Leftrightarrow & x = \frac{-1060}{49} & & \\ & V = \left\{ \frac{-1060}{49} \right\} & \\\end{align}\)
  5. \(\text{546 is het kleinste gemene veelvoud van 6, 13 en 7} \\ \begin{align} & \color{blue}{546.} (\frac{x}{6}-\frac{4}{13})& = & (\frac{1}{7}x+7) \color{blue}{.546} \\\Leftrightarrow & 91x-168& = & 78x+3822 \\\Leftrightarrow & 91x \color{red}{-168} \color{blue}{+168} \color{blue}{-78x} & = & \color{red}{78x} +3822 \color{blue}{-78x} \color{blue}{+168} \\\Leftrightarrow & 13x& = & 3990 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = & \frac{3990}{13} \\\Leftrightarrow & x = \frac{3990}{13} & & \\ & V = \left\{ \frac{3990}{13} \right\} & \\\end{align}\)
  6. \(\text{385 is het kleinste gemene veelvoud van 5, 11 en 7} \\ \begin{align} & \color{blue}{385.} (\frac{x}{5}+\frac{2}{11})& = & (\frac{6}{7}x+3) \color{blue}{.385} \\\Leftrightarrow & 77x+70& = & 330x+1155 \\\Leftrightarrow & 77x \color{red}{+70} \color{blue}{-70} \color{blue}{-330x} & = & \color{red}{330x} +1155 \color{blue}{-330x} \color{blue}{-70} \\\Leftrightarrow & -253x& = & 1085 \\\Leftrightarrow & \frac{-253x}{ \color{red}{-253} }& = & \frac{1085}{-253} \\\Leftrightarrow & x = \frac{-1085}{253} & & \\ & V = \left\{ \frac{-1085}{253} \right\} & \\\end{align}\)
  7. \(\text{154 is het kleinste gemene veelvoud van 7, 11 en 2} \\ \begin{align} & \color{blue}{154.} (\frac{x}{7}+\frac{3}{11})& = & (\frac{3}{2}x-2) \color{blue}{.154} \\\Leftrightarrow & 22x+42& = & 231x-308 \\\Leftrightarrow & 22x \color{red}{+42} \color{blue}{-42} \color{blue}{-231x} & = & \color{red}{231x} -308 \color{blue}{-231x} \color{blue}{-42} \\\Leftrightarrow & -209x& = & -350 \\\Leftrightarrow & \frac{-209x}{ \color{red}{-209} }& = & \frac{-350}{-209} \\\Leftrightarrow & x = \frac{350}{209} & & \\ & V = \left\{ \frac{350}{209} \right\} & \\\end{align}\)
  8. \(\text{105 is het kleinste gemene veelvoud van 3, 15 en 7} \\ \begin{align} & \color{blue}{105.} (\frac{x}{3}+\frac{4}{15})& = & (\frac{5}{7}x+2) \color{blue}{.105} \\\Leftrightarrow & 35x+28& = & 75x+210 \\\Leftrightarrow & 35x \color{red}{+28} \color{blue}{-28} \color{blue}{-75x} & = & \color{red}{75x} +210 \color{blue}{-75x} \color{blue}{-28} \\\Leftrightarrow & -40x& = & 182 \\\Leftrightarrow & \frac{-40x}{ \color{red}{-40} }& = & \frac{182}{-40} \\\Leftrightarrow & x = \frac{-91}{20} & & \\ & V = \left\{ \frac{-91}{20} \right\} & \\\end{align}\)
  9. \(\text{84 is het kleinste gemene veelvoud van 7, 12 en 2} \\ \begin{align} & \color{blue}{84.} (\frac{x}{7}+\frac{5}{12})& = & (\frac{3}{2}x-5) \color{blue}{.84} \\\Leftrightarrow & 12x+35& = & 126x-420 \\\Leftrightarrow & 12x \color{red}{+35} \color{blue}{-35} \color{blue}{-126x} & = & \color{red}{126x} -420 \color{blue}{-126x} \color{blue}{-35} \\\Leftrightarrow & -114x& = & -455 \\\Leftrightarrow & \frac{-114x}{ \color{red}{-114} }& = & \frac{-455}{-114} \\\Leftrightarrow & x = \frac{455}{114} & & \\ & V = \left\{ \frac{455}{114} \right\} & \\\end{align}\)
  10. \(\text{336 is het kleinste gemene veelvoud van 3, 16 en 7} \\ \begin{align} & \color{blue}{336.} (\frac{x}{3}+\frac{3}{16})& = & (\frac{6}{7}x+3) \color{blue}{.336} \\\Leftrightarrow & 112x+63& = & 288x+1008 \\\Leftrightarrow & 112x \color{red}{+63} \color{blue}{-63} \color{blue}{-288x} & = & \color{red}{288x} +1008 \color{blue}{-288x} \color{blue}{-63} \\\Leftrightarrow & -176x& = & 945 \\\Leftrightarrow & \frac{-176x}{ \color{red}{-176} }& = & \frac{945}{-176} \\\Leftrightarrow & x = \frac{-945}{176} & & \\ & V = \left\{ \frac{-945}{176} \right\} & \\\end{align}\)
  11. \(\text{60 is het kleinste gemene veelvoud van 4, 15 en 3} \\ \begin{align} & \color{blue}{60.} (\frac{x}{4}+\frac{4}{15})& = & (\frac{5}{3}x-4) \color{blue}{.60} \\\Leftrightarrow & 15x+16& = & 100x-240 \\\Leftrightarrow & 15x \color{red}{+16} \color{blue}{-16} \color{blue}{-100x} & = & \color{red}{100x} -240 \color{blue}{-100x} \color{blue}{-16} \\\Leftrightarrow & -85x& = & -256 \\\Leftrightarrow & \frac{-85x}{ \color{red}{-85} }& = & \frac{-256}{-85} \\\Leftrightarrow & x = \frac{256}{85} & & \\ & V = \left\{ \frac{256}{85} \right\} & \\\end{align}\)
  12. \(\text{28 is het kleinste gemene veelvoud van 7, 7 en 4} \\ \begin{align} & \color{blue}{28.} (\frac{x}{7}-\frac{3}{7})& = & (\frac{-3}{4}x+2) \color{blue}{.28} \\\Leftrightarrow & 4x-12& = & -21x+56 \\\Leftrightarrow & 4x \color{red}{-12} \color{blue}{+12} \color{blue}{+21x} & = & \color{red}{-21x} +56 \color{blue}{+21x} \color{blue}{+12} \\\Leftrightarrow & 25x& = & 68 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = & \frac{68}{25} \\\Leftrightarrow & x = \frac{68}{25} & & \\ & V = \left\{ \frac{68}{25} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-04-26 07:20:17