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

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

Verbetersleutel

  1. \(\text{42 is het kleinste gemene veelvoud van 6, 7 en 7} \\ \begin{align} & \color{blue}{42.} (\frac{x}{6}-\frac{2}{7})& = & (\frac{1}{7}x-8) \color{blue}{.42} \\\Leftrightarrow & 7x-12& = & 6x-336 \\\Leftrightarrow & 7x \color{red}{-12} \color{blue}{+12} \color{blue}{-6x} & = & \color{red}{6x} -336 \color{blue}{-6x} \color{blue}{+12} \\\Leftrightarrow & x& = & -324 \\ & V = \left\{ -324 \right\} & \\\end{align}\)
  2. \(\text{308 is het kleinste gemene veelvoud van 4, 11 en 7} \\ \begin{align} & \color{blue}{308.} (\frac{x}{4}+\frac{4}{11})& = & (\frac{4}{7}x+1) \color{blue}{.308} \\\Leftrightarrow & 77x+112& = & 176x+308 \\\Leftrightarrow & 77x \color{red}{+112} \color{blue}{-112} \color{blue}{-176x} & = & \color{red}{176x} +308 \color{blue}{-176x} \color{blue}{-112} \\\Leftrightarrow & -99x& = & 196 \\\Leftrightarrow & \frac{-99x}{ \color{red}{-99} }& = & \frac{196}{-99} \\\Leftrightarrow & x = \frac{-196}{99} & & \\ & V = \left\{ \frac{-196}{99} \right\} & \\\end{align}\)
  3. \(\text{90 is het kleinste gemene veelvoud van 5, 9 en 2} \\ \begin{align} & \color{blue}{90.} (\frac{x}{5}-\frac{4}{9})& = & (\frac{3}{2}x-5) \color{blue}{.90} \\\Leftrightarrow & 18x-40& = & 135x-450 \\\Leftrightarrow & 18x \color{red}{-40} \color{blue}{+40} \color{blue}{-135x} & = & \color{red}{135x} -450 \color{blue}{-135x} \color{blue}{+40} \\\Leftrightarrow & -117x& = & -410 \\\Leftrightarrow & \frac{-117x}{ \color{red}{-117} }& = & \frac{-410}{-117} \\\Leftrightarrow & x = \frac{410}{117} & & \\ & V = \left\{ \frac{410}{117} \right\} & \\\end{align}\)
  4. \(\text{30 is het kleinste gemene veelvoud van 2, 15 en 5} \\ \begin{align} & \color{blue}{30.} (\frac{x}{2}-\frac{4}{15})& = & (\frac{3}{5}x+8) \color{blue}{.30} \\\Leftrightarrow & 15x-8& = & 18x+240 \\\Leftrightarrow & 15x \color{red}{-8} \color{blue}{+8} \color{blue}{-18x} & = & \color{red}{18x} +240 \color{blue}{-18x} \color{blue}{+8} \\\Leftrightarrow & -3x& = & 248 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = & \frac{248}{-3} \\\Leftrightarrow & x = \frac{-248}{3} & & \\ & V = \left\{ \frac{-248}{3} \right\} & \\\end{align}\)
  5. \(\text{105 is het kleinste gemene veelvoud van 3, 15 en 7} \\ \begin{align} & \color{blue}{105.} (\frac{x}{3}-\frac{2}{15})& = & (\frac{3}{7}x+7) \color{blue}{.105} \\\Leftrightarrow & 35x-14& = & 45x+735 \\\Leftrightarrow & 35x \color{red}{-14} \color{blue}{+14} \color{blue}{-45x} & = & \color{red}{45x} +735 \color{blue}{-45x} \color{blue}{+14} \\\Leftrightarrow & -10x& = & 749 \\\Leftrightarrow & \frac{-10x}{ \color{red}{-10} }& = & \frac{749}{-10} \\\Leftrightarrow & x = \frac{-749}{10} & & \\ & V = \left\{ \frac{-749}{10} \right\} & \\\end{align}\)
  6. \(\text{30 is het kleinste gemene veelvoud van 3, 10 en 5} \\ \begin{align} & \color{blue}{30.} (\frac{x}{3}-\frac{3}{10})& = & (\frac{7}{5}x-5) \color{blue}{.30} \\\Leftrightarrow & 10x-9& = & 42x-150 \\\Leftrightarrow & 10x \color{red}{-9} \color{blue}{+9} \color{blue}{-42x} & = & \color{red}{42x} -150 \color{blue}{-42x} \color{blue}{+9} \\\Leftrightarrow & -32x& = & -141 \\\Leftrightarrow & \frac{-32x}{ \color{red}{-32} }& = & \frac{-141}{-32} \\\Leftrightarrow & x = \frac{141}{32} & & \\ & V = \left\{ \frac{141}{32} \right\} & \\\end{align}\)
  7. \(\text{63 is het kleinste gemene veelvoud van 3, 9 en 7} \\ \begin{align} & \color{blue}{63.} (\frac{x}{3}+\frac{2}{9})& = & (\frac{8}{7}x+6) \color{blue}{.63} \\\Leftrightarrow & 21x+14& = & 72x+378 \\\Leftrightarrow & 21x \color{red}{+14} \color{blue}{-14} \color{blue}{-72x} & = & \color{red}{72x} +378 \color{blue}{-72x} \color{blue}{-14} \\\Leftrightarrow & -51x& = & 364 \\\Leftrightarrow & \frac{-51x}{ \color{red}{-51} }& = & \frac{364}{-51} \\\Leftrightarrow & x = \frac{-364}{51} & & \\ & V = \left\{ \frac{-364}{51} \right\} & \\\end{align}\)
  8. \(\text{56 is het kleinste gemene veelvoud van 4, 8 en 7} \\ \begin{align} & \color{blue}{56.} (\frac{x}{4}-\frac{3}{8})& = & (\frac{5}{7}x+3) \color{blue}{.56} \\\Leftrightarrow & 14x-21& = & 40x+168 \\\Leftrightarrow & 14x \color{red}{-21} \color{blue}{+21} \color{blue}{-40x} & = & \color{red}{40x} +168 \color{blue}{-40x} \color{blue}{+21} \\\Leftrightarrow & -26x& = & 189 \\\Leftrightarrow & \frac{-26x}{ \color{red}{-26} }& = & \frac{189}{-26} \\\Leftrightarrow & x = \frac{-189}{26} & & \\ & V = \left\{ \frac{-189}{26} \right\} & \\\end{align}\)
  9. \(\text{231 is het kleinste gemene veelvoud van 7, 11 en 3} \\ \begin{align} & \color{blue}{231.} (\frac{x}{7}+\frac{5}{11})& = & (\frac{7}{3}x-6) \color{blue}{.231} \\\Leftrightarrow & 33x+105& = & 539x-1386 \\\Leftrightarrow & 33x \color{red}{+105} \color{blue}{-105} \color{blue}{-539x} & = & \color{red}{539x} -1386 \color{blue}{-539x} \color{blue}{-105} \\\Leftrightarrow & -506x& = & -1491 \\\Leftrightarrow & \frac{-506x}{ \color{red}{-506} }& = & \frac{-1491}{-506} \\\Leftrightarrow & x = \frac{1491}{506} & & \\ & V = \left\{ \frac{1491}{506} \right\} & \\\end{align}\)
  10. \(\text{476 is het kleinste gemene veelvoud van 4, 17 en 7} \\ \begin{align} & \color{blue}{476.} (\frac{x}{4}+\frac{2}{17})& = & (\frac{-2}{7}x+2) \color{blue}{.476} \\\Leftrightarrow & 119x+56& = & -136x+952 \\\Leftrightarrow & 119x \color{red}{+56} \color{blue}{-56} \color{blue}{+136x} & = & \color{red}{-136x} +952 \color{blue}{+136x} \color{blue}{-56} \\\Leftrightarrow & 255x& = & 896 \\\Leftrightarrow & \frac{255x}{ \color{red}{255} }& = & \frac{896}{255} \\\Leftrightarrow & x = \frac{896}{255} & & \\ & V = \left\{ \frac{896}{255} \right\} & \\\end{align}\)
  11. \(\text{420 is het kleinste gemene veelvoud van 4, 15 en 7} \\ \begin{align} & \color{blue}{420.} (\frac{x}{4}-\frac{4}{15})& = & (\frac{4}{7}x-3) \color{blue}{.420} \\\Leftrightarrow & 105x-112& = & 240x-1260 \\\Leftrightarrow & 105x \color{red}{-112} \color{blue}{+112} \color{blue}{-240x} & = & \color{red}{240x} -1260 \color{blue}{-240x} \color{blue}{+112} \\\Leftrightarrow & -135x& = & -1148 \\\Leftrightarrow & \frac{-135x}{ \color{red}{-135} }& = & \frac{-1148}{-135} \\\Leftrightarrow & x = \frac{1148}{135} & & \\ & V = \left\{ \frac{1148}{135} \right\} & \\\end{align}\)
  12. \(\text{63 is het kleinste gemene veelvoud van 7, 9 en 3} \\ \begin{align} & \color{blue}{63.} (\frac{x}{7}-\frac{2}{9})& = & (\frac{4}{3}x-3) \color{blue}{.63} \\\Leftrightarrow & 9x-14& = & 84x-189 \\\Leftrightarrow & 9x \color{red}{-14} \color{blue}{+14} \color{blue}{-84x} & = & \color{red}{84x} -189 \color{blue}{-84x} \color{blue}{+14} \\\Leftrightarrow & -75x& = & -175 \\\Leftrightarrow & \frac{-75x}{ \color{red}{-75} }& = & \frac{-175}{-75} \\\Leftrightarrow & x = \frac{7}{3} & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-05-02 11:17:45