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

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

Verbetersleutel

  1. \(\text{130 is het kleinste gemene veelvoud van 2, 13 en 5} \\ \begin{align} & \color{blue}{130.} (\frac{x}{2}+\frac{2}{13})& = & (\frac{-4}{5}x-8) \color{blue}{.130} \\\Leftrightarrow & 65x+20& = & -104x-1040 \\\Leftrightarrow & 65x \color{red}{+20} \color{blue}{-20} \color{blue}{+104x} & = & \color{red}{-104x} -1040 \color{blue}{+104x} \color{blue}{-20} \\\Leftrightarrow & 169x& = & -1060 \\\Leftrightarrow & \frac{169x}{ \color{red}{169} }& = & \frac{-1060}{169} \\\Leftrightarrow & x = \frac{-1060}{169} & & \\ & V = \left\{ \frac{-1060}{169} \right\} & \\\end{align}\)
  2. \(\text{60 is het kleinste gemene veelvoud van 4, 10 en 3} \\ \begin{align} & \color{blue}{60.} (\frac{x}{4}-\frac{3}{10})& = & (\frac{8}{3}x+2) \color{blue}{.60} \\\Leftrightarrow & 15x-18& = & 160x+120 \\\Leftrightarrow & 15x \color{red}{-18} \color{blue}{+18} \color{blue}{-160x} & = & \color{red}{160x} +120 \color{blue}{-160x} \color{blue}{+18} \\\Leftrightarrow & -145x& = & 138 \\\Leftrightarrow & \frac{-145x}{ \color{red}{-145} }& = & \frac{138}{-145} \\\Leftrightarrow & x = \frac{-138}{145} & & \\ & V = \left\{ \frac{-138}{145} \right\} & \\\end{align}\)
  3. \(\text{238 is het kleinste gemene veelvoud van 2, 17 en 7} \\ \begin{align} & \color{blue}{238.} (\frac{x}{2}-\frac{4}{17})& = & (\frac{5}{7}x+3) \color{blue}{.238} \\\Leftrightarrow & 119x-56& = & 170x+714 \\\Leftrightarrow & 119x \color{red}{-56} \color{blue}{+56} \color{blue}{-170x} & = & \color{red}{170x} +714 \color{blue}{-170x} \color{blue}{+56} \\\Leftrightarrow & -51x& = & 770 \\\Leftrightarrow & \frac{-51x}{ \color{red}{-51} }& = & \frac{770}{-51} \\\Leftrightarrow & x = \frac{-770}{51} & & \\ & V = \left\{ \frac{-770}{51} \right\} & \\\end{align}\)
  4. \(\text{273 is het kleinste gemene veelvoud van 7, 13 en 3} \\ \begin{align} & \color{blue}{273.} (\frac{x}{7}-\frac{4}{13})& = & (\frac{-8}{3}x-5) \color{blue}{.273} \\\Leftrightarrow & 39x-84& = & -728x-1365 \\\Leftrightarrow & 39x \color{red}{-84} \color{blue}{+84} \color{blue}{+728x} & = & \color{red}{-728x} -1365 \color{blue}{+728x} \color{blue}{+84} \\\Leftrightarrow & 767x& = & -1281 \\\Leftrightarrow & \frac{767x}{ \color{red}{767} }& = & \frac{-1281}{767} \\\Leftrightarrow & x = \frac{-1281}{767} & & \\ & V = \left\{ \frac{-1281}{767} \right\} & \\\end{align}\)
  5. \(\text{35 is het kleinste gemene veelvoud van 5, 7 en 7} \\ \begin{align} & \color{blue}{35.} (\frac{x}{5}-\frac{4}{7})& = & (\frac{2}{7}x-1) \color{blue}{.35} \\\Leftrightarrow & 7x-20& = & 10x-35 \\\Leftrightarrow & 7x \color{red}{-20} \color{blue}{+20} \color{blue}{-10x} & = & \color{red}{10x} -35 \color{blue}{-10x} \color{blue}{+20} \\\Leftrightarrow & -3x& = & -15 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = & \frac{-15}{-3} \\\Leftrightarrow & x = 5 & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
  6. \(\text{42 is het kleinste gemene veelvoud van 6, 7 en 7} \\ \begin{align} & \color{blue}{42.} (\frac{x}{6}+\frac{5}{7})& = & (\frac{-2}{7}x-8) \color{blue}{.42} \\\Leftrightarrow & 7x+30& = & -12x-336 \\\Leftrightarrow & 7x \color{red}{+30} \color{blue}{-30} \color{blue}{+12x} & = & \color{red}{-12x} -336 \color{blue}{+12x} \color{blue}{-30} \\\Leftrightarrow & 19x& = & -366 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = & \frac{-366}{19} \\\Leftrightarrow & x = \frac{-366}{19} & & \\ & V = \left\{ \frac{-366}{19} \right\} & \\\end{align}\)
  7. \(\text{210 is het kleinste gemene veelvoud van 2, 15 en 7} \\ \begin{align} & \color{blue}{210.} (\frac{x}{2}-\frac{2}{15})& = & (\frac{8}{7}x+4) \color{blue}{.210} \\\Leftrightarrow & 105x-28& = & 240x+840 \\\Leftrightarrow & 105x \color{red}{-28} \color{blue}{+28} \color{blue}{-240x} & = & \color{red}{240x} +840 \color{blue}{-240x} \color{blue}{+28} \\\Leftrightarrow & -135x& = & 868 \\\Leftrightarrow & \frac{-135x}{ \color{red}{-135} }& = & \frac{868}{-135} \\\Leftrightarrow & x = \frac{-868}{135} & & \\ & V = \left\{ \frac{-868}{135} \right\} & \\\end{align}\)
  8. \(\text{195 is het kleinste gemene veelvoud van 3, 13 en 5} \\ \begin{align} & \color{blue}{195.} (\frac{x}{3}-\frac{2}{13})& = & (\frac{6}{5}x-2) \color{blue}{.195} \\\Leftrightarrow & 65x-30& = & 234x-390 \\\Leftrightarrow & 65x \color{red}{-30} \color{blue}{+30} \color{blue}{-234x} & = & \color{red}{234x} -390 \color{blue}{-234x} \color{blue}{+30} \\\Leftrightarrow & -169x& = & -360 \\\Leftrightarrow & \frac{-169x}{ \color{red}{-169} }& = & \frac{-360}{-169} \\\Leftrightarrow & x = \frac{360}{169} & & \\ & V = \left\{ \frac{360}{169} \right\} & \\\end{align}\)
  9. \(\text{30 is het kleinste gemene veelvoud van 5, 15 en 6} \\ \begin{align} & \color{blue}{30.} (\frac{x}{5}-\frac{4}{15})& = & (\frac{7}{6}x-4) \color{blue}{.30} \\\Leftrightarrow & 6x-8& = & 35x-120 \\\Leftrightarrow & 6x \color{red}{-8} \color{blue}{+8} \color{blue}{-35x} & = & \color{red}{35x} -120 \color{blue}{-35x} \color{blue}{+8} \\\Leftrightarrow & -29x& = & -112 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = & \frac{-112}{-29} \\\Leftrightarrow & x = \frac{112}{29} & & \\ & V = \left\{ \frac{112}{29} \right\} & \\\end{align}\)
  10. \(\text{45 is het kleinste gemene veelvoud van 3, 9 en 5} \\ \begin{align} & \color{blue}{45.} (\frac{x}{3}-\frac{2}{9})& = & (\frac{4}{5}x+3) \color{blue}{.45} \\\Leftrightarrow & 15x-10& = & 36x+135 \\\Leftrightarrow & 15x \color{red}{-10} \color{blue}{+10} \color{blue}{-36x} & = & \color{red}{36x} +135 \color{blue}{-36x} \color{blue}{+10} \\\Leftrightarrow & -21x& = & 145 \\\Leftrightarrow & \frac{-21x}{ \color{red}{-21} }& = & \frac{145}{-21} \\\Leftrightarrow & x = \frac{-145}{21} & & \\ & V = \left\{ \frac{-145}{21} \right\} & \\\end{align}\)
  11. \(\text{126 is het kleinste gemene veelvoud van 2, 9 en 7} \\ \begin{align} & \color{blue}{126.} (\frac{x}{2}+\frac{5}{9})& = & (\frac{2}{7}x+8) \color{blue}{.126} \\\Leftrightarrow & 63x+70& = & 36x+1008 \\\Leftrightarrow & 63x \color{red}{+70} \color{blue}{-70} \color{blue}{-36x} & = & \color{red}{36x} +1008 \color{blue}{-36x} \color{blue}{-70} \\\Leftrightarrow & 27x& = & 938 \\\Leftrightarrow & \frac{27x}{ \color{red}{27} }& = & \frac{938}{27} \\\Leftrightarrow & x = \frac{938}{27} & & \\ & V = \left\{ \frac{938}{27} \right\} & \\\end{align}\)
  12. \(\text{84 is het kleinste gemene veelvoud van 3, 7 en 4} \\ \begin{align} & \color{blue}{84.} (\frac{x}{3}+\frac{2}{7})& = & (\frac{5}{4}x-3) \color{blue}{.84} \\\Leftrightarrow & 28x+24& = & 105x-252 \\\Leftrightarrow & 28x \color{red}{+24} \color{blue}{-24} \color{blue}{-105x} & = & \color{red}{105x} -252 \color{blue}{-105x} \color{blue}{-24} \\\Leftrightarrow & -77x& = & -276 \\\Leftrightarrow & \frac{-77x}{ \color{red}{-77} }& = & \frac{-276}{-77} \\\Leftrightarrow & x = \frac{276}{77} & & \\ & V = \left\{ \frac{276}{77} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-04-02 05:54:58