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

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

Verbetersleutel

  1. \(\text{30 is het kleinste gemene veelvoud van 6, 15 en 5} \\ \begin{align} & \color{blue}{30.} (\frac{x}{6}-\frac{4}{15})& = & (\frac{-7}{5}x-1) \color{blue}{.30} \\\Leftrightarrow & 5x-8& = & -42x-30 \\\Leftrightarrow & 5x \color{red}{-8} \color{blue}{+8} \color{blue}{+42x} & = & \color{red}{-42x} -30 \color{blue}{+42x} \color{blue}{+8} \\\Leftrightarrow & 47x& = & -22 \\\Leftrightarrow & \frac{47x}{ \color{red}{47} }& = & \frac{-22}{47} \\\Leftrightarrow & x = \frac{-22}{47} & & \\ & V = \left\{ \frac{-22}{47} \right\} & \\\end{align}\)
  2. \(\text{255 is het kleinste gemene veelvoud van 3, 17 en 5} \\ \begin{align} & \color{blue}{255.} (\frac{x}{3}-\frac{5}{17})& = & (\frac{6}{5}x+7) \color{blue}{.255} \\\Leftrightarrow & 85x-75& = & 306x+1785 \\\Leftrightarrow & 85x \color{red}{-75} \color{blue}{+75} \color{blue}{-306x} & = & \color{red}{306x} +1785 \color{blue}{-306x} \color{blue}{+75} \\\Leftrightarrow & -221x& = & 1860 \\\Leftrightarrow & \frac{-221x}{ \color{red}{-221} }& = & \frac{1860}{-221} \\\Leftrightarrow & x = \frac{-1860}{221} & & \\ & V = \left\{ \frac{-1860}{221} \right\} & \\\end{align}\)
  3. \(\text{210 is het kleinste gemene veelvoud van 6, 7 en 5} \\ \begin{align} & \color{blue}{210.} (\frac{x}{6}+\frac{2}{7})& = & (\frac{8}{5}x-3) \color{blue}{.210} \\\Leftrightarrow & 35x+60& = & 336x-630 \\\Leftrightarrow & 35x \color{red}{+60} \color{blue}{-60} \color{blue}{-336x} & = & \color{red}{336x} -630 \color{blue}{-336x} \color{blue}{-60} \\\Leftrightarrow & -301x& = & -690 \\\Leftrightarrow & \frac{-301x}{ \color{red}{-301} }& = & \frac{-690}{-301} \\\Leftrightarrow & x = \frac{690}{301} & & \\ & V = \left\{ \frac{690}{301} \right\} & \\\end{align}\)
  4. \(\text{252 is het kleinste gemene veelvoud van 7, 9 en 4} \\ \begin{align} & \color{blue}{252.} (\frac{x}{7}+\frac{4}{9})& = & (\frac{3}{4}x-6) \color{blue}{.252} \\\Leftrightarrow & 36x+112& = & 189x-1512 \\\Leftrightarrow & 36x \color{red}{+112} \color{blue}{-112} \color{blue}{-189x} & = & \color{red}{189x} -1512 \color{blue}{-189x} \color{blue}{-112} \\\Leftrightarrow & -153x& = & -1624 \\\Leftrightarrow & \frac{-153x}{ \color{red}{-153} }& = & \frac{-1624}{-153} \\\Leftrightarrow & x = \frac{1624}{153} & & \\ & V = \left\{ \frac{1624}{153} \right\} & \\\end{align}\)
  5. \(\text{84 is het kleinste gemene veelvoud van 4, 7 en 3} \\ \begin{align} & \color{blue}{84.} (\frac{x}{4}-\frac{2}{7})& = & (\frac{4}{3}x+4) \color{blue}{.84} \\\Leftrightarrow & 21x-24& = & 112x+336 \\\Leftrightarrow & 21x \color{red}{-24} \color{blue}{+24} \color{blue}{-112x} & = & \color{red}{112x} +336 \color{blue}{-112x} \color{blue}{+24} \\\Leftrightarrow & -91x& = & 360 \\\Leftrightarrow & \frac{-91x}{ \color{red}{-91} }& = & \frac{360}{-91} \\\Leftrightarrow & x = \frac{-360}{91} & & \\ & V = \left\{ \frac{-360}{91} \right\} & \\\end{align}\)
  6. \(\text{210 is het kleinste gemene veelvoud van 6, 7 en 5} \\ \begin{align} & \color{blue}{210.} (\frac{x}{6}-\frac{3}{7})& = & (\frac{3}{5}x+3) \color{blue}{.210} \\\Leftrightarrow & 35x-90& = & 126x+630 \\\Leftrightarrow & 35x \color{red}{-90} \color{blue}{+90} \color{blue}{-126x} & = & \color{red}{126x} +630 \color{blue}{-126x} \color{blue}{+90} \\\Leftrightarrow & -91x& = & 720 \\\Leftrightarrow & \frac{-91x}{ \color{red}{-91} }& = & \frac{720}{-91} \\\Leftrightarrow & x = \frac{-720}{91} & & \\ & V = \left\{ \frac{-720}{91} \right\} & \\\end{align}\)
  7. \(\text{182 is het kleinste gemene veelvoud van 2, 13 en 7} \\ \begin{align} & \color{blue}{182.} (\frac{x}{2}-\frac{3}{13})& = & (\frac{2}{7}x-8) \color{blue}{.182} \\\Leftrightarrow & 91x-42& = & 52x-1456 \\\Leftrightarrow & 91x \color{red}{-42} \color{blue}{+42} \color{blue}{-52x} & = & \color{red}{52x} -1456 \color{blue}{-52x} \color{blue}{+42} \\\Leftrightarrow & 39x& = & -1414 \\\Leftrightarrow & \frac{39x}{ \color{red}{39} }& = & \frac{-1414}{39} \\\Leftrightarrow & x = \frac{-1414}{39} & & \\ & V = \left\{ \frac{-1414}{39} \right\} & \\\end{align}\)
  8. \(\text{63 is het kleinste gemene veelvoud van 7, 9 en 3} \\ \begin{align} & \color{blue}{63.} (\frac{x}{7}+\frac{2}{9})& = & (\frac{4}{3}x+3) \color{blue}{.63} \\\Leftrightarrow & 9x+14& = & 84x+189 \\\Leftrightarrow & 9x \color{red}{+14} \color{blue}{-14} \color{blue}{-84x} & = & \color{red}{84x} +189 \color{blue}{-84x} \color{blue}{-14} \\\Leftrightarrow & -75x& = & 175 \\\Leftrightarrow & \frac{-75x}{ \color{red}{-75} }& = & \frac{175}{-75} \\\Leftrightarrow & x = \frac{-7}{3} & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
  9. \(\text{40 is het kleinste gemene veelvoud van 5, 8 en 2} \\ \begin{align} & \color{blue}{40.} (\frac{x}{5}+\frac{3}{8})& = & (\frac{1}{2}x+7) \color{blue}{.40} \\\Leftrightarrow & 8x+15& = & 20x+280 \\\Leftrightarrow & 8x \color{red}{+15} \color{blue}{-15} \color{blue}{-20x} & = & \color{red}{20x} +280 \color{blue}{-20x} \color{blue}{-15} \\\Leftrightarrow & -12x& = & 265 \\\Leftrightarrow & \frac{-12x}{ \color{red}{-12} }& = & \frac{265}{-12} \\\Leftrightarrow & x = \frac{-265}{12} & & \\ & V = \left\{ \frac{-265}{12} \right\} & \\\end{align}\)
  10. \(\text{70 is het kleinste gemene veelvoud van 7, 10 en 2} \\ \begin{align} & \color{blue}{70.} (\frac{x}{7}-\frac{3}{10})& = & (\frac{5}{2}x-6) \color{blue}{.70} \\\Leftrightarrow & 10x-21& = & 175x-420 \\\Leftrightarrow & 10x \color{red}{-21} \color{blue}{+21} \color{blue}{-175x} & = & \color{red}{175x} -420 \color{blue}{-175x} \color{blue}{+21} \\\Leftrightarrow & -165x& = & -399 \\\Leftrightarrow & \frac{-165x}{ \color{red}{-165} }& = & \frac{-399}{-165} \\\Leftrightarrow & x = \frac{133}{55} & & \\ & V = \left\{ \frac{133}{55} \right\} & \\\end{align}\)
  11. \(\text{510 is het kleinste gemene veelvoud van 5, 17 en 6} \\ \begin{align} & \color{blue}{510.} (\frac{x}{5}+\frac{4}{17})& = & (\frac{5}{6}x+4) \color{blue}{.510} \\\Leftrightarrow & 102x+120& = & 425x+2040 \\\Leftrightarrow & 102x \color{red}{+120} \color{blue}{-120} \color{blue}{-425x} & = & \color{red}{425x} +2040 \color{blue}{-425x} \color{blue}{-120} \\\Leftrightarrow & -323x& = & 1920 \\\Leftrightarrow & \frac{-323x}{ \color{red}{-323} }& = & \frac{1920}{-323} \\\Leftrightarrow & x = \frac{-1920}{323} & & \\ & V = \left\{ \frac{-1920}{323} \right\} & \\\end{align}\)
  12. \(\text{357 is het kleinste gemene veelvoud van 3, 17 en 7} \\ \begin{align} & \color{blue}{357.} (\frac{x}{3}+\frac{4}{17})& = & (\frac{4}{7}x-4) \color{blue}{.357} \\\Leftrightarrow & 119x+84& = & 204x-1428 \\\Leftrightarrow & 119x \color{red}{+84} \color{blue}{-84} \color{blue}{-204x} & = & \color{red}{204x} -1428 \color{blue}{-204x} \color{blue}{-84} \\\Leftrightarrow & -85x& = & -1512 \\\Leftrightarrow & \frac{-85x}{ \color{red}{-85} }& = & \frac{-1512}{-85} \\\Leftrightarrow & x = \frac{1512}{85} & & \\ & V = \left\{ \frac{1512}{85} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-11-21 11:24:19