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. \(\frac{x}{2}+\frac{2}{9}=\frac{-7}{5}x+1\)
  2. \(\frac{x}{4}-\frac{4}{9}=\frac{-4}{5}x+6\)
  3. \(\frac{x}{2}+\frac{2}{13}=\frac{4}{3}x-8\)
  4. \(\frac{x}{3}-\frac{3}{8}=\frac{1}{2}x-5\)
  5. \(\frac{x}{5}-\frac{2}{11}=\frac{7}{6}x+6\)
  6. \(\frac{x}{2}+\frac{4}{7}=\frac{-5}{3}x+2\)
  7. \(\frac{x}{2}+\frac{3}{16}=\frac{2}{5}x+7\)
  8. \(\frac{x}{6}+\frac{2}{7}=\frac{6}{7}x+5\)
  9. \(\frac{x}{4}-\frac{3}{13}=\frac{2}{3}x-5\)
  10. \(\frac{x}{3}+\frac{5}{17}=\frac{5}{2}x+3\)
  11. \(\frac{x}{3}-\frac{5}{6}=\frac{2}{5}x-5\)
  12. \(\frac{x}{5}-\frac{4}{11}=\frac{8}{7}x-5\)

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

Verbetersleutel

  1. \(\text{90 is het kleinste gemene veelvoud van 2, 9 en 5} \\ \begin{align} & \color{blue}{90.} (\frac{x}{2}+\frac{2}{9})& = & (\frac{-7}{5}x+1) \color{blue}{.90} \\\Leftrightarrow & 45x+20& = & -126x+90 \\\Leftrightarrow & 45x \color{red}{+20} \color{blue}{-20} \color{blue}{+126x} & = & \color{red}{-126x} +90 \color{blue}{+126x} \color{blue}{-20} \\\Leftrightarrow & 171x& = & 70 \\\Leftrightarrow & \frac{171x}{ \color{red}{171} }& = & \frac{70}{171} \\\Leftrightarrow & x = \frac{70}{171} & & \\ & V = \left\{ \frac{70}{171} \right\} & \\\end{align}\)
  2. \(\text{180 is het kleinste gemene veelvoud van 4, 9 en 5} \\ \begin{align} & \color{blue}{180.} (\frac{x}{4}-\frac{4}{9})& = & (\frac{-4}{5}x+6) \color{blue}{.180} \\\Leftrightarrow & 45x-80& = & -144x+1080 \\\Leftrightarrow & 45x \color{red}{-80} \color{blue}{+80} \color{blue}{+144x} & = & \color{red}{-144x} +1080 \color{blue}{+144x} \color{blue}{+80} \\\Leftrightarrow & 189x& = & 1160 \\\Leftrightarrow & \frac{189x}{ \color{red}{189} }& = & \frac{1160}{189} \\\Leftrightarrow & x = \frac{1160}{189} & & \\ & V = \left\{ \frac{1160}{189} \right\} & \\\end{align}\)
  3. \(\text{78 is het kleinste gemene veelvoud van 2, 13 en 3} \\ \begin{align} & \color{blue}{78.} (\frac{x}{2}+\frac{2}{13})& = & (\frac{4}{3}x-8) \color{blue}{.78} \\\Leftrightarrow & 39x+12& = & 104x-624 \\\Leftrightarrow & 39x \color{red}{+12} \color{blue}{-12} \color{blue}{-104x} & = & \color{red}{104x} -624 \color{blue}{-104x} \color{blue}{-12} \\\Leftrightarrow & -65x& = & -636 \\\Leftrightarrow & \frac{-65x}{ \color{red}{-65} }& = & \frac{-636}{-65} \\\Leftrightarrow & x = \frac{636}{65} & & \\ & V = \left\{ \frac{636}{65} \right\} & \\\end{align}\)
  4. \(\text{24 is het kleinste gemene veelvoud van 3, 8 en 2} \\ \begin{align} & \color{blue}{24.} (\frac{x}{3}-\frac{3}{8})& = & (\frac{1}{2}x-5) \color{blue}{.24} \\\Leftrightarrow & 8x-9& = & 12x-120 \\\Leftrightarrow & 8x \color{red}{-9} \color{blue}{+9} \color{blue}{-12x} & = & \color{red}{12x} -120 \color{blue}{-12x} \color{blue}{+9} \\\Leftrightarrow & -4x& = & -111 \\\Leftrightarrow & \frac{-4x}{ \color{red}{-4} }& = & \frac{-111}{-4} \\\Leftrightarrow & x = \frac{111}{4} & & \\ & V = \left\{ \frac{111}{4} \right\} & \\\end{align}\)
  5. \(\text{330 is het kleinste gemene veelvoud van 5, 11 en 6} \\ \begin{align} & \color{blue}{330.} (\frac{x}{5}-\frac{2}{11})& = & (\frac{7}{6}x+6) \color{blue}{.330} \\\Leftrightarrow & 66x-60& = & 385x+1980 \\\Leftrightarrow & 66x \color{red}{-60} \color{blue}{+60} \color{blue}{-385x} & = & \color{red}{385x} +1980 \color{blue}{-385x} \color{blue}{+60} \\\Leftrightarrow & -319x& = & 2040 \\\Leftrightarrow & \frac{-319x}{ \color{red}{-319} }& = & \frac{2040}{-319} \\\Leftrightarrow & x = \frac{-2040}{319} & & \\ & V = \left\{ \frac{-2040}{319} \right\} & \\\end{align}\)
  6. \(\text{42 is het kleinste gemene veelvoud van 2, 7 en 3} \\ \begin{align} & \color{blue}{42.} (\frac{x}{2}+\frac{4}{7})& = & (\frac{-5}{3}x+2) \color{blue}{.42} \\\Leftrightarrow & 21x+24& = & -70x+84 \\\Leftrightarrow & 21x \color{red}{+24} \color{blue}{-24} \color{blue}{+70x} & = & \color{red}{-70x} +84 \color{blue}{+70x} \color{blue}{-24} \\\Leftrightarrow & 91x& = & 60 \\\Leftrightarrow & \frac{91x}{ \color{red}{91} }& = & \frac{60}{91} \\\Leftrightarrow & x = \frac{60}{91} & & \\ & V = \left\{ \frac{60}{91} \right\} & \\\end{align}\)
  7. \(\text{80 is het kleinste gemene veelvoud van 2, 16 en 5} \\ \begin{align} & \color{blue}{80.} (\frac{x}{2}+\frac{3}{16})& = & (\frac{2}{5}x+7) \color{blue}{.80} \\\Leftrightarrow & 40x+15& = & 32x+560 \\\Leftrightarrow & 40x \color{red}{+15} \color{blue}{-15} \color{blue}{-32x} & = & \color{red}{32x} +560 \color{blue}{-32x} \color{blue}{-15} \\\Leftrightarrow & 8x& = & 545 \\\Leftrightarrow & \frac{8x}{ \color{red}{8} }& = & \frac{545}{8} \\\Leftrightarrow & x = \frac{545}{8} & & \\ & V = \left\{ \frac{545}{8} \right\} & \\\end{align}\)
  8. \(\text{42 is het kleinste gemene veelvoud van 6, 7 en 7} \\ \begin{align} & \color{blue}{42.} (\frac{x}{6}+\frac{2}{7})& = & (\frac{6}{7}x+5) \color{blue}{.42} \\\Leftrightarrow & 7x+12& = & 36x+210 \\\Leftrightarrow & 7x \color{red}{+12} \color{blue}{-12} \color{blue}{-36x} & = & \color{red}{36x} +210 \color{blue}{-36x} \color{blue}{-12} \\\Leftrightarrow & -29x& = & 198 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = & \frac{198}{-29} \\\Leftrightarrow & x = \frac{-198}{29} & & \\ & V = \left\{ \frac{-198}{29} \right\} & \\\end{align}\)
  9. \(\text{156 is het kleinste gemene veelvoud van 4, 13 en 3} \\ \begin{align} & \color{blue}{156.} (\frac{x}{4}-\frac{3}{13})& = & (\frac{2}{3}x-5) \color{blue}{.156} \\\Leftrightarrow & 39x-36& = & 104x-780 \\\Leftrightarrow & 39x \color{red}{-36} \color{blue}{+36} \color{blue}{-104x} & = & \color{red}{104x} -780 \color{blue}{-104x} \color{blue}{+36} \\\Leftrightarrow & -65x& = & -744 \\\Leftrightarrow & \frac{-65x}{ \color{red}{-65} }& = & \frac{-744}{-65} \\\Leftrightarrow & x = \frac{744}{65} & & \\ & V = \left\{ \frac{744}{65} \right\} & \\\end{align}\)
  10. \(\text{102 is het kleinste gemene veelvoud van 3, 17 en 2} \\ \begin{align} & \color{blue}{102.} (\frac{x}{3}+\frac{5}{17})& = & (\frac{5}{2}x+3) \color{blue}{.102} \\\Leftrightarrow & 34x+30& = & 255x+306 \\\Leftrightarrow & 34x \color{red}{+30} \color{blue}{-30} \color{blue}{-255x} & = & \color{red}{255x} +306 \color{blue}{-255x} \color{blue}{-30} \\\Leftrightarrow & -221x& = & 276 \\\Leftrightarrow & \frac{-221x}{ \color{red}{-221} }& = & \frac{276}{-221} \\\Leftrightarrow & x = \frac{-276}{221} & & \\ & V = \left\{ \frac{-276}{221} \right\} & \\\end{align}\)
  11. \(\text{30 is het kleinste gemene veelvoud van 3, 6 en 5} \\ \begin{align} & \color{blue}{30.} (\frac{x}{3}-\frac{5}{6})& = & (\frac{2}{5}x-5) \color{blue}{.30} \\\Leftrightarrow & 10x-25& = & 12x-150 \\\Leftrightarrow & 10x \color{red}{-25} \color{blue}{+25} \color{blue}{-12x} & = & \color{red}{12x} -150 \color{blue}{-12x} \color{blue}{+25} \\\Leftrightarrow & -2x& = & -125 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = & \frac{-125}{-2} \\\Leftrightarrow & x = \frac{125}{2} & & \\ & V = \left\{ \frac{125}{2} \right\} & \\\end{align}\)
  12. \(\text{385 is het kleinste gemene veelvoud van 5, 11 en 7} \\ \begin{align} & \color{blue}{385.} (\frac{x}{5}-\frac{4}{11})& = & (\frac{8}{7}x-5) \color{blue}{.385} \\\Leftrightarrow & 77x-140& = & 440x-1925 \\\Leftrightarrow & 77x \color{red}{-140} \color{blue}{+140} \color{blue}{-440x} & = & \color{red}{440x} -1925 \color{blue}{-440x} \color{blue}{+140} \\\Leftrightarrow & -363x& = & -1785 \\\Leftrightarrow & \frac{-363x}{ \color{red}{-363} }& = & \frac{-1785}{-363} \\\Leftrightarrow & x = \frac{595}{121} & & \\ & V = \left\{ \frac{595}{121} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-05-14 21:04:40