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. \(\frac{x}{2}+\frac{4}{13}=\frac{7}{3}x+8\)
  2. \(\frac{x}{6}-\frac{3}{13}=\frac{3}{5}x+6\)
  3. \(\frac{x}{7}+\frac{5}{17}=\frac{1}{2}x-3\)
  4. \(\frac{x}{6}+\frac{5}{16}=\frac{6}{7}x+3\)
  5. \(\frac{x}{7}-\frac{4}{13}=\frac{8}{5}x-4\)
  6. \(\frac{x}{3}-\frac{2}{15}=\frac{1}{4}x-1\)
  7. \(\frac{x}{7}+\frac{2}{7}=\frac{4}{5}x+4\)
  8. \(\frac{x}{4}+\frac{4}{17}=\frac{-2}{5}x-8\)
  9. \(\frac{x}{6}+\frac{2}{15}=\frac{2}{7}x-7\)
  10. \(\frac{x}{5}-\frac{4}{9}=\frac{1}{2}x-1\)
  11. \(\frac{x}{4}-\frac{5}{7}=\frac{-7}{5}x+1\)
  12. \(\frac{x}{3}-\frac{3}{7}=\frac{3}{7}x-1\)

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

Verbetersleutel

  1. \(\text{78 is het kleinste gemene veelvoud van 2, 13 en 3} \\ \begin{align} & \color{blue}{78.} (\frac{x}{2}+\frac{4}{13})& = & (\frac{7}{3}x+8) \color{blue}{.78} \\\Leftrightarrow & 39x+24& = & 182x+624 \\\Leftrightarrow & 39x \color{red}{+24} \color{blue}{-24} \color{blue}{-182x} & = & \color{red}{182x} +624 \color{blue}{-182x} \color{blue}{-24} \\\Leftrightarrow & -143x& = & 600 \\\Leftrightarrow & \frac{-143x}{ \color{red}{-143} }& = & \frac{600}{-143} \\\Leftrightarrow & x = \frac{-600}{143} & & \\\end{align}\)
  2. \(\text{390 is het kleinste gemene veelvoud van 6, 13 en 5} \\ \begin{align} & \color{blue}{390.} (\frac{x}{6}-\frac{3}{13})& = & (\frac{3}{5}x+6) \color{blue}{.390} \\\Leftrightarrow & 65x-90& = & 234x+2340 \\\Leftrightarrow & 65x \color{red}{-90} \color{blue}{+90} \color{blue}{-234x} & = & \color{red}{234x} +2340 \color{blue}{-234x} \color{blue}{+90} \\\Leftrightarrow & -169x& = & 2430 \\\Leftrightarrow & \frac{-169x}{ \color{red}{-169} }& = & \frac{2430}{-169} \\\Leftrightarrow & x = \frac{-2430}{169} & & \\\end{align}\)
  3. \(\text{238 is het kleinste gemene veelvoud van 7, 17 en 2} \\ \begin{align} & \color{blue}{238.} (\frac{x}{7}+\frac{5}{17})& = & (\frac{1}{2}x-3) \color{blue}{.238} \\\Leftrightarrow & 34x+70& = & 119x-714 \\\Leftrightarrow & 34x \color{red}{+70} \color{blue}{-70} \color{blue}{-119x} & = & \color{red}{119x} -714 \color{blue}{-119x} \color{blue}{-70} \\\Leftrightarrow & -85x& = & -784 \\\Leftrightarrow & \frac{-85x}{ \color{red}{-85} }& = & \frac{-784}{-85} \\\Leftrightarrow & x = \frac{784}{85} & & \\\end{align}\)
  4. \(\text{336 is het kleinste gemene veelvoud van 6, 16 en 7} \\ \begin{align} & \color{blue}{336.} (\frac{x}{6}+\frac{5}{16})& = & (\frac{6}{7}x+3) \color{blue}{.336} \\\Leftrightarrow & 56x+105& = & 288x+1008 \\\Leftrightarrow & 56x \color{red}{+105} \color{blue}{-105} \color{blue}{-288x} & = & \color{red}{288x} +1008 \color{blue}{-288x} \color{blue}{-105} \\\Leftrightarrow & -232x& = & 903 \\\Leftrightarrow & \frac{-232x}{ \color{red}{-232} }& = & \frac{903}{-232} \\\Leftrightarrow & x = \frac{-903}{232} & & \\\end{align}\)
  5. \(\text{455 is het kleinste gemene veelvoud van 7, 13 en 5} \\ \begin{align} & \color{blue}{455.} (\frac{x}{7}-\frac{4}{13})& = & (\frac{8}{5}x-4) \color{blue}{.455} \\\Leftrightarrow & 65x-140& = & 728x-1820 \\\Leftrightarrow & 65x \color{red}{-140} \color{blue}{+140} \color{blue}{-728x} & = & \color{red}{728x} -1820 \color{blue}{-728x} \color{blue}{+140} \\\Leftrightarrow & -663x& = & -1680 \\\Leftrightarrow & \frac{-663x}{ \color{red}{-663} }& = & \frac{-1680}{-663} \\\Leftrightarrow & x = \frac{560}{221} & & \\\end{align}\)
  6. \(\text{60 is het kleinste gemene veelvoud van 3, 15 en 4} \\ \begin{align} & \color{blue}{60.} (\frac{x}{3}-\frac{2}{15})& = & (\frac{1}{4}x-1) \color{blue}{.60} \\\Leftrightarrow & 20x-8& = & 15x-60 \\\Leftrightarrow & 20x \color{red}{-8} \color{blue}{+8} \color{blue}{-15x} & = & \color{red}{15x} -60 \color{blue}{-15x} \color{blue}{+8} \\\Leftrightarrow & 5x& = & -52 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = & \frac{-52}{5} \\\Leftrightarrow & x = \frac{-52}{5} & & \\\end{align}\)
  7. \(\text{35 is het kleinste gemene veelvoud van 7, 7 en 5} \\ \begin{align} & \color{blue}{35.} (\frac{x}{7}+\frac{2}{7})& = & (\frac{4}{5}x+4) \color{blue}{.35} \\\Leftrightarrow & 5x+10& = & 28x+140 \\\Leftrightarrow & 5x \color{red}{+10} \color{blue}{-10} \color{blue}{-28x} & = & \color{red}{28x} +140 \color{blue}{-28x} \color{blue}{-10} \\\Leftrightarrow & -23x& = & 130 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = & \frac{130}{-23} \\\Leftrightarrow & x = \frac{-130}{23} & & \\\end{align}\)
  8. \(\text{340 is het kleinste gemene veelvoud van 4, 17 en 5} \\ \begin{align} & \color{blue}{340.} (\frac{x}{4}+\frac{4}{17})& = & (\frac{-2}{5}x-8) \color{blue}{.340} \\\Leftrightarrow & 85x+80& = & -136x-2720 \\\Leftrightarrow & 85x \color{red}{+80} \color{blue}{-80} \color{blue}{+136x} & = & \color{red}{-136x} -2720 \color{blue}{+136x} \color{blue}{-80} \\\Leftrightarrow & 221x& = & -2800 \\\Leftrightarrow & \frac{221x}{ \color{red}{221} }& = & \frac{-2800}{221} \\\Leftrightarrow & x = \frac{-2800}{221} & & \\\end{align}\)
  9. \(\text{210 is het kleinste gemene veelvoud van 6, 15 en 7} \\ \begin{align} & \color{blue}{210.} (\frac{x}{6}+\frac{2}{15})& = & (\frac{2}{7}x-7) \color{blue}{.210} \\\Leftrightarrow & 35x+28& = & 60x-1470 \\\Leftrightarrow & 35x \color{red}{+28} \color{blue}{-28} \color{blue}{-60x} & = & \color{red}{60x} -1470 \color{blue}{-60x} \color{blue}{-28} \\\Leftrightarrow & -25x& = & -1498 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = & \frac{-1498}{-25} \\\Leftrightarrow & x = \frac{1498}{25} & & \\\end{align}\)
  10. \(\text{90 is het kleinste gemene veelvoud van 5, 9 en 2} \\ \begin{align} & \color{blue}{90.} (\frac{x}{5}-\frac{4}{9})& = & (\frac{1}{2}x-1) \color{blue}{.90} \\\Leftrightarrow & 18x-40& = & 45x-90 \\\Leftrightarrow & 18x \color{red}{-40} \color{blue}{+40} \color{blue}{-45x} & = & \color{red}{45x} -90 \color{blue}{-45x} \color{blue}{+40} \\\Leftrightarrow & -27x& = & -50 \\\Leftrightarrow & \frac{-27x}{ \color{red}{-27} }& = & \frac{-50}{-27} \\\Leftrightarrow & x = \frac{50}{27} & & \\\end{align}\)
  11. \(\text{140 is het kleinste gemene veelvoud van 4, 7 en 5} \\ \begin{align} & \color{blue}{140.} (\frac{x}{4}-\frac{5}{7})& = & (\frac{-7}{5}x+1) \color{blue}{.140} \\\Leftrightarrow & 35x-100& = & -196x+140 \\\Leftrightarrow & 35x \color{red}{-100} \color{blue}{+100} \color{blue}{+196x} & = & \color{red}{-196x} +140 \color{blue}{+196x} \color{blue}{+100} \\\Leftrightarrow & 231x& = & 240 \\\Leftrightarrow & \frac{231x}{ \color{red}{231} }& = & \frac{240}{231} \\\Leftrightarrow & x = \frac{80}{77} & & \\\end{align}\)
  12. \(\text{21 is het kleinste gemene veelvoud van 3, 7 en 7} \\ \begin{align} & \color{blue}{21.} (\frac{x}{3}-\frac{3}{7})& = & (\frac{3}{7}x-1) \color{blue}{.21} \\\Leftrightarrow & 7x-9& = & 9x-21 \\\Leftrightarrow & 7x \color{red}{-9} \color{blue}{+9} \color{blue}{-9x} & = & \color{red}{9x} -21 \color{blue}{-9x} \color{blue}{+9} \\\Leftrightarrow & -2x& = & -12 \\\Leftrightarrow & \frac{-2x}{ \color{red}{-2} }& = & \frac{-12}{-2} \\\Leftrightarrow & x = 6 & & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2021-12-02 01:43:31