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Alles samen. Gebruik stappenplan en ZRM!

  1. \(2(-4x-\frac{2}{7})=3x+\frac{5}{6}\)
  2. \(4(5x-\frac{2}{13})=7x+\frac{8}{7}\)
  3. \(-4(3x+\frac{4}{7})=5x+\frac{10}{9}\)
  4. \((x-\frac{2}{5})=3x+\frac{2}{11}\)
  5. \(-2(3x+\frac{3}{8})=x+\frac{9}{14}\)
  6. \(-7(x-\frac{2}{7})=-10x+\frac{2}{15}\)
  7. \(-2(-4x+\frac{3}{8})=5x+\frac{8}{11}\)
  8. \(-6(-2x-\frac{2}{11})=5x+\frac{3}{10}\)
  9. \((-4x+\frac{3}{5})=x+\frac{5}{12}\)
  10. \(-(5x+\frac{3}{2})=-9x+\frac{3}{10}\)
  11. \(5(5x-\frac{5}{11})=-9x+\frac{2}{9}\)
  12. \(-7(-5x-\frac{5}{2})=-8x+\frac{2}{5}\)

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{2}{7})& = & 3x+\frac{5}{6} \\\Leftrightarrow & -8x-\frac{4}{7}& = & 3x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(-8x-\frac{4}{7})& = & (3x+\frac{5}{6}). \color{blue}{42} \\\Leftrightarrow & -336x \color{red}{-24} & = & \color{red}{126x} +35 \\\Leftrightarrow & -336x \color{red}{-24} \color{blue}{+24} \color{blue}{-126x} & = & \color{red}{126x} +35 \color{blue}{-126x} \color{blue}{+24} \\\Leftrightarrow & -336x-126x& = & 35+24 \\\Leftrightarrow & \color{red}{-462} x& = & 59 \\\Leftrightarrow & x = \frac{59}{-462} & & \\\Leftrightarrow & x = \frac{-59}{462} & & \\ & V = \left\{ \frac{-59}{462} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{2}{13})& = & 7x+\frac{8}{7} \\\Leftrightarrow & 20x-\frac{8}{13}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 13 en 7 is 91} \\\Leftrightarrow & \color{blue}{91} .(20x-\frac{8}{13})& = & (7x+\frac{8}{7}). \color{blue}{91} \\\Leftrightarrow & 1820x \color{red}{-56} & = & \color{red}{637x} +104 \\\Leftrightarrow & 1820x \color{red}{-56} \color{blue}{+56} \color{blue}{-637x} & = & \color{red}{637x} +104 \color{blue}{-637x} \color{blue}{+56} \\\Leftrightarrow & 1820x-637x& = & 104+56 \\\Leftrightarrow & \color{red}{1183} x& = & 160 \\\Leftrightarrow & x = \frac{160}{1183} & & \\ & V = \left\{ \frac{160}{1183} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{4}{7})& = & 5x+\frac{10}{9} \\\Leftrightarrow & -12x-\frac{16}{7}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(-12x-\frac{16}{7})& = & (5x+\frac{10}{9}). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{-144} & = & \color{red}{315x} +70 \\\Leftrightarrow & -756x \color{red}{-144} \color{blue}{+144} \color{blue}{-315x} & = & \color{red}{315x} +70 \color{blue}{-315x} \color{blue}{+144} \\\Leftrightarrow & -756x-315x& = & 70+144 \\\Leftrightarrow & \color{red}{-1071} x& = & 214 \\\Leftrightarrow & x = \frac{214}{-1071} & & \\\Leftrightarrow & x = \frac{-214}{1071} & & \\ & V = \left\{ \frac{-214}{1071} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (x-\frac{2}{5})& = & 3x+\frac{2}{11} \\\Leftrightarrow & x-\frac{2}{5}& = & 3x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(x-\frac{2}{5})& = & (3x+\frac{2}{11}). \color{blue}{55} \\\Leftrightarrow & 55x \color{red}{-22} & = & \color{red}{165x} +10 \\\Leftrightarrow & 55x \color{red}{-22} \color{blue}{+22} \color{blue}{-165x} & = & \color{red}{165x} +10 \color{blue}{-165x} \color{blue}{+22} \\\Leftrightarrow & 55x-165x& = & 10+22 \\\Leftrightarrow & \color{red}{-110} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-110} & & \\\Leftrightarrow & x = \frac{-16}{55} & & \\ & V = \left\{ \frac{-16}{55} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{3}{8})& = & x+\frac{9}{14} \\\Leftrightarrow & -6x-\frac{3}{4}& = & x+\frac{9}{14} \\ & & & \text{kgv van noemers 4 en 14 is 28} \\\Leftrightarrow & \color{blue}{28} .(-6x-\frac{3}{4})& = & (x+\frac{9}{14}). \color{blue}{28} \\\Leftrightarrow & -168x \color{red}{-21} & = & \color{red}{28x} +18 \\\Leftrightarrow & -168x \color{red}{-21} \color{blue}{+21} \color{blue}{-28x} & = & \color{red}{28x} +18 \color{blue}{-28x} \color{blue}{+21} \\\Leftrightarrow & -168x-28x& = & 18+21 \\\Leftrightarrow & \color{red}{-196} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-196} & & \\\Leftrightarrow & x = \frac{-39}{196} & & \\ & V = \left\{ \frac{-39}{196} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (x-\frac{2}{7})& = & -10x+\frac{2}{15} \\\Leftrightarrow & -7x+2& = & -10x+\frac{2}{15} \\ & & & \text{kgv van noemers 1 en 15 is 15} \\\Leftrightarrow & \color{blue}{15} .(-7x+2)& = & (-10x+\frac{2}{15}). \color{blue}{15} \\\Leftrightarrow & -105x \color{red}{+30} & = & \color{red}{-150x} +2 \\\Leftrightarrow & -105x \color{red}{+30} \color{blue}{-30} \color{blue}{+150x} & = & \color{red}{-150x} +2 \color{blue}{+150x} \color{blue}{-30} \\\Leftrightarrow & -105x+150x& = & 2-30 \\\Leftrightarrow & \color{red}{45} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{45} & & \\ & V = \left\{ \frac{-28}{45} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{3}{8})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 8x-\frac{3}{4}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(8x-\frac{3}{4})& = & (5x+\frac{8}{11}). \color{blue}{44} \\\Leftrightarrow & 352x \color{red}{-33} & = & \color{red}{220x} +32 \\\Leftrightarrow & 352x \color{red}{-33} \color{blue}{+33} \color{blue}{-220x} & = & \color{red}{220x} +32 \color{blue}{-220x} \color{blue}{+33} \\\Leftrightarrow & 352x-220x& = & 32+33 \\\Leftrightarrow & \color{red}{132} x& = & 65 \\\Leftrightarrow & x = \frac{65}{132} & & \\ & V = \left\{ \frac{65}{132} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{2}{11})& = & 5x+\frac{3}{10} \\\Leftrightarrow & 12x+\frac{12}{11}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(12x+\frac{12}{11})& = & (5x+\frac{3}{10}). \color{blue}{110} \\\Leftrightarrow & 1320x \color{red}{+120} & = & \color{red}{550x} +33 \\\Leftrightarrow & 1320x \color{red}{+120} \color{blue}{-120} \color{blue}{-550x} & = & \color{red}{550x} +33 \color{blue}{-550x} \color{blue}{-120} \\\Leftrightarrow & 1320x-550x& = & 33-120 \\\Leftrightarrow & \color{red}{770} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{770} & & \\ & V = \left\{ \frac{-87}{770} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (-4x+\frac{3}{5})& = & x+\frac{5}{12} \\\Leftrightarrow & -4x+\frac{3}{5}& = & x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(-4x+\frac{3}{5})& = & (x+\frac{5}{12}). \color{blue}{60} \\\Leftrightarrow & -240x \color{red}{+36} & = & \color{red}{60x} +25 \\\Leftrightarrow & -240x \color{red}{+36} \color{blue}{-36} \color{blue}{-60x} & = & \color{red}{60x} +25 \color{blue}{-60x} \color{blue}{-36} \\\Leftrightarrow & -240x-60x& = & 25-36 \\\Leftrightarrow & \color{red}{-300} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-300} & & \\\Leftrightarrow & x = \frac{11}{300} & & \\ & V = \left\{ \frac{11}{300} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-} (5x+\frac{3}{2})& = & -9x+\frac{3}{10} \\\Leftrightarrow & -5x-\frac{3}{2}& = & -9x+\frac{3}{10} \\ & & & \text{kgv van noemers 2 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(-5x-\frac{3}{2})& = & (-9x+\frac{3}{10}). \color{blue}{10} \\\Leftrightarrow & -50x \color{red}{-15} & = & \color{red}{-90x} +3 \\\Leftrightarrow & -50x \color{red}{-15} \color{blue}{+15} \color{blue}{+90x} & = & \color{red}{-90x} +3 \color{blue}{+90x} \color{blue}{+15} \\\Leftrightarrow & -50x+90x& = & 3+15 \\\Leftrightarrow & \color{red}{40} x& = & 18 \\\Leftrightarrow & x = \frac{18}{40} & & \\\Leftrightarrow & x = \frac{9}{20} & & \\ & V = \left\{ \frac{9}{20} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{5}{11})& = & -9x+\frac{2}{9} \\\Leftrightarrow & 25x-\frac{25}{11}& = & -9x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(25x-\frac{25}{11})& = & (-9x+\frac{2}{9}). \color{blue}{99} \\\Leftrightarrow & 2475x \color{red}{-225} & = & \color{red}{-891x} +22 \\\Leftrightarrow & 2475x \color{red}{-225} \color{blue}{+225} \color{blue}{+891x} & = & \color{red}{-891x} +22 \color{blue}{+891x} \color{blue}{+225} \\\Leftrightarrow & 2475x+891x& = & 22+225 \\\Leftrightarrow & \color{red}{3366} x& = & 247 \\\Leftrightarrow & x = \frac{247}{3366} & & \\ & V = \left\{ \frac{247}{3366} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{5}{2})& = & -8x+\frac{2}{5} \\\Leftrightarrow & 35x+\frac{35}{2}& = & -8x+\frac{2}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(35x+\frac{35}{2})& = & (-8x+\frac{2}{5}). \color{blue}{10} \\\Leftrightarrow & 350x \color{red}{+175} & = & \color{red}{-80x} +4 \\\Leftrightarrow & 350x \color{red}{+175} \color{blue}{-175} \color{blue}{+80x} & = & \color{red}{-80x} +4 \color{blue}{+80x} \color{blue}{-175} \\\Leftrightarrow & 350x+80x& = & 4-175 \\\Leftrightarrow & \color{red}{430} x& = & -171 \\\Leftrightarrow & x = \frac{-171}{430} & & \\ & V = \left\{ \frac{-171}{430} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2026-03-07 03:53:54