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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-} (5x+\frac{4}{11})& = & -7x+\frac{4}{11} \\\Leftrightarrow & -5x-\frac{4}{11}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(-5x-\frac{4}{11})& = & (-7x+\frac{4}{11}). \color{blue}{11} \\\Leftrightarrow & -55x \color{red}{-4} & = & \color{red}{-77x} +4 \\\Leftrightarrow & -55x \color{red}{-4} \color{blue}{+4} \color{blue}{+77x} & = & \color{red}{-77x} +4 \color{blue}{+77x} \color{blue}{+4} \\\Leftrightarrow & -55x+77x& = & 4+4 \\\Leftrightarrow & \color{red}{22} x& = & 8 \\\Leftrightarrow & x = \frac{8}{22} & & \\\Leftrightarrow & x = \frac{4}{11} & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{4}{7})& = & 7x+\frac{2}{9} \\\Leftrightarrow & -12x-\frac{12}{7}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(-12x-\frac{12}{7})& = & (7x+\frac{2}{9}). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{-108} & = & \color{red}{441x} +14 \\\Leftrightarrow & -756x \color{red}{-108} \color{blue}{+108} \color{blue}{-441x} & = & \color{red}{441x} +14 \color{blue}{-441x} \color{blue}{+108} \\\Leftrightarrow & -756x-441x& = & 14+108 \\\Leftrightarrow & \color{red}{-1197} x& = & 122 \\\Leftrightarrow & x = \frac{122}{-1197} & & \\\Leftrightarrow & x = \frac{-122}{1197} & & \\ & V = \left\{ \frac{-122}{1197} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{4}{5})& = & x+\frac{5}{12} \\\Leftrightarrow & -24x-\frac{24}{5}& = & x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(-24x-\frac{24}{5})& = & (x+\frac{5}{12}). \color{blue}{60} \\\Leftrightarrow & -1440x \color{red}{-288} & = & \color{red}{60x} +25 \\\Leftrightarrow & -1440x \color{red}{-288} \color{blue}{+288} \color{blue}{-60x} & = & \color{red}{60x} +25 \color{blue}{-60x} \color{blue}{+288} \\\Leftrightarrow & -1440x-60x& = & 25+288 \\\Leftrightarrow & \color{red}{-1500} x& = & 313 \\\Leftrightarrow & x = \frac{313}{-1500} & & \\\Leftrightarrow & x = \frac{-313}{1500} & & \\ & V = \left\{ \frac{-313}{1500} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (x+\frac{2}{7})& = & 2x+\frac{8}{5} \\\Leftrightarrow & -3x-\frac{6}{7}& = & 2x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(-3x-\frac{6}{7})& = & (2x+\frac{8}{5}). \color{blue}{35} \\\Leftrightarrow & -105x \color{red}{-30} & = & \color{red}{70x} +56 \\\Leftrightarrow & -105x \color{red}{-30} \color{blue}{+30} \color{blue}{-70x} & = & \color{red}{70x} +56 \color{blue}{-70x} \color{blue}{+30} \\\Leftrightarrow & -105x-70x& = & 56+30 \\\Leftrightarrow & \color{red}{-175} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-175} & & \\\Leftrightarrow & x = \frac{-86}{175} & & \\ & V = \left\{ \frac{-86}{175} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{4}{3})& = & -3x+\frac{5}{4} \\\Leftrightarrow & 16x-\frac{16}{3}& = & -3x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(16x-\frac{16}{3})& = & (-3x+\frac{5}{4}). \color{blue}{12} \\\Leftrightarrow & 192x \color{red}{-64} & = & \color{red}{-36x} +15 \\\Leftrightarrow & 192x \color{red}{-64} \color{blue}{+64} \color{blue}{+36x} & = & \color{red}{-36x} +15 \color{blue}{+36x} \color{blue}{+64} \\\Leftrightarrow & 192x+36x& = & 15+64 \\\Leftrightarrow & \color{red}{228} x& = & 79 \\\Leftrightarrow & x = \frac{79}{228} & & \\ & V = \left\{ \frac{79}{228} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-} (3x+\frac{3}{5})& = & -2x+\frac{9}{8} \\\Leftrightarrow & -3x-\frac{3}{5}& = & -2x+\frac{9}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(-3x-\frac{3}{5})& = & (-2x+\frac{9}{8}). \color{blue}{40} \\\Leftrightarrow & -120x \color{red}{-24} & = & \color{red}{-80x} +45 \\\Leftrightarrow & -120x \color{red}{-24} \color{blue}{+24} \color{blue}{+80x} & = & \color{red}{-80x} +45 \color{blue}{+80x} \color{blue}{+24} \\\Leftrightarrow & -120x+80x& = & 45+24 \\\Leftrightarrow & \color{red}{-40} x& = & 69 \\\Leftrightarrow & x = \frac{69}{-40} & & \\\Leftrightarrow & x = \frac{-69}{40} & & \\ & V = \left\{ \frac{-69}{40} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{3}{8})& = & -7x+\frac{3}{13} \\\Leftrightarrow & -25x-\frac{15}{8}& = & -7x+\frac{3}{13} \\ & & & \text{kgv van noemers 8 en 13 is 104} \\\Leftrightarrow & \color{blue}{104} .(-25x-\frac{15}{8})& = & (-7x+\frac{3}{13}). \color{blue}{104} \\\Leftrightarrow & -2600x \color{red}{-195} & = & \color{red}{-728x} +24 \\\Leftrightarrow & -2600x \color{red}{-195} \color{blue}{+195} \color{blue}{+728x} & = & \color{red}{-728x} +24 \color{blue}{+728x} \color{blue}{+195} \\\Leftrightarrow & -2600x+728x& = & 24+195 \\\Leftrightarrow & \color{red}{-1872} x& = & 219 \\\Leftrightarrow & x = \frac{219}{-1872} & & \\\Leftrightarrow & x = \frac{-73}{624} & & \\ & V = \left\{ \frac{-73}{624} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-x+\frac{3}{11})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 6x-\frac{18}{11}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(6x-\frac{18}{11})& = & (7x+\frac{4}{9}). \color{blue}{99} \\\Leftrightarrow & 594x \color{red}{-162} & = & \color{red}{693x} +44 \\\Leftrightarrow & 594x \color{red}{-162} \color{blue}{+162} \color{blue}{-693x} & = & \color{red}{693x} +44 \color{blue}{-693x} \color{blue}{+162} \\\Leftrightarrow & 594x-693x& = & 44+162 \\\Leftrightarrow & \color{red}{-99} x& = & 206 \\\Leftrightarrow & x = \frac{206}{-99} & & \\\Leftrightarrow & x = \frac{-206}{99} & & \\ & V = \left\{ \frac{-206}{99} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{3}{2})& = & 17x+\frac{10}{3} \\\Leftrightarrow & -18x-9& = & 17x+\frac{10}{3} \\ & & & \text{kgv van noemers 1 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(-18x-9)& = & (17x+\frac{10}{3}). \color{blue}{3} \\\Leftrightarrow & -54x \color{red}{-27} & = & \color{red}{51x} +10 \\\Leftrightarrow & -54x \color{red}{-27} \color{blue}{+27} \color{blue}{-51x} & = & \color{red}{51x} +10 \color{blue}{-51x} \color{blue}{+27} \\\Leftrightarrow & -54x-51x& = & 10+27 \\\Leftrightarrow & \color{red}{-105} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-105} & & \\\Leftrightarrow & x = \frac{-37}{105} & & \\ & V = \left\{ \frac{-37}{105} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (-3x-\frac{4}{15})& = & x+\frac{6}{7} \\\Leftrightarrow & -3x-\frac{4}{15}& = & x+\frac{6}{7} \\ & & & \text{kgv van noemers 15 en 7 is 105} \\\Leftrightarrow & \color{blue}{105} .(-3x-\frac{4}{15})& = & (x+\frac{6}{7}). \color{blue}{105} \\\Leftrightarrow & -315x \color{red}{-28} & = & \color{red}{105x} +90 \\\Leftrightarrow & -315x \color{red}{-28} \color{blue}{+28} \color{blue}{-105x} & = & \color{red}{105x} +90 \color{blue}{-105x} \color{blue}{+28} \\\Leftrightarrow & -315x-105x& = & 90+28 \\\Leftrightarrow & \color{red}{-420} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-420} & & \\\Leftrightarrow & x = \frac{-59}{210} & & \\ & V = \left\{ \frac{-59}{210} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{4}{13})& = & 3x+\frac{4}{5} \\\Leftrightarrow & -20x+\frac{20}{13}& = & 3x+\frac{4}{5} \\ & & & \text{kgv van noemers 13 en 5 is 65} \\\Leftrightarrow & \color{blue}{65} .(-20x+\frac{20}{13})& = & (3x+\frac{4}{5}). \color{blue}{65} \\\Leftrightarrow & -1300x \color{red}{+100} & = & \color{red}{195x} +52 \\\Leftrightarrow & -1300x \color{red}{+100} \color{blue}{-100} \color{blue}{-195x} & = & \color{red}{195x} +52 \color{blue}{-195x} \color{blue}{-100} \\\Leftrightarrow & -1300x-195x& = & 52-100 \\\Leftrightarrow & \color{red}{-1495} x& = & -48 \\\Leftrightarrow & x = \frac{-48}{-1495} & & \\\Leftrightarrow & x = \frac{48}{1495} & & \\ & V = \left\{ \frac{48}{1495} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{4}{9})& = & 3x+\frac{4}{3} \\\Leftrightarrow & -35x-\frac{28}{9}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(-35x-\frac{28}{9})& = & (3x+\frac{4}{3}). \color{blue}{9} \\\Leftrightarrow & -315x \color{red}{-28} & = & \color{red}{27x} +12 \\\Leftrightarrow & -315x \color{red}{-28} \color{blue}{+28} \color{blue}{-27x} & = & \color{red}{27x} +12 \color{blue}{-27x} \color{blue}{+28} \\\Leftrightarrow & -315x-27x& = & 12+28 \\\Leftrightarrow & \color{red}{-342} x& = & 40 \\\Leftrightarrow & x = \frac{40}{-342} & & \\\Leftrightarrow & x = \frac{-20}{171} & & \\ & V = \left\{ \frac{-20}{171} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-05-30 04:34:36