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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{5})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -4x+\frac{6}{5}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-60}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -60x \color{red}{+18} & = & \color{red}{-135x} +10 \\\Leftrightarrow & -60x \color{red}{+18} \color{blue}{-18} \color{blue}{+135x} & = & \color{red}{-135x} +10 \color{blue}{+135x} \color{blue}{-18} \\\Leftrightarrow & -60x+135x& = & 10-18 \\\Leftrightarrow & \color{red}{75} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{75} & & \\ & V = \left\{ \frac{-8}{75} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{8})& = & -3x+\frac{10}{3} \\\Leftrightarrow & -14x-\frac{21}{8}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-336}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -336x \color{red}{-63} & = & \color{red}{-72x} +80 \\\Leftrightarrow & -336x \color{red}{-63} \color{blue}{+63} \color{blue}{+72x} & = & \color{red}{-72x} +80 \color{blue}{+72x} \color{blue}{+63} \\\Leftrightarrow & -336x+72x& = & 80+63 \\\Leftrightarrow & \color{red}{-264} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-264} & & \\\Leftrightarrow & x = \frac{-13}{24} & & \\ & V = \left\{ \frac{-13}{24} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{2}{5})& = & -5x+\frac{2}{7} \\\Leftrightarrow & 24x+\frac{12}{5}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{840}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 840x \color{red}{+84} & = & \color{red}{-175x} +10 \\\Leftrightarrow & 840x \color{red}{+84} \color{blue}{-84} \color{blue}{+175x} & = & \color{red}{-175x} +10 \color{blue}{+175x} \color{blue}{-84} \\\Leftrightarrow & 840x+175x& = & 10-84 \\\Leftrightarrow & \color{red}{1015} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{1015} & & \\ & V = \left\{ \frac{-74}{1015} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{3})& = & 3x+\frac{3}{7} \\\Leftrightarrow & 20x-\frac{20}{3}& = & 3x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{-140} & = & \color{red}{63x} +9 \\\Leftrightarrow & 420x \color{red}{-140} \color{blue}{+140} \color{blue}{-63x} & = & \color{red}{63x} +9 \color{blue}{-63x} \color{blue}{+140} \\\Leftrightarrow & 420x-63x& = & 9+140 \\\Leftrightarrow & \color{red}{357} x& = & 149 \\\Leftrightarrow & x = \frac{149}{357} & & \\ & V = \left\{ \frac{149}{357} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{4})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -20x-\frac{15}{4}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-880}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{40}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -880x \color{red}{-165} & = & \color{red}{308x} +40 \\\Leftrightarrow & -880x \color{red}{-165} \color{blue}{+165} \color{blue}{-308x} & = & \color{red}{308x} +40 \color{blue}{-308x} \color{blue}{+165} \\\Leftrightarrow & -880x-308x& = & 40+165 \\\Leftrightarrow & \color{red}{-1188} x& = & 205 \\\Leftrightarrow & x = \frac{205}{-1188} & & \\\Leftrightarrow & x = \frac{-205}{1188} & & \\ & V = \left\{ \frac{-205}{1188} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & -7x+\frac{9}{5} \\\Leftrightarrow & 15x+\frac{12}{5}& = & -7x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{75}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 75x \color{red}{+12} & = & \color{red}{-35x} +9 \\\Leftrightarrow & 75x \color{red}{+12} \color{blue}{-12} \color{blue}{+35x} & = & \color{red}{-35x} +9 \color{blue}{+35x} \color{blue}{-12} \\\Leftrightarrow & 75x+35x& = & 9-12 \\\Leftrightarrow & \color{red}{110} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{110} & & \\ & V = \left\{ \frac{-3}{110} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{2}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 20x-\frac{10}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{-30} & = & \color{red}{231x} +22 \\\Leftrightarrow & 660x \color{red}{-30} \color{blue}{+30} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{+30} \\\Leftrightarrow & 660x-231x& = & 22+30 \\\Leftrightarrow & \color{red}{429} x& = & 52 \\\Leftrightarrow & x = \frac{52}{429} & & \\\Leftrightarrow & x = \frac{4}{33} & & \\ & V = \left\{ \frac{4}{33} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{3}{4})& = & 8x+\frac{8}{11} \\\Leftrightarrow & 25x+\frac{15}{4}& = & 8x+\frac{8}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1100}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{352}{ \color{blue}{44} }x+ \frac{32}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1100x \color{red}{+165} & = & \color{red}{352x} +32 \\\Leftrightarrow & 1100x \color{red}{+165} \color{blue}{-165} \color{blue}{-352x} & = & \color{red}{352x} +32 \color{blue}{-352x} \color{blue}{-165} \\\Leftrightarrow & 1100x-352x& = & 32-165 \\\Leftrightarrow & \color{red}{748} x& = & -133 \\\Leftrightarrow & x = \frac{-133}{748} & & \\ & V = \left\{ \frac{-133}{748} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{2}{3})& = & -5x+\frac{3}{10} \\\Leftrightarrow & -12x-\frac{8}{3}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-360}{ \color{blue}{30} }x- \frac{80}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -360x \color{red}{-80} & = & \color{red}{-150x} +9 \\\Leftrightarrow & -360x \color{red}{-80} \color{blue}{+80} \color{blue}{+150x} & = & \color{red}{-150x} +9 \color{blue}{+150x} \color{blue}{+80} \\\Leftrightarrow & -360x+150x& = & 9+80 \\\Leftrightarrow & \color{red}{-210} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-210} & & \\\Leftrightarrow & x = \frac{-89}{210} & & \\ & V = \left\{ \frac{-89}{210} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{9})& = & -9x+\frac{9}{10} \\\Leftrightarrow & -20x-\frac{25}{9}& = & -9x+\frac{9}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-1800}{ \color{blue}{90} }x- \frac{250}{ \color{blue}{90} })& = & (\frac{-810}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -1800x \color{red}{-250} & = & \color{red}{-810x} +81 \\\Leftrightarrow & -1800x \color{red}{-250} \color{blue}{+250} \color{blue}{+810x} & = & \color{red}{-810x} +81 \color{blue}{+810x} \color{blue}{+250} \\\Leftrightarrow & -1800x+810x& = & 81+250 \\\Leftrightarrow & \color{red}{-990} x& = & 331 \\\Leftrightarrow & x = \frac{331}{-990} & & \\\Leftrightarrow & x = \frac{-331}{990} & & \\ & V = \left\{ \frac{-331}{990} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{3}{5})& = & -5x+\frac{9}{4} \\\Leftrightarrow & -12x-\frac{18}{5}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x- \frac{72}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{-72} & = & \color{red}{-100x} +45 \\\Leftrightarrow & -240x \color{red}{-72} \color{blue}{+72} \color{blue}{+100x} & = & \color{red}{-100x} +45 \color{blue}{+100x} \color{blue}{+72} \\\Leftrightarrow & -240x+100x& = & 45+72 \\\Leftrightarrow & \color{red}{-140} x& = & 117 \\\Leftrightarrow & x = \frac{117}{-140} & & \\\Leftrightarrow & x = \frac{-117}{140} & & \\ & V = \left\{ \frac{-117}{140} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{7})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -12x-\frac{30}{7}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{-30} & = & \color{red}{-35x} +10 \\\Leftrightarrow & -84x \color{red}{-30} \color{blue}{+30} \color{blue}{+35x} & = & \color{red}{-35x} +10 \color{blue}{+35x} \color{blue}{+30} \\\Leftrightarrow & -84x+35x& = & 10+30 \\\Leftrightarrow & \color{red}{-49} x& = & 40 \\\Leftrightarrow & x = \frac{40}{-49} & & \\\Leftrightarrow & x = \frac{-40}{49} & & \\ & V = \left\{ \frac{-40}{49} \right\} & \\\end{align}\)
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