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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{11})& = & -2x+\frac{3}{4} \\\Leftrightarrow & 15x+\frac{20}{11}& = & -2x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{660}{ \color{blue}{44} }x+ \frac{80}{ \color{blue}{44} })& = & (\frac{-88}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 660x \color{red}{+80} & = & \color{red}{-88x} +33 \\\Leftrightarrow & 660x \color{red}{+80} \color{blue}{-80} \color{blue}{+88x} & = & \color{red}{-88x} +33 \color{blue}{+88x} \color{blue}{-80} \\\Leftrightarrow & 660x+88x& = & 33-80 \\\Leftrightarrow & \color{red}{748} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{748} & & \\ & V = \left\{ \frac{-47}{748} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{7})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 12x-\frac{30}{7}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{-90} & = & \color{red}{-105x} +70 \\\Leftrightarrow & 252x \color{red}{-90} \color{blue}{+90} \color{blue}{+105x} & = & \color{red}{-105x} +70 \color{blue}{+105x} \color{blue}{+90} \\\Leftrightarrow & 252x+105x& = & 70+90 \\\Leftrightarrow & \color{red}{357} x& = & 160 \\\Leftrightarrow & x = \frac{160}{357} & & \\ & V = \left\{ \frac{160}{357} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{2}{7})& = & 7x+\frac{8}{7} \\\Leftrightarrow & 15x-\frac{10}{7}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{105}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 105x \color{red}{-10} & = & \color{red}{49x} +8 \\\Leftrightarrow & 105x \color{red}{-10} \color{blue}{+10} \color{blue}{-49x} & = & \color{red}{49x} +8 \color{blue}{-49x} \color{blue}{+10} \\\Leftrightarrow & 105x-49x& = & 8+10 \\\Leftrightarrow & \color{red}{56} x& = & 18 \\\Leftrightarrow & x = \frac{18}{56} & & \\\Leftrightarrow & x = \frac{9}{28} & & \\ & V = \left\{ \frac{9}{28} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{5}{6})& = & -8x+\frac{9}{11} \\\Leftrightarrow & -21x-\frac{35}{6}& = & -8x+\frac{9}{11} \\ & & & \text{kgv van noemers 6 en 11 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1386}{ \color{blue}{66} }x- \frac{385}{ \color{blue}{66} })& = & (\frac{-528}{ \color{blue}{66} }x+ \frac{54}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1386x \color{red}{-385} & = & \color{red}{-528x} +54 \\\Leftrightarrow & -1386x \color{red}{-385} \color{blue}{+385} \color{blue}{+528x} & = & \color{red}{-528x} +54 \color{blue}{+528x} \color{blue}{+385} \\\Leftrightarrow & -1386x+528x& = & 54+385 \\\Leftrightarrow & \color{red}{-858} x& = & 439 \\\Leftrightarrow & x = \frac{439}{-858} & & \\\Leftrightarrow & x = \frac{-439}{858} & & \\ & V = \left\{ \frac{-439}{858} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{11})& = & -9x+\frac{7}{4} \\\Leftrightarrow & -35x-\frac{35}{11}& = & -9x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1540}{ \color{blue}{44} }x- \frac{140}{ \color{blue}{44} })& = & (\frac{-396}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1540x \color{red}{-140} & = & \color{red}{-396x} +77 \\\Leftrightarrow & -1540x \color{red}{-140} \color{blue}{+140} \color{blue}{+396x} & = & \color{red}{-396x} +77 \color{blue}{+396x} \color{blue}{+140} \\\Leftrightarrow & -1540x+396x& = & 77+140 \\\Leftrightarrow & \color{red}{-1144} x& = & 217 \\\Leftrightarrow & x = \frac{217}{-1144} & & \\\Leftrightarrow & x = \frac{-217}{1144} & & \\ & V = \left\{ \frac{-217}{1144} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{4}{11})& = & 5x+\frac{3}{4} \\\Leftrightarrow & 18x-\frac{24}{11}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{792}{ \color{blue}{44} }x- \frac{96}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 792x \color{red}{-96} & = & \color{red}{220x} +33 \\\Leftrightarrow & 792x \color{red}{-96} \color{blue}{+96} \color{blue}{-220x} & = & \color{red}{220x} +33 \color{blue}{-220x} \color{blue}{+96} \\\Leftrightarrow & 792x-220x& = & 33+96 \\\Leftrightarrow & \color{red}{572} x& = & 129 \\\Leftrightarrow & x = \frac{129}{572} & & \\ & V = \left\{ \frac{129}{572} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{4}{3})& = & 8x+\frac{6}{5} \\\Leftrightarrow & -21x+\frac{28}{3}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-315}{ \color{blue}{15} }x+ \frac{140}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -315x \color{red}{+140} & = & \color{red}{120x} +18 \\\Leftrightarrow & -315x \color{red}{+140} \color{blue}{-140} \color{blue}{-120x} & = & \color{red}{120x} +18 \color{blue}{-120x} \color{blue}{-140} \\\Leftrightarrow & -315x-120x& = & 18-140 \\\Leftrightarrow & \color{red}{-435} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{-435} & & \\\Leftrightarrow & x = \frac{122}{435} & & \\ & V = \left\{ \frac{122}{435} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{5}{9})& = & 6x+\frac{5}{12} \\\Leftrightarrow & 25x+\frac{25}{9}& = & 6x+\frac{5}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{900}{ \color{blue}{36} }x+ \frac{100}{ \color{blue}{36} })& = & (\frac{216}{ \color{blue}{36} }x+ \frac{15}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 900x \color{red}{+100} & = & \color{red}{216x} +15 \\\Leftrightarrow & 900x \color{red}{+100} \color{blue}{-100} \color{blue}{-216x} & = & \color{red}{216x} +15 \color{blue}{-216x} \color{blue}{-100} \\\Leftrightarrow & 900x-216x& = & 15-100 \\\Leftrightarrow & \color{red}{684} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{684} & & \\ & V = \left\{ \frac{-85}{684} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{11})& = & -3x+\frac{7}{10} \\\Leftrightarrow & 20x+\frac{20}{11}& = & -3x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{2200}{ \color{blue}{110} }x+ \frac{200}{ \color{blue}{110} })& = & (\frac{-330}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 2200x \color{red}{+200} & = & \color{red}{-330x} +77 \\\Leftrightarrow & 2200x \color{red}{+200} \color{blue}{-200} \color{blue}{+330x} & = & \color{red}{-330x} +77 \color{blue}{+330x} \color{blue}{-200} \\\Leftrightarrow & 2200x+330x& = & 77-200 \\\Leftrightarrow & \color{red}{2530} x& = & -123 \\\Leftrightarrow & x = \frac{-123}{2530} & & \\ & V = \left\{ \frac{-123}{2530} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{5}{6})& = & 3x+\frac{5}{7} \\\Leftrightarrow & 25x-\frac{25}{6}& = & 3x+\frac{5}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{1050}{ \color{blue}{42} }x- \frac{175}{ \color{blue}{42} })& = & (\frac{126}{ \color{blue}{42} }x+ \frac{30}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 1050x \color{red}{-175} & = & \color{red}{126x} +30 \\\Leftrightarrow & 1050x \color{red}{-175} \color{blue}{+175} \color{blue}{-126x} & = & \color{red}{126x} +30 \color{blue}{-126x} \color{blue}{+175} \\\Leftrightarrow & 1050x-126x& = & 30+175 \\\Leftrightarrow & \color{red}{924} x& = & 205 \\\Leftrightarrow & x = \frac{205}{924} & & \\ & V = \left\{ \frac{205}{924} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{3}{11})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -4x-\frac{6}{11}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-132}{ \color{blue}{33} }x- \frac{18}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -132x \color{red}{-18} & = & \color{red}{165x} +22 \\\Leftrightarrow & -132x \color{red}{-18} \color{blue}{+18} \color{blue}{-165x} & = & \color{red}{165x} +22 \color{blue}{-165x} \color{blue}{+18} \\\Leftrightarrow & -132x-165x& = & 22+18 \\\Leftrightarrow & \color{red}{-297} x& = & 40 \\\Leftrightarrow & x = \frac{40}{-297} & & \\\Leftrightarrow & x = \frac{-40}{297} & & \\ & V = \left\{ \frac{-40}{297} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{5})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -12x+\frac{9}{5}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+99} & = & \color{red}{275x} +25 \\\Leftrightarrow & -660x \color{red}{+99} \color{blue}{-99} \color{blue}{-275x} & = & \color{red}{275x} +25 \color{blue}{-275x} \color{blue}{-99} \\\Leftrightarrow & -660x-275x& = & 25-99 \\\Leftrightarrow & \color{red}{-935} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{-935} & & \\\Leftrightarrow & x = \frac{74}{935} & & \\ & V = \left\{ \frac{74}{935} \right\} & \\\end{align}\)
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