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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{3}{2})& = & 5x+\frac{9}{7} \\\Leftrightarrow & 6x-\frac{9}{2}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{84}{ \color{blue}{14} }x- \frac{63}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{18}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 84x \color{red}{-63} & = & \color{red}{70x} +18 \\\Leftrightarrow & 84x \color{red}{-63} \color{blue}{+63} \color{blue}{-70x} & = & \color{red}{70x} +18 \color{blue}{-70x} \color{blue}{+63} \\\Leftrightarrow & 84x-70x& = & 18+63 \\\Leftrightarrow & \color{red}{14} x& = & 81 \\\Leftrightarrow & x = \frac{81}{14} & & \\ & V = \left\{ \frac{81}{14} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{7})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 12x-\frac{30}{7}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{-90} & = & \color{red}{-147x} +56 \\\Leftrightarrow & 252x \color{red}{-90} \color{blue}{+90} \color{blue}{+147x} & = & \color{red}{-147x} +56 \color{blue}{+147x} \color{blue}{+90} \\\Leftrightarrow & 252x+147x& = & 56+90 \\\Leftrightarrow & \color{red}{399} x& = & 146 \\\Leftrightarrow & x = \frac{146}{399} & & \\ & V = \left\{ \frac{146}{399} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{9})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 20x-\frac{20}{9}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1980}{ \color{blue}{99} }x- \frac{220}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1980x \color{red}{-220} & = & \color{red}{-693x} +54 \\\Leftrightarrow & 1980x \color{red}{-220} \color{blue}{+220} \color{blue}{+693x} & = & \color{red}{-693x} +54 \color{blue}{+693x} \color{blue}{+220} \\\Leftrightarrow & 1980x+693x& = & 54+220 \\\Leftrightarrow & \color{red}{2673} x& = & 274 \\\Leftrightarrow & x = \frac{274}{2673} & & \\ & V = \left\{ \frac{274}{2673} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{5}{7})& = & -8x+\frac{4}{9} \\\Leftrightarrow & -18x-\frac{30}{7}& = & -8x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1134}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{-504}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1134x \color{red}{-270} & = & \color{red}{-504x} +28 \\\Leftrightarrow & -1134x \color{red}{-270} \color{blue}{+270} \color{blue}{+504x} & = & \color{red}{-504x} +28 \color{blue}{+504x} \color{blue}{+270} \\\Leftrightarrow & -1134x+504x& = & 28+270 \\\Leftrightarrow & \color{red}{-630} x& = & 298 \\\Leftrightarrow & x = \frac{298}{-630} & & \\\Leftrightarrow & x = \frac{-149}{315} & & \\ & V = \left\{ \frac{-149}{315} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{5}{11})& = & 9x+\frac{5}{9} \\\Leftrightarrow & -18x+\frac{30}{11}& = & 9x+\frac{5}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1782}{ \color{blue}{99} }x+ \frac{270}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{55}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1782x \color{red}{+270} & = & \color{red}{891x} +55 \\\Leftrightarrow & -1782x \color{red}{+270} \color{blue}{-270} \color{blue}{-891x} & = & \color{red}{891x} +55 \color{blue}{-891x} \color{blue}{-270} \\\Leftrightarrow & -1782x-891x& = & 55-270 \\\Leftrightarrow & \color{red}{-2673} x& = & -215 \\\Leftrightarrow & x = \frac{-215}{-2673} & & \\\Leftrightarrow & x = \frac{215}{2673} & & \\ & V = \left\{ \frac{215}{2673} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{11})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -20x-\frac{16}{11}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{48}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-48} & = & \color{red}{231x} +88 \\\Leftrightarrow & -660x \color{red}{-48} \color{blue}{+48} \color{blue}{-231x} & = & \color{red}{231x} +88 \color{blue}{-231x} \color{blue}{+48} \\\Leftrightarrow & -660x-231x& = & 88+48 \\\Leftrightarrow & \color{red}{-891} x& = & 136 \\\Leftrightarrow & x = \frac{136}{-891} & & \\\Leftrightarrow & x = \frac{-136}{891} & & \\ & V = \left\{ \frac{-136}{891} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{2}{11})& = & -4x+\frac{5}{12} \\\Leftrightarrow & -18x-\frac{12}{11}& = & -4x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-2376}{ \color{blue}{132} }x- \frac{144}{ \color{blue}{132} })& = & (\frac{-528}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -2376x \color{red}{-144} & = & \color{red}{-528x} +55 \\\Leftrightarrow & -2376x \color{red}{-144} \color{blue}{+144} \color{blue}{+528x} & = & \color{red}{-528x} +55 \color{blue}{+528x} \color{blue}{+144} \\\Leftrightarrow & -2376x+528x& = & 55+144 \\\Leftrightarrow & \color{red}{-1848} x& = & 199 \\\Leftrightarrow & x = \frac{199}{-1848} & & \\\Leftrightarrow & x = \frac{-199}{1848} & & \\ & V = \left\{ \frac{-199}{1848} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{5})& = & -5x+\frac{8}{5} \\\Leftrightarrow & -12x+\frac{9}{5}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{+9} & = & \color{red}{-25x} +8 \\\Leftrightarrow & -60x \color{red}{+9} \color{blue}{-9} \color{blue}{+25x} & = & \color{red}{-25x} +8 \color{blue}{+25x} \color{blue}{-9} \\\Leftrightarrow & -60x+25x& = & 8-9 \\\Leftrightarrow & \color{red}{-35} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-35} & & \\\Leftrightarrow & x = \frac{1}{35} & & \\ & V = \left\{ \frac{1}{35} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{7})& = & 7x+\frac{4}{7} \\\Leftrightarrow & 18x+\frac{30}{7}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{126}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 126x \color{red}{+30} & = & \color{red}{49x} +4 \\\Leftrightarrow & 126x \color{red}{+30} \color{blue}{-30} \color{blue}{-49x} & = & \color{red}{49x} +4 \color{blue}{-49x} \color{blue}{-30} \\\Leftrightarrow & 126x-49x& = & 4-30 \\\Leftrightarrow & \color{red}{77} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{77} & & \\ & V = \left\{ \frac{-26}{77} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{5}{8})& = & 7x+\frac{7}{10} \\\Leftrightarrow & 12x+\frac{15}{8}& = & 7x+\frac{7}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{28}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{+75} & = & \color{red}{280x} +28 \\\Leftrightarrow & 480x \color{red}{+75} \color{blue}{-75} \color{blue}{-280x} & = & \color{red}{280x} +28 \color{blue}{-280x} \color{blue}{-75} \\\Leftrightarrow & 480x-280x& = & 28-75 \\\Leftrightarrow & \color{red}{200} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{200} & & \\ & V = \left\{ \frac{-47}{200} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{11})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -20x-\frac{25}{11}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{75}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-75} & = & \color{red}{231x} +44 \\\Leftrightarrow & -660x \color{red}{-75} \color{blue}{+75} \color{blue}{-231x} & = & \color{red}{231x} +44 \color{blue}{-231x} \color{blue}{+75} \\\Leftrightarrow & -660x-231x& = & 44+75 \\\Leftrightarrow & \color{red}{-891} x& = & 119 \\\Leftrightarrow & x = \frac{119}{-891} & & \\\Leftrightarrow & x = \frac{-119}{891} & & \\ & V = \left\{ \frac{-119}{891} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{3}{5})& = & -2x+\frac{6}{11} \\\Leftrightarrow & 21x-\frac{21}{5}& = & -2x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1155}{ \color{blue}{55} }x- \frac{231}{ \color{blue}{55} })& = & (\frac{-110}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1155x \color{red}{-231} & = & \color{red}{-110x} +30 \\\Leftrightarrow & 1155x \color{red}{-231} \color{blue}{+231} \color{blue}{+110x} & = & \color{red}{-110x} +30 \color{blue}{+110x} \color{blue}{+231} \\\Leftrightarrow & 1155x+110x& = & 30+231 \\\Leftrightarrow & \color{red}{1265} x& = & 261 \\\Leftrightarrow & x = \frac{261}{1265} & & \\ & V = \left\{ \frac{261}{1265} \right\} & \\\end{align}\)
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