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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{2}{5})& = & -5x+\frac{10}{11} \\\Leftrightarrow & -24x+\frac{12}{5}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{+132} & = & \color{red}{-275x} +50 \\\Leftrightarrow & -1320x \color{red}{+132} \color{blue}{-132} \color{blue}{+275x} & = & \color{red}{-275x} +50 \color{blue}{+275x} \color{blue}{-132} \\\Leftrightarrow & -1320x+275x& = & 50-132 \\\Leftrightarrow & \color{red}{-1045} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-1045} & & \\\Leftrightarrow & x = \frac{82}{1045} & & \\ & V = \left\{ \frac{82}{1045} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{4}{3})& = & 5x+\frac{7}{8} \\\Leftrightarrow & 14x-\frac{28}{3}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{336}{ \color{blue}{24} }x- \frac{224}{ \color{blue}{24} })& = & (\frac{120}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 336x \color{red}{-224} & = & \color{red}{120x} +21 \\\Leftrightarrow & 336x \color{red}{-224} \color{blue}{+224} \color{blue}{-120x} & = & \color{red}{120x} +21 \color{blue}{-120x} \color{blue}{+224} \\\Leftrightarrow & 336x-120x& = & 21+224 \\\Leftrightarrow & \color{red}{216} x& = & 245 \\\Leftrightarrow & x = \frac{245}{216} & & \\ & V = \left\{ \frac{245}{216} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{5}{3})& = & 9x+\frac{6}{11} \\\Leftrightarrow & -8x-\frac{10}{3}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x- \frac{110}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{-110} & = & \color{red}{297x} +18 \\\Leftrightarrow & -264x \color{red}{-110} \color{blue}{+110} \color{blue}{-297x} & = & \color{red}{297x} +18 \color{blue}{-297x} \color{blue}{+110} \\\Leftrightarrow & -264x-297x& = & 18+110 \\\Leftrightarrow & \color{red}{-561} x& = & 128 \\\Leftrightarrow & x = \frac{128}{-561} & & \\\Leftrightarrow & x = \frac{-128}{561} & & \\ & V = \left\{ \frac{-128}{561} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{1}{2})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -28x-\frac{7}{2}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-280}{ \color{blue}{10} }x- \frac{35}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -280x \color{red}{-35} & = & \color{red}{90x} +12 \\\Leftrightarrow & -280x \color{red}{-35} \color{blue}{+35} \color{blue}{-90x} & = & \color{red}{90x} +12 \color{blue}{-90x} \color{blue}{+35} \\\Leftrightarrow & -280x-90x& = & 12+35 \\\Leftrightarrow & \color{red}{-370} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-370} & & \\\Leftrightarrow & x = \frac{-47}{370} & & \\ & V = \left\{ \frac{-47}{370} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{3}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -25x-\frac{15}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1375}{ \color{blue}{55} }x- \frac{75}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1375x \color{red}{-75} & = & \color{red}{-385x} +66 \\\Leftrightarrow & -1375x \color{red}{-75} \color{blue}{+75} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{+75} \\\Leftrightarrow & -1375x+385x& = & 66+75 \\\Leftrightarrow & \color{red}{-990} x& = & 141 \\\Leftrightarrow & x = \frac{141}{-990} & & \\\Leftrightarrow & x = \frac{-47}{330} & & \\ & V = \left\{ \frac{-47}{330} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{2}{7})& = & 5x+\frac{5}{8} \\\Leftrightarrow & -9x-\frac{6}{7}& = & 5x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-504}{ \color{blue}{56} }x- \frac{48}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -504x \color{red}{-48} & = & \color{red}{280x} +35 \\\Leftrightarrow & -504x \color{red}{-48} \color{blue}{+48} \color{blue}{-280x} & = & \color{red}{280x} +35 \color{blue}{-280x} \color{blue}{+48} \\\Leftrightarrow & -504x-280x& = & 35+48 \\\Leftrightarrow & \color{red}{-784} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-784} & & \\\Leftrightarrow & x = \frac{-83}{784} & & \\ & V = \left\{ \frac{-83}{784} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{5}{7})& = & -9x+\frac{9}{4} \\\Leftrightarrow & -8x-\frac{10}{7}& = & -9x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-224}{ \color{blue}{28} }x- \frac{40}{ \color{blue}{28} })& = & (\frac{-252}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -224x \color{red}{-40} & = & \color{red}{-252x} +63 \\\Leftrightarrow & -224x \color{red}{-40} \color{blue}{+40} \color{blue}{+252x} & = & \color{red}{-252x} +63 \color{blue}{+252x} \color{blue}{+40} \\\Leftrightarrow & -224x+252x& = & 63+40 \\\Leftrightarrow & \color{red}{28} x& = & 103 \\\Leftrightarrow & x = \frac{103}{28} & & \\ & V = \left\{ \frac{103}{28} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{2}{5})& = & 5x+\frac{3}{8} \\\Leftrightarrow & 24x+\frac{12}{5}& = & 5x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{960}{ \color{blue}{40} }x+ \frac{96}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 960x \color{red}{+96} & = & \color{red}{200x} +15 \\\Leftrightarrow & 960x \color{red}{+96} \color{blue}{-96} \color{blue}{-200x} & = & \color{red}{200x} +15 \color{blue}{-200x} \color{blue}{-96} \\\Leftrightarrow & 960x-200x& = & 15-96 \\\Leftrightarrow & \color{red}{760} x& = & -81 \\\Leftrightarrow & x = \frac{-81}{760} & & \\ & V = \left\{ \frac{-81}{760} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{2}{3})& = & -2x+\frac{8}{9} \\\Leftrightarrow & -28x-\frac{14}{3}& = & -2x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-252}{ \color{blue}{9} }x- \frac{42}{ \color{blue}{9} })& = & (\frac{-18}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -252x \color{red}{-42} & = & \color{red}{-18x} +8 \\\Leftrightarrow & -252x \color{red}{-42} \color{blue}{+42} \color{blue}{+18x} & = & \color{red}{-18x} +8 \color{blue}{+18x} \color{blue}{+42} \\\Leftrightarrow & -252x+18x& = & 8+42 \\\Leftrightarrow & \color{red}{-234} x& = & 50 \\\Leftrightarrow & x = \frac{50}{-234} & & \\\Leftrightarrow & x = \frac{-25}{117} & & \\ & V = \left\{ \frac{-25}{117} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{3}{8})& = & 4x+\frac{6}{5} \\\Leftrightarrow & -15x-\frac{15}{8}& = & 4x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-600}{ \color{blue}{40} }x- \frac{75}{ \color{blue}{40} })& = & (\frac{160}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -600x \color{red}{-75} & = & \color{red}{160x} +48 \\\Leftrightarrow & -600x \color{red}{-75} \color{blue}{+75} \color{blue}{-160x} & = & \color{red}{160x} +48 \color{blue}{-160x} \color{blue}{+75} \\\Leftrightarrow & -600x-160x& = & 48+75 \\\Leftrightarrow & \color{red}{-760} x& = & 123 \\\Leftrightarrow & x = \frac{123}{-760} & & \\\Leftrightarrow & x = \frac{-123}{760} & & \\ & V = \left\{ \frac{-123}{760} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{11})& = & -5x+\frac{3}{10} \\\Leftrightarrow & 6x+\frac{6}{11}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{660}{ \color{blue}{110} }x+ \frac{60}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 660x \color{red}{+60} & = & \color{red}{-550x} +33 \\\Leftrightarrow & 660x \color{red}{+60} \color{blue}{-60} \color{blue}{+550x} & = & \color{red}{-550x} +33 \color{blue}{+550x} \color{blue}{-60} \\\Leftrightarrow & 660x+550x& = & 33-60 \\\Leftrightarrow & \color{red}{1210} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{1210} & & \\ & V = \left\{ \frac{-27}{1210} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{3}{5})& = & 7x+\frac{8}{9} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{+108} & = & \color{red}{315x} +40 \\\Leftrightarrow & 540x \color{red}{+108} \color{blue}{-108} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{-108} \\\Leftrightarrow & 540x-315x& = & 40-108 \\\Leftrightarrow & \color{red}{225} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{225} & & \\ & V = \left\{ \frac{-68}{225} \right\} & \\\end{align}\)
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