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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{2}{9})& = & 3x+\frac{5}{6} \\\Leftrightarrow & 10x+\frac{4}{9}& = & 3x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{180}{ \color{blue}{18} }x+ \frac{8}{ \color{blue}{18} })& = & (\frac{54}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 180x \color{red}{+8} & = & \color{red}{54x} +15 \\\Leftrightarrow & 180x \color{red}{+8} \color{blue}{-8} \color{blue}{-54x} & = & \color{red}{54x} +15 \color{blue}{-54x} \color{blue}{-8} \\\Leftrightarrow & 180x-54x& = & 15-8 \\\Leftrightarrow & \color{red}{126} x& = & 7 \\\Leftrightarrow & x = \frac{7}{126} & & \\\Leftrightarrow & x = \frac{1}{18} & & \\ & V = \left\{ \frac{1}{18} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{9})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -6x+\frac{10}{9}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{+110} & = & \color{red}{-693x} +45 \\\Leftrightarrow & -594x \color{red}{+110} \color{blue}{-110} \color{blue}{+693x} & = & \color{red}{-693x} +45 \color{blue}{+693x} \color{blue}{-110} \\\Leftrightarrow & -594x+693x& = & 45-110 \\\Leftrightarrow & \color{red}{99} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{99} & & \\ & V = \left\{ \frac{-65}{99} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{9})& = & -8x+\frac{9}{7} \\\Leftrightarrow & -28x-\frac{28}{9}& = & -8x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1764}{ \color{blue}{63} }x- \frac{196}{ \color{blue}{63} })& = & (\frac{-504}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1764x \color{red}{-196} & = & \color{red}{-504x} +81 \\\Leftrightarrow & -1764x \color{red}{-196} \color{blue}{+196} \color{blue}{+504x} & = & \color{red}{-504x} +81 \color{blue}{+504x} \color{blue}{+196} \\\Leftrightarrow & -1764x+504x& = & 81+196 \\\Leftrightarrow & \color{red}{-1260} x& = & 277 \\\Leftrightarrow & x = \frac{277}{-1260} & & \\\Leftrightarrow & x = \frac{-277}{1260} & & \\ & V = \left\{ \frac{-277}{1260} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{2}{11})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 10x+\frac{10}{11}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+70} & = & \color{red}{-539x} +110 \\\Leftrightarrow & 770x \color{red}{+70} \color{blue}{-70} \color{blue}{+539x} & = & \color{red}{-539x} +110 \color{blue}{+539x} \color{blue}{-70} \\\Leftrightarrow & 770x+539x& = & 110-70 \\\Leftrightarrow & \color{red}{1309} x& = & 40 \\\Leftrightarrow & x = \frac{40}{1309} & & \\ & V = \left\{ \frac{40}{1309} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{3}{5})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -12x-\frac{18}{5}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{54}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-54} & = & \color{red}{75x} +50 \\\Leftrightarrow & -180x \color{red}{-54} \color{blue}{+54} \color{blue}{-75x} & = & \color{red}{75x} +50 \color{blue}{-75x} \color{blue}{+54} \\\Leftrightarrow & -180x-75x& = & 50+54 \\\Leftrightarrow & \color{red}{-255} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-255} & & \\\Leftrightarrow & x = \frac{-104}{255} & & \\ & V = \left\{ \frac{-104}{255} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{8})& = & 7x+\frac{10}{9} \\\Leftrightarrow & -20x-\frac{15}{8}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1440}{ \color{blue}{72} }x- \frac{135}{ \color{blue}{72} })& = & (\frac{504}{ \color{blue}{72} }x+ \frac{80}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1440x \color{red}{-135} & = & \color{red}{504x} +80 \\\Leftrightarrow & -1440x \color{red}{-135} \color{blue}{+135} \color{blue}{-504x} & = & \color{red}{504x} +80 \color{blue}{-504x} \color{blue}{+135} \\\Leftrightarrow & -1440x-504x& = & 80+135 \\\Leftrightarrow & \color{red}{-1944} x& = & 215 \\\Leftrightarrow & x = \frac{215}{-1944} & & \\\Leftrightarrow & x = \frac{-215}{1944} & & \\ & V = \left\{ \frac{-215}{1944} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{4}{3})& = & 7x+\frac{2}{9} \\\Leftrightarrow & 8x+\frac{8}{3}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{+24} & = & \color{red}{63x} +2 \\\Leftrightarrow & 72x \color{red}{+24} \color{blue}{-24} \color{blue}{-63x} & = & \color{red}{63x} +2 \color{blue}{-63x} \color{blue}{-24} \\\Leftrightarrow & 72x-63x& = & 2-24 \\\Leftrightarrow & \color{red}{9} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{9} & & \\ & V = \left\{ \frac{-22}{9} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -10x+\frac{4}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{+20} & = & \color{red}{-385x} +66 \\\Leftrightarrow & -550x \color{red}{+20} \color{blue}{-20} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{-20} \\\Leftrightarrow & -550x+385x& = & 66-20 \\\Leftrightarrow & \color{red}{-165} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-165} & & \\\Leftrightarrow & x = \frac{-46}{165} & & \\ & V = \left\{ \frac{-46}{165} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{2}{5})& = & 5x+\frac{3}{2} \\\Leftrightarrow & -4x+\frac{4}{5}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-40}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -40x \color{red}{+8} & = & \color{red}{50x} +15 \\\Leftrightarrow & -40x \color{red}{+8} \color{blue}{-8} \color{blue}{-50x} & = & \color{red}{50x} +15 \color{blue}{-50x} \color{blue}{-8} \\\Leftrightarrow & -40x-50x& = & 15-8 \\\Leftrightarrow & \color{red}{-90} x& = & 7 \\\Leftrightarrow & x = \frac{7}{-90} & & \\\Leftrightarrow & x = \frac{-7}{90} & & \\ & V = \left\{ \frac{-7}{90} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{2}{5})& = & 3x+\frac{10}{3} \\\Leftrightarrow & -18x-\frac{12}{5}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-270}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -270x \color{red}{-36} & = & \color{red}{45x} +50 \\\Leftrightarrow & -270x \color{red}{-36} \color{blue}{+36} \color{blue}{-45x} & = & \color{red}{45x} +50 \color{blue}{-45x} \color{blue}{+36} \\\Leftrightarrow & -270x-45x& = & 50+36 \\\Leftrightarrow & \color{red}{-315} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-315} & & \\\Leftrightarrow & x = \frac{-86}{315} & & \\ & V = \left\{ \frac{-86}{315} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{2}{5})& = & -3x+\frac{5}{6} \\\Leftrightarrow & -14x+\frac{14}{5}& = & -3x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-420}{ \color{blue}{30} }x+ \frac{84}{ \color{blue}{30} })& = & (\frac{-90}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -420x \color{red}{+84} & = & \color{red}{-90x} +25 \\\Leftrightarrow & -420x \color{red}{+84} \color{blue}{-84} \color{blue}{+90x} & = & \color{red}{-90x} +25 \color{blue}{+90x} \color{blue}{-84} \\\Leftrightarrow & -420x+90x& = & 25-84 \\\Leftrightarrow & \color{red}{-330} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{-330} & & \\\Leftrightarrow & x = \frac{59}{330} & & \\ & V = \left\{ \frac{59}{330} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{11})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 24x+\frac{24}{11}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{792}{ \color{blue}{33} }x+ \frac{72}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{+72} & = & \color{red}{-165x} +44 \\\Leftrightarrow & 792x \color{red}{+72} \color{blue}{-72} \color{blue}{+165x} & = & \color{red}{-165x} +44 \color{blue}{+165x} \color{blue}{-72} \\\Leftrightarrow & 792x+165x& = & 44-72 \\\Leftrightarrow & \color{red}{957} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{957} & & \\ & V = \left\{ \frac{-28}{957} \right\} & \\\end{align}\)
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