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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{2}{5})& = & 5x+\frac{2}{7} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+84} & = & \color{red}{175x} +10 \\\Leftrightarrow & -420x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +10 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & -420x-175x& = & 10-84 \\\Leftrightarrow & \color{red}{-595} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{-595} & & \\\Leftrightarrow & x = \frac{74}{595} & & \\ & V = \left\{ \frac{74}{595} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{2}{11})& = & 7x+\frac{5}{2} \\\Leftrightarrow & 30x-\frac{12}{11}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{660}{ \color{blue}{22} }x- \frac{24}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 660x \color{red}{-24} & = & \color{red}{154x} +55 \\\Leftrightarrow & 660x \color{red}{-24} \color{blue}{+24} \color{blue}{-154x} & = & \color{red}{154x} +55 \color{blue}{-154x} \color{blue}{+24} \\\Leftrightarrow & 660x-154x& = & 55+24 \\\Leftrightarrow & \color{red}{506} x& = & 79 \\\Leftrightarrow & x = \frac{79}{506} & & \\ & V = \left\{ \frac{79}{506} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{4}{11})& = & -7x+\frac{5}{9} \\\Leftrightarrow & 12x-\frac{24}{11}& = & -7x+\frac{5}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1188}{ \color{blue}{99} }x- \frac{216}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{55}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1188x \color{red}{-216} & = & \color{red}{-693x} +55 \\\Leftrightarrow & 1188x \color{red}{-216} \color{blue}{+216} \color{blue}{+693x} & = & \color{red}{-693x} +55 \color{blue}{+693x} \color{blue}{+216} \\\Leftrightarrow & 1188x+693x& = & 55+216 \\\Leftrightarrow & \color{red}{1881} x& = & 271 \\\Leftrightarrow & x = \frac{271}{1881} & & \\ & V = \left\{ \frac{271}{1881} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{3})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -10x-\frac{10}{3}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x- \frac{50}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{-50} & = & \color{red}{-105x} +18 \\\Leftrightarrow & -150x \color{red}{-50} \color{blue}{+50} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{+50} \\\Leftrightarrow & -150x+105x& = & 18+50 \\\Leftrightarrow & \color{red}{-45} x& = & 68 \\\Leftrightarrow & x = \frac{68}{-45} & & \\\Leftrightarrow & x = \frac{-68}{45} & & \\ & V = \left\{ \frac{-68}{45} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{5}{9})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 8x+\frac{20}{9}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{360}{ \color{blue}{45} }x+ \frac{100}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 360x \color{red}{+100} & = & \color{red}{-225x} +54 \\\Leftrightarrow & 360x \color{red}{+100} \color{blue}{-100} \color{blue}{+225x} & = & \color{red}{-225x} +54 \color{blue}{+225x} \color{blue}{-100} \\\Leftrightarrow & 360x+225x& = & 54-100 \\\Leftrightarrow & \color{red}{585} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{585} & & \\ & V = \left\{ \frac{-46}{585} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{4}{5})& = & 5x+\frac{5}{8} \\\Leftrightarrow & 6x-\frac{12}{5}& = & 5x+\frac{5}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{240}{ \color{blue}{40} }x- \frac{96}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{25}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 240x \color{red}{-96} & = & \color{red}{200x} +25 \\\Leftrightarrow & 240x \color{red}{-96} \color{blue}{+96} \color{blue}{-200x} & = & \color{red}{200x} +25 \color{blue}{-200x} \color{blue}{+96} \\\Leftrightarrow & 240x-200x& = & 25+96 \\\Leftrightarrow & \color{red}{40} x& = & 121 \\\Leftrightarrow & x = \frac{121}{40} & & \\ & V = \left\{ \frac{121}{40} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{2}{7})& = & 7x+\frac{7}{2} \\\Leftrightarrow & 15x-\frac{10}{7}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{210}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 210x \color{red}{-20} & = & \color{red}{98x} +49 \\\Leftrightarrow & 210x \color{red}{-20} \color{blue}{+20} \color{blue}{-98x} & = & \color{red}{98x} +49 \color{blue}{-98x} \color{blue}{+20} \\\Leftrightarrow & 210x-98x& = & 49+20 \\\Leftrightarrow & \color{red}{112} x& = & 69 \\\Leftrightarrow & x = \frac{69}{112} & & \\ & V = \left\{ \frac{69}{112} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{5}{11})& = & -7x+\frac{3}{5} \\\Leftrightarrow & -24x-\frac{30}{11}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x- \frac{150}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{-150} & = & \color{red}{-385x} +33 \\\Leftrightarrow & -1320x \color{red}{-150} \color{blue}{+150} \color{blue}{+385x} & = & \color{red}{-385x} +33 \color{blue}{+385x} \color{blue}{+150} \\\Leftrightarrow & -1320x+385x& = & 33+150 \\\Leftrightarrow & \color{red}{-935} x& = & 183 \\\Leftrightarrow & x = \frac{183}{-935} & & \\\Leftrightarrow & x = \frac{-183}{935} & & \\ & V = \left\{ \frac{-183}{935} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{3}{5})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 24x-\frac{18}{5}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{360}{ \color{blue}{15} }x- \frac{54}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 360x \color{red}{-54} & = & \color{red}{-75x} +40 \\\Leftrightarrow & 360x \color{red}{-54} \color{blue}{+54} \color{blue}{+75x} & = & \color{red}{-75x} +40 \color{blue}{+75x} \color{blue}{+54} \\\Leftrightarrow & 360x+75x& = & 40+54 \\\Leftrightarrow & \color{red}{435} x& = & 94 \\\Leftrightarrow & x = \frac{94}{435} & & \\ & V = \left\{ \frac{94}{435} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{2}{7})& = & 9x+\frac{4}{5} \\\Leftrightarrow & 4x+\frac{4}{7}& = & 9x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{+20} & = & \color{red}{315x} +28 \\\Leftrightarrow & 140x \color{red}{+20} \color{blue}{-20} \color{blue}{-315x} & = & \color{red}{315x} +28 \color{blue}{-315x} \color{blue}{-20} \\\Leftrightarrow & 140x-315x& = & 28-20 \\\Leftrightarrow & \color{red}{-175} x& = & 8 \\\Leftrightarrow & x = \frac{8}{-175} & & \\\Leftrightarrow & x = \frac{-8}{175} & & \\ & V = \left\{ \frac{-8}{175} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{3}{8})& = & 3x+\frac{5}{12} \\\Leftrightarrow & -14x+\frac{21}{8}& = & 3x+\frac{5}{12} \\ & & & \text{kgv van noemers 8 en 12 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-336}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{72}{ \color{blue}{24} }x+ \frac{10}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -336x \color{red}{+63} & = & \color{red}{72x} +10 \\\Leftrightarrow & -336x \color{red}{+63} \color{blue}{-63} \color{blue}{-72x} & = & \color{red}{72x} +10 \color{blue}{-72x} \color{blue}{-63} \\\Leftrightarrow & -336x-72x& = & 10-63 \\\Leftrightarrow & \color{red}{-408} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-408} & & \\\Leftrightarrow & x = \frac{53}{408} & & \\ & V = \left\{ \frac{53}{408} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{2}{5})& = & 5x+\frac{7}{6} \\\Leftrightarrow & -24x+\frac{12}{5}& = & 5x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-720}{ \color{blue}{30} }x+ \frac{72}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -720x \color{red}{+72} & = & \color{red}{150x} +35 \\\Leftrightarrow & -720x \color{red}{+72} \color{blue}{-72} \color{blue}{-150x} & = & \color{red}{150x} +35 \color{blue}{-150x} \color{blue}{-72} \\\Leftrightarrow & -720x-150x& = & 35-72 \\\Leftrightarrow & \color{red}{-870} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-870} & & \\\Leftrightarrow & x = \frac{37}{870} & & \\ & V = \left\{ \frac{37}{870} \right\} & \\\end{align}\)
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