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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{5}{4})& = & -4x+\frac{4}{3} \\\Leftrightarrow & -28x-\frac{35}{4}& = & -4x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-336}{ \color{blue}{12} }x- \frac{105}{ \color{blue}{12} })& = & (\frac{-48}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -336x \color{red}{-105} & = & \color{red}{-48x} +16 \\\Leftrightarrow & -336x \color{red}{-105} \color{blue}{+105} \color{blue}{+48x} & = & \color{red}{-48x} +16 \color{blue}{+48x} \color{blue}{+105} \\\Leftrightarrow & -336x+48x& = & 16+105 \\\Leftrightarrow & \color{red}{-288} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-288} & & \\\Leftrightarrow & x = \frac{-121}{288} & & \\ & V = \left\{ \frac{-121}{288} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{5}{6})& = & -7x+\frac{3}{10} \\\Leftrightarrow & -10x-\frac{25}{6}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 6 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-300}{ \color{blue}{30} }x- \frac{125}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -300x \color{red}{-125} & = & \color{red}{-210x} +9 \\\Leftrightarrow & -300x \color{red}{-125} \color{blue}{+125} \color{blue}{+210x} & = & \color{red}{-210x} +9 \color{blue}{+210x} \color{blue}{+125} \\\Leftrightarrow & -300x+210x& = & 9+125 \\\Leftrightarrow & \color{red}{-90} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-90} & & \\\Leftrightarrow & x = \frac{-67}{45} & & \\ & V = \left\{ \frac{-67}{45} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{3}{2})& = & 7x+\frac{2}{7} \\\Leftrightarrow & 15x+\frac{15}{2}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{210}{ \color{blue}{14} }x+ \frac{105}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{4}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 210x \color{red}{+105} & = & \color{red}{98x} +4 \\\Leftrightarrow & 210x \color{red}{+105} \color{blue}{-105} \color{blue}{-98x} & = & \color{red}{98x} +4 \color{blue}{-98x} \color{blue}{-105} \\\Leftrightarrow & 210x-98x& = & 4-105 \\\Leftrightarrow & \color{red}{112} x& = & -101 \\\Leftrightarrow & x = \frac{-101}{112} & & \\ & V = \left\{ \frac{-101}{112} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{3}{5})& = & 7x+\frac{4}{5} \\\Leftrightarrow & 8x+\frac{6}{5}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{40}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 40x \color{red}{+6} & = & \color{red}{35x} +4 \\\Leftrightarrow & 40x \color{red}{+6} \color{blue}{-6} \color{blue}{-35x} & = & \color{red}{35x} +4 \color{blue}{-35x} \color{blue}{-6} \\\Leftrightarrow & 40x-35x& = & 4-6 \\\Leftrightarrow & \color{red}{5} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{5} & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{4}{9})& = & 7x+\frac{5}{2} \\\Leftrightarrow & 8x+\frac{16}{9}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{144}{ \color{blue}{18} }x+ \frac{32}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 144x \color{red}{+32} & = & \color{red}{126x} +45 \\\Leftrightarrow & 144x \color{red}{+32} \color{blue}{-32} \color{blue}{-126x} & = & \color{red}{126x} +45 \color{blue}{-126x} \color{blue}{-32} \\\Leftrightarrow & 144x-126x& = & 45-32 \\\Leftrightarrow & \color{red}{18} x& = & 13 \\\Leftrightarrow & x = \frac{13}{18} & & \\ & V = \left\{ \frac{13}{18} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{9})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 20x+\frac{8}{9}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{360}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 360x \color{red}{+16} & = & \color{red}{-126x} +81 \\\Leftrightarrow & 360x \color{red}{+16} \color{blue}{-16} \color{blue}{+126x} & = & \color{red}{-126x} +81 \color{blue}{+126x} \color{blue}{-16} \\\Leftrightarrow & 360x+126x& = & 81-16 \\\Leftrightarrow & \color{red}{486} x& = & 65 \\\Leftrightarrow & x = \frac{65}{486} & & \\ & V = \left\{ \frac{65}{486} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{5}{12})& = & 6x+\frac{2}{3} \\\Leftrightarrow & -25x-\frac{25}{12}& = & 6x+\frac{2}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-300}{ \color{blue}{12} }x- \frac{25}{ \color{blue}{12} })& = & (\frac{72}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -300x \color{red}{-25} & = & \color{red}{72x} +8 \\\Leftrightarrow & -300x \color{red}{-25} \color{blue}{+25} \color{blue}{-72x} & = & \color{red}{72x} +8 \color{blue}{-72x} \color{blue}{+25} \\\Leftrightarrow & -300x-72x& = & 8+25 \\\Leftrightarrow & \color{red}{-372} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-372} & & \\\Leftrightarrow & x = \frac{-11}{124} & & \\ & V = \left\{ \frac{-11}{124} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{3}{5})& = & -5x+\frac{6}{7} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+84} & = & \color{red}{-175x} +30 \\\Leftrightarrow & -420x \color{red}{+84} \color{blue}{-84} \color{blue}{+175x} & = & \color{red}{-175x} +30 \color{blue}{+175x} \color{blue}{-84} \\\Leftrightarrow & -420x+175x& = & 30-84 \\\Leftrightarrow & \color{red}{-245} x& = & -54 \\\Leftrightarrow & x = \frac{-54}{-245} & & \\\Leftrightarrow & x = \frac{54}{245} & & \\ & V = \left\{ \frac{54}{245} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{10})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -12x+\frac{9}{10}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1320}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{50}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1320x \color{red}{+99} & = & \color{red}{550x} +50 \\\Leftrightarrow & -1320x \color{red}{+99} \color{blue}{-99} \color{blue}{-550x} & = & \color{red}{550x} +50 \color{blue}{-550x} \color{blue}{-99} \\\Leftrightarrow & -1320x-550x& = & 50-99 \\\Leftrightarrow & \color{red}{-1870} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{-1870} & & \\\Leftrightarrow & x = \frac{49}{1870} & & \\ & V = \left\{ \frac{49}{1870} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{3}{2})& = & 3x+\frac{10}{3} \\\Leftrightarrow & -14x+\frac{21}{2}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-84}{ \color{blue}{6} }x+ \frac{63}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -84x \color{red}{+63} & = & \color{red}{18x} +20 \\\Leftrightarrow & -84x \color{red}{+63} \color{blue}{-63} \color{blue}{-18x} & = & \color{red}{18x} +20 \color{blue}{-18x} \color{blue}{-63} \\\Leftrightarrow & -84x-18x& = & 20-63 \\\Leftrightarrow & \color{red}{-102} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-102} & & \\\Leftrightarrow & x = \frac{43}{102} & & \\ & V = \left\{ \frac{43}{102} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{2}{11})& = & 3x+\frac{4}{9} \\\Leftrightarrow & 10x+\frac{4}{11}& = & 3x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{990}{ \color{blue}{99} }x+ \frac{36}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{+36} & = & \color{red}{297x} +44 \\\Leftrightarrow & 990x \color{red}{+36} \color{blue}{-36} \color{blue}{-297x} & = & \color{red}{297x} +44 \color{blue}{-297x} \color{blue}{-36} \\\Leftrightarrow & 990x-297x& = & 44-36 \\\Leftrightarrow & \color{red}{693} x& = & 8 \\\Leftrightarrow & x = \frac{8}{693} & & \\ & V = \left\{ \frac{8}{693} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{5}{7})& = & -9x+\frac{4}{7} \\\Leftrightarrow & 8x-\frac{20}{7}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{56}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{-63}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 56x \color{red}{-20} & = & \color{red}{-63x} +4 \\\Leftrightarrow & 56x \color{red}{-20} \color{blue}{+20} \color{blue}{+63x} & = & \color{red}{-63x} +4 \color{blue}{+63x} \color{blue}{+20} \\\Leftrightarrow & 56x+63x& = & 4+20 \\\Leftrightarrow & \color{red}{119} x& = & 24 \\\Leftrightarrow & x = \frac{24}{119} & & \\ & V = \left\{ \frac{24}{119} \right\} & \\\end{align}\)
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