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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{3}{5})& = & 9x+\frac{6}{5} \\\Leftrightarrow & 8x-\frac{6}{5}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{40}{ \color{blue}{5} }x- \frac{6}{ \color{blue}{5} })& = & (\frac{45}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 40x \color{red}{-6} & = & \color{red}{45x} +6 \\\Leftrightarrow & 40x \color{red}{-6} \color{blue}{+6} \color{blue}{-45x} & = & \color{red}{45x} +6 \color{blue}{-45x} \color{blue}{+6} \\\Leftrightarrow & 40x-45x& = & 6+6 \\\Leftrightarrow & \color{red}{-5} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-5} & & \\\Leftrightarrow & x = \frac{-12}{5} & & \\ & V = \left\{ \frac{-12}{5} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{3}{11})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 24x-\frac{18}{11}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{264}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 264x \color{red}{-18} & = & \color{red}{55x} +5 \\\Leftrightarrow & 264x \color{red}{-18} \color{blue}{+18} \color{blue}{-55x} & = & \color{red}{55x} +5 \color{blue}{-55x} \color{blue}{+18} \\\Leftrightarrow & 264x-55x& = & 5+18 \\\Leftrightarrow & \color{red}{209} x& = & 23 \\\Leftrightarrow & x = \frac{23}{209} & & \\ & V = \left\{ \frac{23}{209} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{3}{11})& = & -4x+\frac{6}{11} \\\Leftrightarrow & -15x-\frac{9}{11}& = & -4x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-165}{ \color{blue}{11} }x- \frac{9}{ \color{blue}{11} })& = & (\frac{-44}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -165x \color{red}{-9} & = & \color{red}{-44x} +6 \\\Leftrightarrow & -165x \color{red}{-9} \color{blue}{+9} \color{blue}{+44x} & = & \color{red}{-44x} +6 \color{blue}{+44x} \color{blue}{+9} \\\Leftrightarrow & -165x+44x& = & 6+9 \\\Leftrightarrow & \color{red}{-121} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-121} & & \\\Leftrightarrow & x = \frac{-15}{121} & & \\ & V = \left\{ \frac{-15}{121} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{4}{5})& = & 5x+\frac{9}{10} \\\Leftrightarrow & 12x-\frac{24}{5}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{48}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-48} & = & \color{red}{50x} +9 \\\Leftrightarrow & 120x \color{red}{-48} \color{blue}{+48} \color{blue}{-50x} & = & \color{red}{50x} +9 \color{blue}{-50x} \color{blue}{+48} \\\Leftrightarrow & 120x-50x& = & 9+48 \\\Leftrightarrow & \color{red}{70} x& = & 57 \\\Leftrightarrow & x = \frac{57}{70} & & \\ & V = \left\{ \frac{57}{70} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & -5x+\frac{5}{3} \\\Leftrightarrow & -12x-\frac{18}{11}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-54} & = & \color{red}{-165x} +55 \\\Leftrightarrow & -396x \color{red}{-54} \color{blue}{+54} \color{blue}{+165x} & = & \color{red}{-165x} +55 \color{blue}{+165x} \color{blue}{+54} \\\Leftrightarrow & -396x+165x& = & 55+54 \\\Leftrightarrow & \color{red}{-231} x& = & 109 \\\Leftrightarrow & x = \frac{109}{-231} & & \\\Leftrightarrow & x = \frac{-109}{231} & & \\ & V = \left\{ \frac{-109}{231} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{4}{9})& = & 7x+\frac{9}{8} \\\Leftrightarrow & -6x+\frac{8}{9}& = & 7x+\frac{9}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-432}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} })& = & (\frac{504}{ \color{blue}{72} }x+ \frac{81}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -432x \color{red}{+64} & = & \color{red}{504x} +81 \\\Leftrightarrow & -432x \color{red}{+64} \color{blue}{-64} \color{blue}{-504x} & = & \color{red}{504x} +81 \color{blue}{-504x} \color{blue}{-64} \\\Leftrightarrow & -432x-504x& = & 81-64 \\\Leftrightarrow & \color{red}{-936} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-936} & & \\\Leftrightarrow & x = \frac{-17}{936} & & \\ & V = \left\{ \frac{-17}{936} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{5}{8})& = & -7x+\frac{6}{7} \\\Leftrightarrow & -9x-\frac{15}{8}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-504}{ \color{blue}{56} }x- \frac{105}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -504x \color{red}{-105} & = & \color{red}{-392x} +48 \\\Leftrightarrow & -504x \color{red}{-105} \color{blue}{+105} \color{blue}{+392x} & = & \color{red}{-392x} +48 \color{blue}{+392x} \color{blue}{+105} \\\Leftrightarrow & -504x+392x& = & 48+105 \\\Leftrightarrow & \color{red}{-112} x& = & 153 \\\Leftrightarrow & x = \frac{153}{-112} & & \\\Leftrightarrow & x = \frac{-153}{112} & & \\ & V = \left\{ \frac{-153}{112} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{4}{5})& = & 5x+\frac{5}{6} \\\Leftrightarrow & -9x-\frac{12}{5}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-270}{ \color{blue}{30} }x- \frac{72}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -270x \color{red}{-72} & = & \color{red}{150x} +25 \\\Leftrightarrow & -270x \color{red}{-72} \color{blue}{+72} \color{blue}{-150x} & = & \color{red}{150x} +25 \color{blue}{-150x} \color{blue}{+72} \\\Leftrightarrow & -270x-150x& = & 25+72 \\\Leftrightarrow & \color{red}{-420} x& = & 97 \\\Leftrightarrow & x = \frac{97}{-420} & & \\\Leftrightarrow & x = \frac{-97}{420} & & \\ & V = \left\{ \frac{-97}{420} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{9})& = & 3x+\frac{3}{7} \\\Leftrightarrow & 8x+\frac{4}{9}& = & 3x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{+28} & = & \color{red}{189x} +27 \\\Leftrightarrow & 504x \color{red}{+28} \color{blue}{-28} \color{blue}{-189x} & = & \color{red}{189x} +27 \color{blue}{-189x} \color{blue}{-28} \\\Leftrightarrow & 504x-189x& = & 27-28 \\\Leftrightarrow & \color{red}{315} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{315} & & \\ & V = \left\{ \frac{-1}{315} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{3}{7})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 6x-\frac{6}{7}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{-18} & = & \color{red}{147x} +56 \\\Leftrightarrow & 126x \color{red}{-18} \color{blue}{+18} \color{blue}{-147x} & = & \color{red}{147x} +56 \color{blue}{-147x} \color{blue}{+18} \\\Leftrightarrow & 126x-147x& = & 56+18 \\\Leftrightarrow & \color{red}{-21} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-21} & & \\\Leftrightarrow & x = \frac{-74}{21} & & \\ & V = \left\{ \frac{-74}{21} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{3}{8})& = & 9x+\frac{7}{2} \\\Leftrightarrow & 28x-\frac{21}{8}& = & 9x+\frac{7}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{224}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{72}{ \color{blue}{8} }x+ \frac{28}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 224x \color{red}{-21} & = & \color{red}{72x} +28 \\\Leftrightarrow & 224x \color{red}{-21} \color{blue}{+21} \color{blue}{-72x} & = & \color{red}{72x} +28 \color{blue}{-72x} \color{blue}{+21} \\\Leftrightarrow & 224x-72x& = & 28+21 \\\Leftrightarrow & \color{red}{152} x& = & 49 \\\Leftrightarrow & x = \frac{49}{152} & & \\ & V = \left\{ \frac{49}{152} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{9})& = & 3x+\frac{4}{7} \\\Leftrightarrow & -28x-\frac{28}{9}& = & 3x+\frac{4}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1764}{ \color{blue}{63} }x- \frac{196}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{36}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1764x \color{red}{-196} & = & \color{red}{189x} +36 \\\Leftrightarrow & -1764x \color{red}{-196} \color{blue}{+196} \color{blue}{-189x} & = & \color{red}{189x} +36 \color{blue}{-189x} \color{blue}{+196} \\\Leftrightarrow & -1764x-189x& = & 36+196 \\\Leftrightarrow & \color{red}{-1953} x& = & 232 \\\Leftrightarrow & x = \frac{232}{-1953} & & \\\Leftrightarrow & x = \frac{-232}{1953} & & \\ & V = \left\{ \frac{-232}{1953} \right\} & \\\end{align}\)
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