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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{3}{7})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 4x-\frac{6}{7}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{-18} & = & \color{red}{147x} +70 \\\Leftrightarrow & 84x \color{red}{-18} \color{blue}{+18} \color{blue}{-147x} & = & \color{red}{147x} +70 \color{blue}{-147x} \color{blue}{+18} \\\Leftrightarrow & 84x-147x& = & 70+18 \\\Leftrightarrow & \color{red}{-63} x& = & 88 \\\Leftrightarrow & x = \frac{88}{-63} & & \\\Leftrightarrow & x = \frac{-88}{63} & & \\ & V = \left\{ \frac{-88}{63} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{4}{11})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 30x+\frac{24}{11}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{330}{ \color{blue}{11} }x+ \frac{24}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 330x \color{red}{+24} & = & \color{red}{-77x} +6 \\\Leftrightarrow & 330x \color{red}{+24} \color{blue}{-24} \color{blue}{+77x} & = & \color{red}{-77x} +6 \color{blue}{+77x} \color{blue}{-24} \\\Leftrightarrow & 330x+77x& = & 6-24 \\\Leftrightarrow & \color{red}{407} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{407} & & \\ & V = \left\{ \frac{-18}{407} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{4}{11})& = & -5x+\frac{7}{11} \\\Leftrightarrow & 18x-\frac{24}{11}& = & -5x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{198}{ \color{blue}{11} }x- \frac{24}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 198x \color{red}{-24} & = & \color{red}{-55x} +7 \\\Leftrightarrow & 198x \color{red}{-24} \color{blue}{+24} \color{blue}{+55x} & = & \color{red}{-55x} +7 \color{blue}{+55x} \color{blue}{+24} \\\Leftrightarrow & 198x+55x& = & 7+24 \\\Leftrightarrow & \color{red}{253} x& = & 31 \\\Leftrightarrow & x = \frac{31}{253} & & \\ & V = \left\{ \frac{31}{253} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{5}{9})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 8x+\frac{10}{9}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{+10} & = & \color{red}{63x} +24 \\\Leftrightarrow & 72x \color{red}{+10} \color{blue}{-10} \color{blue}{-63x} & = & \color{red}{63x} +24 \color{blue}{-63x} \color{blue}{-10} \\\Leftrightarrow & 72x-63x& = & 24-10 \\\Leftrightarrow & \color{red}{9} x& = & 14 \\\Leftrightarrow & x = \frac{14}{9} & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{10})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -9x-\frac{9}{10}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-90}{ \color{blue}{10} }x- \frac{9}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -90x \color{red}{-9} & = & \color{red}{50x} +12 \\\Leftrightarrow & -90x \color{red}{-9} \color{blue}{+9} \color{blue}{-50x} & = & \color{red}{50x} +12 \color{blue}{-50x} \color{blue}{+9} \\\Leftrightarrow & -90x-50x& = & 12+9 \\\Leftrightarrow & \color{red}{-140} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-140} & & \\\Leftrightarrow & x = \frac{-3}{20} & & \\ & V = \left\{ \frac{-3}{20} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{5})& = & -5x+\frac{5}{12} \\\Leftrightarrow & -24x-\frac{18}{5}& = & -5x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1440}{ \color{blue}{60} }x- \frac{216}{ \color{blue}{60} })& = & (\frac{-300}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1440x \color{red}{-216} & = & \color{red}{-300x} +25 \\\Leftrightarrow & -1440x \color{red}{-216} \color{blue}{+216} \color{blue}{+300x} & = & \color{red}{-300x} +25 \color{blue}{+300x} \color{blue}{+216} \\\Leftrightarrow & -1440x+300x& = & 25+216 \\\Leftrightarrow & \color{red}{-1140} x& = & 241 \\\Leftrightarrow & x = \frac{241}{-1140} & & \\\Leftrightarrow & x = \frac{-241}{1140} & & \\ & V = \left\{ \frac{-241}{1140} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{4}{11})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 6x+\frac{12}{11}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{132}{ \color{blue}{22} }x+ \frac{24}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 132x \color{red}{+24} & = & \color{red}{-110x} +33 \\\Leftrightarrow & 132x \color{red}{+24} \color{blue}{-24} \color{blue}{+110x} & = & \color{red}{-110x} +33 \color{blue}{+110x} \color{blue}{-24} \\\Leftrightarrow & 132x+110x& = & 33-24 \\\Leftrightarrow & \color{red}{242} x& = & 9 \\\Leftrightarrow & x = \frac{9}{242} & & \\ & V = \left\{ \frac{9}{242} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{2}{7})& = & 5x+\frac{5}{12} \\\Leftrightarrow & -12x-\frac{6}{7}& = & 5x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-1008}{ \color{blue}{84} }x- \frac{72}{ \color{blue}{84} })& = & (\frac{420}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -1008x \color{red}{-72} & = & \color{red}{420x} +35 \\\Leftrightarrow & -1008x \color{red}{-72} \color{blue}{+72} \color{blue}{-420x} & = & \color{red}{420x} +35 \color{blue}{-420x} \color{blue}{+72} \\\Leftrightarrow & -1008x-420x& = & 35+72 \\\Leftrightarrow & \color{red}{-1428} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-1428} & & \\\Leftrightarrow & x = \frac{-107}{1428} & & \\ & V = \left\{ \frac{-107}{1428} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{3}{5})& = & -5x+\frac{7}{8} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x+ \frac{96}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{+96} & = & \color{red}{-200x} +35 \\\Leftrightarrow & 480x \color{red}{+96} \color{blue}{-96} \color{blue}{+200x} & = & \color{red}{-200x} +35 \color{blue}{+200x} \color{blue}{-96} \\\Leftrightarrow & 480x+200x& = & 35-96 \\\Leftrightarrow & \color{red}{680} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{680} & & \\ & V = \left\{ \frac{-61}{680} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{3}{10})& = & -4x+\frac{4}{11} \\\Leftrightarrow & 35x-\frac{21}{10}& = & -4x+\frac{4}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{3850}{ \color{blue}{110} }x- \frac{231}{ \color{blue}{110} })& = & (\frac{-440}{ \color{blue}{110} }x+ \frac{40}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 3850x \color{red}{-231} & = & \color{red}{-440x} +40 \\\Leftrightarrow & 3850x \color{red}{-231} \color{blue}{+231} \color{blue}{+440x} & = & \color{red}{-440x} +40 \color{blue}{+440x} \color{blue}{+231} \\\Leftrightarrow & 3850x+440x& = & 40+231 \\\Leftrightarrow & \color{red}{4290} x& = & 271 \\\Leftrightarrow & x = \frac{271}{4290} & & \\ & V = \left\{ \frac{271}{4290} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{4}{9})& = & 3x+\frac{5}{2} \\\Leftrightarrow & -8x-\frac{8}{9}& = & 3x+\frac{5}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-144}{ \color{blue}{18} }x- \frac{16}{ \color{blue}{18} })& = & (\frac{54}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -144x \color{red}{-16} & = & \color{red}{54x} +45 \\\Leftrightarrow & -144x \color{red}{-16} \color{blue}{+16} \color{blue}{-54x} & = & \color{red}{54x} +45 \color{blue}{-54x} \color{blue}{+16} \\\Leftrightarrow & -144x-54x& = & 45+16 \\\Leftrightarrow & \color{red}{-198} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-198} & & \\\Leftrightarrow & x = \frac{-61}{198} & & \\ & V = \left\{ \frac{-61}{198} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{2}{9})& = & -3x+\frac{7}{2} \\\Leftrightarrow & 10x+\frac{4}{9}& = & -3x+\frac{7}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{180}{ \color{blue}{18} }x+ \frac{8}{ \color{blue}{18} })& = & (\frac{-54}{ \color{blue}{18} }x+ \frac{63}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 180x \color{red}{+8} & = & \color{red}{-54x} +63 \\\Leftrightarrow & 180x \color{red}{+8} \color{blue}{-8} \color{blue}{+54x} & = & \color{red}{-54x} +63 \color{blue}{+54x} \color{blue}{-8} \\\Leftrightarrow & 180x+54x& = & 63-8 \\\Leftrightarrow & \color{red}{234} x& = & 55 \\\Leftrightarrow & x = \frac{55}{234} & & \\ & V = \left\{ \frac{55}{234} \right\} & \\\end{align}\)
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