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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & 7x+\frac{3}{11} \\\Leftrightarrow & -24x+\frac{18}{11}& = & 7x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-264}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -264x \color{red}{+18} & = & \color{red}{77x} +3 \\\Leftrightarrow & -264x \color{red}{+18} \color{blue}{-18} \color{blue}{-77x} & = & \color{red}{77x} +3 \color{blue}{-77x} \color{blue}{-18} \\\Leftrightarrow & -264x-77x& = & 3-18 \\\Leftrightarrow & \color{red}{-341} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-341} & & \\\Leftrightarrow & x = \frac{15}{341} & & \\ & V = \left\{ \frac{15}{341} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{5}{9})& = & -5x+\frac{2}{9} \\\Leftrightarrow & 8x-\frac{10}{9}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x- \frac{10}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{-10} & = & \color{red}{-45x} +2 \\\Leftrightarrow & 72x \color{red}{-10} \color{blue}{+10} \color{blue}{+45x} & = & \color{red}{-45x} +2 \color{blue}{+45x} \color{blue}{+10} \\\Leftrightarrow & 72x+45x& = & 2+10 \\\Leftrightarrow & \color{red}{117} x& = & 12 \\\Leftrightarrow & x = \frac{12}{117} & & \\\Leftrightarrow & x = \frac{4}{39} & & \\ & V = \left\{ \frac{4}{39} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{7})& = & 7x+\frac{8}{9} \\\Leftrightarrow & 8x-\frac{4}{7}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{36}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-36} & = & \color{red}{441x} +56 \\\Leftrightarrow & 504x \color{red}{-36} \color{blue}{+36} \color{blue}{-441x} & = & \color{red}{441x} +56 \color{blue}{-441x} \color{blue}{+36} \\\Leftrightarrow & 504x-441x& = & 56+36 \\\Leftrightarrow & \color{red}{63} x& = & 92 \\\Leftrightarrow & x = \frac{92}{63} & & \\ & V = \left\{ \frac{92}{63} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{11})& = & -8x+\frac{5}{7} \\\Leftrightarrow & -15x+\frac{6}{11}& = & -8x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} })& = & (\frac{-616}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{+42} & = & \color{red}{-616x} +55 \\\Leftrightarrow & -1155x \color{red}{+42} \color{blue}{-42} \color{blue}{+616x} & = & \color{red}{-616x} +55 \color{blue}{+616x} \color{blue}{-42} \\\Leftrightarrow & -1155x+616x& = & 55-42 \\\Leftrightarrow & \color{red}{-539} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-539} & & \\\Leftrightarrow & x = \frac{-13}{539} & & \\ & V = \left\{ \frac{-13}{539} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{5}{3})& = & 5x+\frac{2}{11} \\\Leftrightarrow & 8x+\frac{10}{3}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{+110} & = & \color{red}{165x} +6 \\\Leftrightarrow & 264x \color{red}{+110} \color{blue}{-110} \color{blue}{-165x} & = & \color{red}{165x} +6 \color{blue}{-165x} \color{blue}{-110} \\\Leftrightarrow & 264x-165x& = & 6-110 \\\Leftrightarrow & \color{red}{99} x& = & -104 \\\Leftrightarrow & x = \frac{-104}{99} & & \\ & V = \left\{ \frac{-104}{99} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{4}{5})& = & -5x+\frac{10}{11} \\\Leftrightarrow & -12x-\frac{16}{5}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{176}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-176} & = & \color{red}{-275x} +50 \\\Leftrightarrow & -660x \color{red}{-176} \color{blue}{+176} \color{blue}{+275x} & = & \color{red}{-275x} +50 \color{blue}{+275x} \color{blue}{+176} \\\Leftrightarrow & -660x+275x& = & 50+176 \\\Leftrightarrow & \color{red}{-385} x& = & 226 \\\Leftrightarrow & x = \frac{226}{-385} & & \\\Leftrightarrow & x = \frac{-226}{385} & & \\ & V = \left\{ \frac{-226}{385} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{3}{5})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+132} & = & \color{red}{275x} +40 \\\Leftrightarrow & 660x \color{red}{+132} \color{blue}{-132} \color{blue}{-275x} & = & \color{red}{275x} +40 \color{blue}{-275x} \color{blue}{-132} \\\Leftrightarrow & 660x-275x& = & 40-132 \\\Leftrightarrow & \color{red}{385} x& = & -92 \\\Leftrightarrow & x = \frac{-92}{385} & & \\ & V = \left\{ \frac{-92}{385} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{4}{3})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -10x+\frac{20}{3}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{+140} & = & \color{red}{147x} +30 \\\Leftrightarrow & -210x \color{red}{+140} \color{blue}{-140} \color{blue}{-147x} & = & \color{red}{147x} +30 \color{blue}{-147x} \color{blue}{-140} \\\Leftrightarrow & -210x-147x& = & 30-140 \\\Leftrightarrow & \color{red}{-357} x& = & -110 \\\Leftrightarrow & x = \frac{-110}{-357} & & \\\Leftrightarrow & x = \frac{110}{357} & & \\ & V = \left\{ \frac{110}{357} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{2}{7})& = & -7x+\frac{8}{9} \\\Leftrightarrow & 12x-\frac{6}{7}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{-54} & = & \color{red}{-441x} +56 \\\Leftrightarrow & 756x \color{red}{-54} \color{blue}{+54} \color{blue}{+441x} & = & \color{red}{-441x} +56 \color{blue}{+441x} \color{blue}{+54} \\\Leftrightarrow & 756x+441x& = & 56+54 \\\Leftrightarrow & \color{red}{1197} x& = & 110 \\\Leftrightarrow & x = \frac{110}{1197} & & \\ & V = \left\{ \frac{110}{1197} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{4}{3})& = & 3x+\frac{8}{3} \\\Leftrightarrow & -20x-\frac{20}{3}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-60}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -60x \color{red}{-20} & = & \color{red}{9x} +8 \\\Leftrightarrow & -60x \color{red}{-20} \color{blue}{+20} \color{blue}{-9x} & = & \color{red}{9x} +8 \color{blue}{-9x} \color{blue}{+20} \\\Leftrightarrow & -60x-9x& = & 8+20 \\\Leftrightarrow & \color{red}{-69} x& = & 28 \\\Leftrightarrow & x = \frac{28}{-69} & & \\\Leftrightarrow & x = \frac{-28}{69} & & \\ & V = \left\{ \frac{-28}{69} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{3}{5})& = & -3x+\frac{7}{8} \\\Leftrightarrow & 16x-\frac{12}{5}& = & -3x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{640}{ \color{blue}{40} }x- \frac{96}{ \color{blue}{40} })& = & (\frac{-120}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 640x \color{red}{-96} & = & \color{red}{-120x} +35 \\\Leftrightarrow & 640x \color{red}{-96} \color{blue}{+96} \color{blue}{+120x} & = & \color{red}{-120x} +35 \color{blue}{+120x} \color{blue}{+96} \\\Leftrightarrow & 640x+120x& = & 35+96 \\\Leftrightarrow & \color{red}{760} x& = & 131 \\\Leftrightarrow & x = \frac{131}{760} & & \\ & V = \left\{ \frac{131}{760} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{4}{5})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 18x-\frac{24}{5}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x- \frac{72}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{-72} & = & \color{red}{75x} +20 \\\Leftrightarrow & 270x \color{red}{-72} \color{blue}{+72} \color{blue}{-75x} & = & \color{red}{75x} +20 \color{blue}{-75x} \color{blue}{+72} \\\Leftrightarrow & 270x-75x& = & 20+72 \\\Leftrightarrow & \color{red}{195} x& = & 92 \\\Leftrightarrow & x = \frac{92}{195} & & \\ & V = \left\{ \frac{92}{195} \right\} & \\\end{align}\)
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