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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{4}{5})& = & 7x+\frac{9}{10} \\\Leftrightarrow & 20x-\frac{16}{5}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{200}{ \color{blue}{10} }x- \frac{32}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 200x \color{red}{-32} & = & \color{red}{70x} +9 \\\Leftrightarrow & 200x \color{red}{-32} \color{blue}{+32} \color{blue}{-70x} & = & \color{red}{70x} +9 \color{blue}{-70x} \color{blue}{+32} \\\Leftrightarrow & 200x-70x& = & 9+32 \\\Leftrightarrow & \color{red}{130} x& = & 41 \\\Leftrightarrow & x = \frac{41}{130} & & \\ & V = \left\{ \frac{41}{130} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{2}{7})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 12x+\frac{12}{7}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{60}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+60} & = & \color{red}{-175x} +28 \\\Leftrightarrow & 420x \color{red}{+60} \color{blue}{-60} \color{blue}{+175x} & = & \color{red}{-175x} +28 \color{blue}{+175x} \color{blue}{-60} \\\Leftrightarrow & 420x+175x& = & 28-60 \\\Leftrightarrow & \color{red}{595} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{595} & & \\ & V = \left\{ \frac{-32}{595} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{4}{9})& = & -3x+\frac{5}{12} \\\Leftrightarrow & 10x+\frac{20}{9}& = & -3x+\frac{5}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{360}{ \color{blue}{36} }x+ \frac{80}{ \color{blue}{36} })& = & (\frac{-108}{ \color{blue}{36} }x+ \frac{15}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 360x \color{red}{+80} & = & \color{red}{-108x} +15 \\\Leftrightarrow & 360x \color{red}{+80} \color{blue}{-80} \color{blue}{+108x} & = & \color{red}{-108x} +15 \color{blue}{+108x} \color{blue}{-80} \\\Leftrightarrow & 360x+108x& = & 15-80 \\\Leftrightarrow & \color{red}{468} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{468} & & \\\Leftrightarrow & x = \frac{-5}{36} & & \\ & V = \left\{ \frac{-5}{36} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{5}{7})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 20x+\frac{20}{7}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+60} & = & \color{red}{-147x} +56 \\\Leftrightarrow & 420x \color{red}{+60} \color{blue}{-60} \color{blue}{+147x} & = & \color{red}{-147x} +56 \color{blue}{+147x} \color{blue}{-60} \\\Leftrightarrow & 420x+147x& = & 56-60 \\\Leftrightarrow & \color{red}{567} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{567} & & \\ & V = \left\{ \frac{-4}{567} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{4}{9})& = & -7x+\frac{5}{11} \\\Leftrightarrow & 20x-\frac{16}{9}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1980}{ \color{blue}{99} }x- \frac{176}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1980x \color{red}{-176} & = & \color{red}{-693x} +45 \\\Leftrightarrow & 1980x \color{red}{-176} \color{blue}{+176} \color{blue}{+693x} & = & \color{red}{-693x} +45 \color{blue}{+693x} \color{blue}{+176} \\\Leftrightarrow & 1980x+693x& = & 45+176 \\\Leftrightarrow & \color{red}{2673} x& = & 221 \\\Leftrightarrow & x = \frac{221}{2673} & & \\ & V = \left\{ \frac{221}{2673} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{8})& = & -3x+\frac{7}{8} \\\Leftrightarrow & -14x-\frac{21}{8}& = & -3x+\frac{7}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-112}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{-24}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -112x \color{red}{-21} & = & \color{red}{-24x} +7 \\\Leftrightarrow & -112x \color{red}{-21} \color{blue}{+21} \color{blue}{+24x} & = & \color{red}{-24x} +7 \color{blue}{+24x} \color{blue}{+21} \\\Leftrightarrow & -112x+24x& = & 7+21 \\\Leftrightarrow & \color{red}{-88} x& = & 28 \\\Leftrightarrow & x = \frac{28}{-88} & & \\\Leftrightarrow & x = \frac{-7}{22} & & \\ & V = \left\{ \frac{-7}{22} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{5}{4})& = & -7x+\frac{7}{4} \\\Leftrightarrow & 6x-\frac{15}{4}& = & -7x+\frac{7}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{24}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{-28}{ \color{blue}{4} }x+ \frac{7}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 24x \color{red}{-15} & = & \color{red}{-28x} +7 \\\Leftrightarrow & 24x \color{red}{-15} \color{blue}{+15} \color{blue}{+28x} & = & \color{red}{-28x} +7 \color{blue}{+28x} \color{blue}{+15} \\\Leftrightarrow & 24x+28x& = & 7+15 \\\Leftrightarrow & \color{red}{52} x& = & 22 \\\Leftrightarrow & x = \frac{22}{52} & & \\\Leftrightarrow & x = \frac{11}{26} & & \\ & V = \left\{ \frac{11}{26} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{2}{3})& = & 3x+\frac{6}{11} \\\Leftrightarrow & -35x-\frac{14}{3}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{-154} & = & \color{red}{99x} +18 \\\Leftrightarrow & -1155x \color{red}{-154} \color{blue}{+154} \color{blue}{-99x} & = & \color{red}{99x} +18 \color{blue}{-99x} \color{blue}{+154} \\\Leftrightarrow & -1155x-99x& = & 18+154 \\\Leftrightarrow & \color{red}{-1254} x& = & 172 \\\Leftrightarrow & x = \frac{172}{-1254} & & \\\Leftrightarrow & x = \frac{-86}{627} & & \\ & V = \left\{ \frac{-86}{627} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{3}{5})& = & -3x+\frac{5}{2} \\\Leftrightarrow & -20x-\frac{12}{5}& = & -3x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-200}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -200x \color{red}{-24} & = & \color{red}{-30x} +25 \\\Leftrightarrow & -200x \color{red}{-24} \color{blue}{+24} \color{blue}{+30x} & = & \color{red}{-30x} +25 \color{blue}{+30x} \color{blue}{+24} \\\Leftrightarrow & -200x+30x& = & 25+24 \\\Leftrightarrow & \color{red}{-170} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-170} & & \\\Leftrightarrow & x = \frac{-49}{170} & & \\ & V = \left\{ \frac{-49}{170} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{5}{7})& = & 3x+\frac{9}{7} \\\Leftrightarrow & -8x-\frac{10}{7}& = & 3x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-56}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -56x \color{red}{-10} & = & \color{red}{21x} +9 \\\Leftrightarrow & -56x \color{red}{-10} \color{blue}{+10} \color{blue}{-21x} & = & \color{red}{21x} +9 \color{blue}{-21x} \color{blue}{+10} \\\Leftrightarrow & -56x-21x& = & 9+10 \\\Leftrightarrow & \color{red}{-77} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-77} & & \\\Leftrightarrow & x = \frac{-19}{77} & & \\ & V = \left\{ \frac{-19}{77} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{2}{5})& = & 9x+\frac{5}{2} \\\Leftrightarrow & -8x-\frac{4}{5}& = & 9x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x- \frac{8}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{-8} & = & \color{red}{90x} +25 \\\Leftrightarrow & -80x \color{red}{-8} \color{blue}{+8} \color{blue}{-90x} & = & \color{red}{90x} +25 \color{blue}{-90x} \color{blue}{+8} \\\Leftrightarrow & -80x-90x& = & 25+8 \\\Leftrightarrow & \color{red}{-170} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-170} & & \\\Leftrightarrow & x = \frac{-33}{170} & & \\ & V = \left\{ \frac{-33}{170} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{5}{11})& = & 5x+\frac{9}{10} \\\Leftrightarrow & -28x+\frac{35}{11}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-3080}{ \color{blue}{110} }x+ \frac{350}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -3080x \color{red}{+350} & = & \color{red}{550x} +99 \\\Leftrightarrow & -3080x \color{red}{+350} \color{blue}{-350} \color{blue}{-550x} & = & \color{red}{550x} +99 \color{blue}{-550x} \color{blue}{-350} \\\Leftrightarrow & -3080x-550x& = & 99-350 \\\Leftrightarrow & \color{red}{-3630} x& = & -251 \\\Leftrightarrow & x = \frac{-251}{-3630} & & \\\Leftrightarrow & x = \frac{251}{3630} & & \\ & V = \left\{ \frac{251}{3630} \right\} & \\\end{align}\)
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