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Alles samen. Gebruik stappenplan en ZRM!

  1. \(7(-4x-\frac{5}{4})=-9x+\frac{2}{11}\)
  2. \(5(2x-\frac{2}{15})=9x+\frac{9}{16}\)
  3. \((2x-\frac{4}{9})=3x+\frac{10}{7}\)
  4. \(-(-x+\frac{5}{9})=5x+\frac{7}{6}\)
  5. \(-5(3x-\frac{5}{9})=x+\frac{4}{3}\)
  6. \(-(-x+\frac{3}{7})=-x+\frac{10}{7}\)
  7. \(-2(-5x+\frac{5}{7})=9x+\frac{8}{5}\)
  8. \(-3(-2x-\frac{4}{13})=-5x+\frac{9}{8}\)
  9. \(-5(-x-\frac{4}{9})=9x+\frac{5}{13}\)
  10. \(4(-x+\frac{4}{13})=7x+\frac{8}{9}\)
  11. \(5(4x+\frac{5}{8})=3x+\frac{6}{5}\)
  12. \(4(2x+\frac{5}{3})=5x+\frac{3}{16}\)

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{5}{4})& = & -9x+\frac{2}{11} \\\Leftrightarrow & -28x-\frac{35}{4}& = & -9x+\frac{2}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(-28x-\frac{35}{4})& = & (-9x+\frac{2}{11}). \color{blue}{44} \\\Leftrightarrow & -1232x \color{red}{-385} & = & \color{red}{-396x} +8 \\\Leftrightarrow & -1232x \color{red}{-385} \color{blue}{+385} \color{blue}{+396x} & = & \color{red}{-396x} +8 \color{blue}{+396x} \color{blue}{+385} \\\Leftrightarrow & -1232x+396x& = & 8+385 \\\Leftrightarrow & \color{red}{-836} x& = & 393 \\\Leftrightarrow & x = \frac{393}{-836} & & \\\Leftrightarrow & x = \frac{-393}{836} & & \\ & V = \left\{ \frac{-393}{836} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{2}{15})& = & 9x+\frac{9}{16} \\\Leftrightarrow & 10x-\frac{2}{3}& = & 9x+\frac{9}{16} \\ & & & \text{kgv van noemers 3 en 16 is 48} \\\Leftrightarrow & \color{blue}{48} .(10x-\frac{2}{3})& = & (9x+\frac{9}{16}). \color{blue}{48} \\\Leftrightarrow & 480x \color{red}{-32} & = & \color{red}{432x} +27 \\\Leftrightarrow & 480x \color{red}{-32} \color{blue}{+32} \color{blue}{-432x} & = & \color{red}{432x} +27 \color{blue}{-432x} \color{blue}{+32} \\\Leftrightarrow & 480x-432x& = & 27+32 \\\Leftrightarrow & \color{red}{48} x& = & 59 \\\Leftrightarrow & x = \frac{59}{48} & & \\ & V = \left\{ \frac{59}{48} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (2x-\frac{4}{9})& = & 3x+\frac{10}{7} \\\Leftrightarrow & 2x-\frac{4}{9}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(2x-\frac{4}{9})& = & (3x+\frac{10}{7}). \color{blue}{63} \\\Leftrightarrow & 126x \color{red}{-28} & = & \color{red}{189x} +90 \\\Leftrightarrow & 126x \color{red}{-28} \color{blue}{+28} \color{blue}{-189x} & = & \color{red}{189x} +90 \color{blue}{-189x} \color{blue}{+28} \\\Leftrightarrow & 126x-189x& = & 90+28 \\\Leftrightarrow & \color{red}{-63} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-63} & & \\\Leftrightarrow & x = \frac{-118}{63} & & \\ & V = \left\{ \frac{-118}{63} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-} (-x+\frac{5}{9})& = & 5x+\frac{7}{6} \\\Leftrightarrow & x-\frac{5}{9}& = & 5x+\frac{7}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(x-\frac{5}{9})& = & (5x+\frac{7}{6}). \color{blue}{18} \\\Leftrightarrow & 18x \color{red}{-10} & = & \color{red}{90x} +21 \\\Leftrightarrow & 18x \color{red}{-10} \color{blue}{+10} \color{blue}{-90x} & = & \color{red}{90x} +21 \color{blue}{-90x} \color{blue}{+10} \\\Leftrightarrow & 18x-90x& = & 21+10 \\\Leftrightarrow & \color{red}{-72} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-72} & & \\\Leftrightarrow & x = \frac{-31}{72} & & \\ & V = \left\{ \frac{-31}{72} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{5}{9})& = & x+\frac{4}{3} \\\Leftrightarrow & -15x+\frac{25}{9}& = & x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(-15x+\frac{25}{9})& = & (x+\frac{4}{3}). \color{blue}{9} \\\Leftrightarrow & -135x \color{red}{+25} & = & \color{red}{9x} +12 \\\Leftrightarrow & -135x \color{red}{+25} \color{blue}{-25} \color{blue}{-9x} & = & \color{red}{9x} +12 \color{blue}{-9x} \color{blue}{-25} \\\Leftrightarrow & -135x-9x& = & 12-25 \\\Leftrightarrow & \color{red}{-144} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-144} & & \\\Leftrightarrow & x = \frac{13}{144} & & \\ & V = \left\{ \frac{13}{144} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-} (-x+\frac{3}{7})& = & -x+\frac{10}{7} \\\Leftrightarrow & x-\frac{3}{7}& = & -x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(x-\frac{3}{7})& = & (-x+\frac{10}{7}). \color{blue}{7} \\\Leftrightarrow & 7x \color{red}{-3} & = & \color{red}{-7x} +10 \\\Leftrightarrow & 7x \color{red}{-3} \color{blue}{+3} \color{blue}{+7x} & = & \color{red}{-7x} +10 \color{blue}{+7x} \color{blue}{+3} \\\Leftrightarrow & 7x+7x& = & 10+3 \\\Leftrightarrow & \color{red}{14} x& = & 13 \\\Leftrightarrow & x = \frac{13}{14} & & \\ & V = \left\{ \frac{13}{14} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{5}{7})& = & 9x+\frac{8}{5} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(10x-\frac{10}{7})& = & (9x+\frac{8}{5}). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{-50} & = & \color{red}{315x} +56 \\\Leftrightarrow & 350x \color{red}{-50} \color{blue}{+50} \color{blue}{-315x} & = & \color{red}{315x} +56 \color{blue}{-315x} \color{blue}{+50} \\\Leftrightarrow & 350x-315x& = & 56+50 \\\Leftrightarrow & \color{red}{35} x& = & 106 \\\Leftrightarrow & x = \frac{106}{35} & & \\ & V = \left\{ \frac{106}{35} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{4}{13})& = & -5x+\frac{9}{8} \\\Leftrightarrow & 6x+\frac{12}{13}& = & -5x+\frac{9}{8} \\ & & & \text{kgv van noemers 13 en 8 is 104} \\\Leftrightarrow & \color{blue}{104} .(6x+\frac{12}{13})& = & (-5x+\frac{9}{8}). \color{blue}{104} \\\Leftrightarrow & 624x \color{red}{+96} & = & \color{red}{-520x} +117 \\\Leftrightarrow & 624x \color{red}{+96} \color{blue}{-96} \color{blue}{+520x} & = & \color{red}{-520x} +117 \color{blue}{+520x} \color{blue}{-96} \\\Leftrightarrow & 624x+520x& = & 117-96 \\\Leftrightarrow & \color{red}{1144} x& = & 21 \\\Leftrightarrow & x = \frac{21}{1144} & & \\ & V = \left\{ \frac{21}{1144} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-x-\frac{4}{9})& = & 9x+\frac{5}{13} \\\Leftrightarrow & 5x+\frac{20}{9}& = & 9x+\frac{5}{13} \\ & & & \text{kgv van noemers 9 en 13 is 117} \\\Leftrightarrow & \color{blue}{117} .(5x+\frac{20}{9})& = & (9x+\frac{5}{13}). \color{blue}{117} \\\Leftrightarrow & 585x \color{red}{+260} & = & \color{red}{1053x} +45 \\\Leftrightarrow & 585x \color{red}{+260} \color{blue}{-260} \color{blue}{-1053x} & = & \color{red}{1053x} +45 \color{blue}{-1053x} \color{blue}{-260} \\\Leftrightarrow & 585x-1053x& = & 45-260 \\\Leftrightarrow & \color{red}{-468} x& = & -215 \\\Leftrightarrow & x = \frac{-215}{-468} & & \\\Leftrightarrow & x = \frac{215}{468} & & \\ & V = \left\{ \frac{215}{468} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-x+\frac{4}{13})& = & 7x+\frac{8}{9} \\\Leftrightarrow & -4x+\frac{16}{13}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 13 en 9 is 117} \\\Leftrightarrow & \color{blue}{117} .(-4x+\frac{16}{13})& = & (7x+\frac{8}{9}). \color{blue}{117} \\\Leftrightarrow & -468x \color{red}{+144} & = & \color{red}{819x} +104 \\\Leftrightarrow & -468x \color{red}{+144} \color{blue}{-144} \color{blue}{-819x} & = & \color{red}{819x} +104 \color{blue}{-819x} \color{blue}{-144} \\\Leftrightarrow & -468x-819x& = & 104-144 \\\Leftrightarrow & \color{red}{-1287} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{-1287} & & \\\Leftrightarrow & x = \frac{40}{1287} & & \\ & V = \left\{ \frac{40}{1287} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{8})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 20x+\frac{25}{8}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(20x+\frac{25}{8})& = & (3x+\frac{6}{5}). \color{blue}{40} \\\Leftrightarrow & 800x \color{red}{+125} & = & \color{red}{120x} +48 \\\Leftrightarrow & 800x \color{red}{+125} \color{blue}{-125} \color{blue}{-120x} & = & \color{red}{120x} +48 \color{blue}{-120x} \color{blue}{-125} \\\Leftrightarrow & 800x-120x& = & 48-125 \\\Leftrightarrow & \color{red}{680} x& = & -77 \\\Leftrightarrow & x = \frac{-77}{680} & & \\ & V = \left\{ \frac{-77}{680} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{5}{3})& = & 5x+\frac{3}{16} \\\Leftrightarrow & 8x+\frac{20}{3}& = & 5x+\frac{3}{16} \\ & & & \text{kgv van noemers 3 en 16 is 48} \\\Leftrightarrow & \color{blue}{48} .(8x+\frac{20}{3})& = & (5x+\frac{3}{16}). \color{blue}{48} \\\Leftrightarrow & 384x \color{red}{+320} & = & \color{red}{240x} +9 \\\Leftrightarrow & 384x \color{red}{+320} \color{blue}{-320} \color{blue}{-240x} & = & \color{red}{240x} +9 \color{blue}{-240x} \color{blue}{-320} \\\Leftrightarrow & 384x-240x& = & 9-320 \\\Leftrightarrow & \color{red}{144} x& = & -311 \\\Leftrightarrow & x = \frac{-311}{144} & & \\ & V = \left\{ \frac{-311}{144} \right\} & \\\end{align}\)
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