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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{5}{6})& = & -3x+\frac{2}{3} \\\Leftrightarrow & 28x+\frac{35}{6}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{168}{ \color{blue}{6} }x+ \frac{35}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 168x \color{red}{+35} & = & \color{red}{-18x} +4 \\\Leftrightarrow & 168x \color{red}{+35} \color{blue}{-35} \color{blue}{+18x} & = & \color{red}{-18x} +4 \color{blue}{+18x} \color{blue}{-35} \\\Leftrightarrow & 168x+18x& = & 4-35 \\\Leftrightarrow & \color{red}{186} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{186} & & \\\Leftrightarrow & x = \frac{-1}{6} & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{5}{11})& = & 3x+\frac{10}{9} \\\Leftrightarrow & -20x-\frac{25}{11}& = & 3x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1980}{ \color{blue}{99} }x- \frac{225}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1980x \color{red}{-225} & = & \color{red}{297x} +110 \\\Leftrightarrow & -1980x \color{red}{-225} \color{blue}{+225} \color{blue}{-297x} & = & \color{red}{297x} +110 \color{blue}{-297x} \color{blue}{+225} \\\Leftrightarrow & -1980x-297x& = & 110+225 \\\Leftrightarrow & \color{red}{-2277} x& = & 335 \\\Leftrightarrow & x = \frac{335}{-2277} & & \\\Leftrightarrow & x = \frac{-335}{2277} & & \\ & V = \left\{ \frac{-335}{2277} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{3}{8})& = & -8x+\frac{8}{5} \\\Leftrightarrow & -21x-\frac{21}{8}& = & -8x+\frac{8}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-840}{ \color{blue}{40} }x- \frac{105}{ \color{blue}{40} })& = & (\frac{-320}{ \color{blue}{40} }x+ \frac{64}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -840x \color{red}{-105} & = & \color{red}{-320x} +64 \\\Leftrightarrow & -840x \color{red}{-105} \color{blue}{+105} \color{blue}{+320x} & = & \color{red}{-320x} +64 \color{blue}{+320x} \color{blue}{+105} \\\Leftrightarrow & -840x+320x& = & 64+105 \\\Leftrightarrow & \color{red}{-520} x& = & 169 \\\Leftrightarrow & x = \frac{169}{-520} & & \\\Leftrightarrow & x = \frac{-13}{40} & & \\ & V = \left\{ \frac{-13}{40} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{2}{11})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 24x+\frac{12}{11}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{792}{ \color{blue}{33} }x+ \frac{36}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{+36} & = & \color{red}{165x} +44 \\\Leftrightarrow & 792x \color{red}{+36} \color{blue}{-36} \color{blue}{-165x} & = & \color{red}{165x} +44 \color{blue}{-165x} \color{blue}{-36} \\\Leftrightarrow & 792x-165x& = & 44-36 \\\Leftrightarrow & \color{red}{627} x& = & 8 \\\Leftrightarrow & x = \frac{8}{627} & & \\ & V = \left\{ \frac{8}{627} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{2}{5})& = & -5x+\frac{5}{7} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+84} & = & \color{red}{-175x} +25 \\\Leftrightarrow & 420x \color{red}{+84} \color{blue}{-84} \color{blue}{+175x} & = & \color{red}{-175x} +25 \color{blue}{+175x} \color{blue}{-84} \\\Leftrightarrow & 420x+175x& = & 25-84 \\\Leftrightarrow & \color{red}{595} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{595} & & \\ & V = \left\{ \frac{-59}{595} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{3}{5})& = & 5x+\frac{10}{11} \\\Leftrightarrow & -12x+\frac{18}{5}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{198}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+198} & = & \color{red}{275x} +50 \\\Leftrightarrow & -660x \color{red}{+198} \color{blue}{-198} \color{blue}{-275x} & = & \color{red}{275x} +50 \color{blue}{-275x} \color{blue}{-198} \\\Leftrightarrow & -660x-275x& = & 50-198 \\\Leftrightarrow & \color{red}{-935} x& = & -148 \\\Leftrightarrow & x = \frac{-148}{-935} & & \\\Leftrightarrow & x = \frac{148}{935} & & \\ & V = \left\{ \frac{148}{935} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{7})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 12x+\frac{8}{7}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{+8} & = & \color{red}{-35x} +10 \\\Leftrightarrow & 84x \color{red}{+8} \color{blue}{-8} \color{blue}{+35x} & = & \color{red}{-35x} +10 \color{blue}{+35x} \color{blue}{-8} \\\Leftrightarrow & 84x+35x& = & 10-8 \\\Leftrightarrow & \color{red}{119} x& = & 2 \\\Leftrightarrow & x = \frac{2}{119} & & \\ & V = \left\{ \frac{2}{119} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{5}{6})& = & 2x+\frac{8}{3} \\\Leftrightarrow & 15x-\frac{25}{6}& = & 2x+\frac{8}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{90}{ \color{blue}{6} }x- \frac{25}{ \color{blue}{6} })& = & (\frac{12}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 90x \color{red}{-25} & = & \color{red}{12x} +16 \\\Leftrightarrow & 90x \color{red}{-25} \color{blue}{+25} \color{blue}{-12x} & = & \color{red}{12x} +16 \color{blue}{-12x} \color{blue}{+25} \\\Leftrightarrow & 90x-12x& = & 16+25 \\\Leftrightarrow & \color{red}{78} x& = & 41 \\\Leftrightarrow & x = \frac{41}{78} & & \\ & V = \left\{ \frac{41}{78} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{3}{7})& = & 9x+\frac{10}{7} \\\Leftrightarrow & 4x-\frac{6}{7}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{28}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{63}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 28x \color{red}{-6} & = & \color{red}{63x} +10 \\\Leftrightarrow & 28x \color{red}{-6} \color{blue}{+6} \color{blue}{-63x} & = & \color{red}{63x} +10 \color{blue}{-63x} \color{blue}{+6} \\\Leftrightarrow & 28x-63x& = & 10+6 \\\Leftrightarrow & \color{red}{-35} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-35} & & \\\Leftrightarrow & x = \frac{-16}{35} & & \\ & V = \left\{ \frac{-16}{35} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{-12} & = & \color{red}{-25x} +6 \\\Leftrightarrow & 60x \color{red}{-12} \color{blue}{+12} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{+12} \\\Leftrightarrow & 60x+25x& = & 6+12 \\\Leftrightarrow & \color{red}{85} x& = & 18 \\\Leftrightarrow & x = \frac{18}{85} & & \\ & V = \left\{ \frac{18}{85} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{2}{9})& = & -2x+\frac{7}{6} \\\Leftrightarrow & -28x+\frac{14}{9}& = & -2x+\frac{7}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-504}{ \color{blue}{18} }x+ \frac{28}{ \color{blue}{18} })& = & (\frac{-36}{ \color{blue}{18} }x+ \frac{21}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -504x \color{red}{+28} & = & \color{red}{-36x} +21 \\\Leftrightarrow & -504x \color{red}{+28} \color{blue}{-28} \color{blue}{+36x} & = & \color{red}{-36x} +21 \color{blue}{+36x} \color{blue}{-28} \\\Leftrightarrow & -504x+36x& = & 21-28 \\\Leftrightarrow & \color{red}{-468} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-468} & & \\\Leftrightarrow & x = \frac{7}{468} & & \\ & V = \left\{ \frac{7}{468} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{3}{8})& = & 9x+\frac{3}{4} \\\Leftrightarrow & 14x+\frac{21}{8}& = & 9x+\frac{3}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{112}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{72}{ \color{blue}{8} }x+ \frac{6}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 112x \color{red}{+21} & = & \color{red}{72x} +6 \\\Leftrightarrow & 112x \color{red}{+21} \color{blue}{-21} \color{blue}{-72x} & = & \color{red}{72x} +6 \color{blue}{-72x} \color{blue}{-21} \\\Leftrightarrow & 112x-72x& = & 6-21 \\\Leftrightarrow & \color{red}{40} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{40} & & \\\Leftrightarrow & x = \frac{-3}{8} & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
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