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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{4}{11})& = & -3x+\frac{6}{7} \\\Leftrightarrow & 20x-\frac{16}{11}& = & -3x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x- \frac{112}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{-112} & = & \color{red}{-231x} +66 \\\Leftrightarrow & 1540x \color{red}{-112} \color{blue}{+112} \color{blue}{+231x} & = & \color{red}{-231x} +66 \color{blue}{+231x} \color{blue}{+112} \\\Leftrightarrow & 1540x+231x& = & 66+112 \\\Leftrightarrow & \color{red}{1771} x& = & 178 \\\Leftrightarrow & x = \frac{178}{1771} & & \\ & V = \left\{ \frac{178}{1771} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{4}{5})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -24x-\frac{24}{5}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{-264} & = & \color{red}{385x} +30 \\\Leftrightarrow & -1320x \color{red}{-264} \color{blue}{+264} \color{blue}{-385x} & = & \color{red}{385x} +30 \color{blue}{-385x} \color{blue}{+264} \\\Leftrightarrow & -1320x-385x& = & 30+264 \\\Leftrightarrow & \color{red}{-1705} x& = & 294 \\\Leftrightarrow & x = \frac{294}{-1705} & & \\\Leftrightarrow & x = \frac{-294}{1705} & & \\ & V = \left\{ \frac{-294}{1705} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{2}{5})& = & 7x+\frac{3}{11} \\\Leftrightarrow & -10x+\frac{4}{5}& = & 7x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{+44} & = & \color{red}{385x} +15 \\\Leftrightarrow & -550x \color{red}{+44} \color{blue}{-44} \color{blue}{-385x} & = & \color{red}{385x} +15 \color{blue}{-385x} \color{blue}{-44} \\\Leftrightarrow & -550x-385x& = & 15-44 \\\Leftrightarrow & \color{red}{-935} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-935} & & \\\Leftrightarrow & x = \frac{29}{935} & & \\ & V = \left\{ \frac{29}{935} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{3}{5})& = & -9x+\frac{8}{3} \\\Leftrightarrow & -8x-\frac{12}{5}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{-36} & = & \color{red}{-135x} +40 \\\Leftrightarrow & -120x \color{red}{-36} \color{blue}{+36} \color{blue}{+135x} & = & \color{red}{-135x} +40 \color{blue}{+135x} \color{blue}{+36} \\\Leftrightarrow & -120x+135x& = & 40+36 \\\Leftrightarrow & \color{red}{15} x& = & 76 \\\Leftrightarrow & x = \frac{76}{15} & & \\ & V = \left\{ \frac{76}{15} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{3}{7})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 12x-\frac{18}{7}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x- \frac{18}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{-18} & = & \color{red}{-35x} +10 \\\Leftrightarrow & 84x \color{red}{-18} \color{blue}{+18} \color{blue}{+35x} & = & \color{red}{-35x} +10 \color{blue}{+35x} \color{blue}{+18} \\\Leftrightarrow & 84x+35x& = & 10+18 \\\Leftrightarrow & \color{red}{119} x& = & 28 \\\Leftrightarrow & x = \frac{28}{119} & & \\\Leftrightarrow & x = \frac{4}{17} & & \\ & V = \left\{ \frac{4}{17} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{3}{5})& = & 4x+\frac{8}{11} \\\Leftrightarrow & -15x-\frac{9}{5}& = & 4x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x- \frac{99}{ \color{blue}{55} })& = & (\frac{220}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{-99} & = & \color{red}{220x} +40 \\\Leftrightarrow & -825x \color{red}{-99} \color{blue}{+99} \color{blue}{-220x} & = & \color{red}{220x} +40 \color{blue}{-220x} \color{blue}{+99} \\\Leftrightarrow & -825x-220x& = & 40+99 \\\Leftrightarrow & \color{red}{-1045} x& = & 139 \\\Leftrightarrow & x = \frac{139}{-1045} & & \\\Leftrightarrow & x = \frac{-139}{1045} & & \\ & V = \left\{ \frac{-139}{1045} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{5})& = & -8x+\frac{4}{11} \\\Leftrightarrow & -15x+\frac{6}{5}& = & -8x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{-440}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{+66} & = & \color{red}{-440x} +20 \\\Leftrightarrow & -825x \color{red}{+66} \color{blue}{-66} \color{blue}{+440x} & = & \color{red}{-440x} +20 \color{blue}{+440x} \color{blue}{-66} \\\Leftrightarrow & -825x+440x& = & 20-66 \\\Leftrightarrow & \color{red}{-385} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{-385} & & \\\Leftrightarrow & x = \frac{46}{385} & & \\ & V = \left\{ \frac{46}{385} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & -7x+\frac{5}{8} \\\Leftrightarrow & 8x+\frac{6}{7}& = & -7x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{448}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 448x \color{red}{+48} & = & \color{red}{-392x} +35 \\\Leftrightarrow & 448x \color{red}{+48} \color{blue}{-48} \color{blue}{+392x} & = & \color{red}{-392x} +35 \color{blue}{+392x} \color{blue}{-48} \\\Leftrightarrow & 448x+392x& = & 35-48 \\\Leftrightarrow & \color{red}{840} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{840} & & \\ & V = \left\{ \frac{-13}{840} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{4}{7})& = & 9x+\frac{4}{9} \\\Leftrightarrow & -20x+\frac{16}{7}& = & 9x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x+ \frac{144}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{+144} & = & \color{red}{567x} +28 \\\Leftrightarrow & -1260x \color{red}{+144} \color{blue}{-144} \color{blue}{-567x} & = & \color{red}{567x} +28 \color{blue}{-567x} \color{blue}{-144} \\\Leftrightarrow & -1260x-567x& = & 28-144 \\\Leftrightarrow & \color{red}{-1827} x& = & -116 \\\Leftrightarrow & x = \frac{-116}{-1827} & & \\\Leftrightarrow & x = \frac{4}{63} & & \\ & V = \left\{ \frac{4}{63} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{2}{3})& = & 5x+\frac{2}{5} \\\Leftrightarrow & -12x+\frac{8}{3}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+40} & = & \color{red}{75x} +6 \\\Leftrightarrow & -180x \color{red}{+40} \color{blue}{-40} \color{blue}{-75x} & = & \color{red}{75x} +6 \color{blue}{-75x} \color{blue}{-40} \\\Leftrightarrow & -180x-75x& = & 6-40 \\\Leftrightarrow & \color{red}{-255} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-255} & & \\\Leftrightarrow & x = \frac{2}{15} & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{5})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 30x+\frac{24}{5}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{450}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 450x \color{red}{+72} & = & \color{red}{105x} +10 \\\Leftrightarrow & 450x \color{red}{+72} \color{blue}{-72} \color{blue}{-105x} & = & \color{red}{105x} +10 \color{blue}{-105x} \color{blue}{-72} \\\Leftrightarrow & 450x-105x& = & 10-72 \\\Leftrightarrow & \color{red}{345} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{345} & & \\ & V = \left\{ \frac{-62}{345} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{3}{5})& = & 7x+\frac{5}{2} \\\Leftrightarrow & 20x-\frac{12}{5}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{200}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 200x \color{red}{-24} & = & \color{red}{70x} +25 \\\Leftrightarrow & 200x \color{red}{-24} \color{blue}{+24} \color{blue}{-70x} & = & \color{red}{70x} +25 \color{blue}{-70x} \color{blue}{+24} \\\Leftrightarrow & 200x-70x& = & 25+24 \\\Leftrightarrow & \color{red}{130} x& = & 49 \\\Leftrightarrow & x = \frac{49}{130} & & \\ & V = \left\{ \frac{49}{130} \right\} & \\\end{align}\)
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