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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{4}{5})& = & 7x+\frac{4}{11} \\\Leftrightarrow & -9x-\frac{12}{5}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{-132} & = & \color{red}{385x} +20 \\\Leftrightarrow & -495x \color{red}{-132} \color{blue}{+132} \color{blue}{-385x} & = & \color{red}{385x} +20 \color{blue}{-385x} \color{blue}{+132} \\\Leftrightarrow & -495x-385x& = & 20+132 \\\Leftrightarrow & \color{red}{-880} x& = & 152 \\\Leftrightarrow & x = \frac{152}{-880} & & \\\Leftrightarrow & x = \frac{-19}{110} & & \\ & V = \left\{ \frac{-19}{110} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{5}{7})& = & -3x+\frac{7}{10} \\\Leftrightarrow & 8x-\frac{20}{7}& = & -3x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{560}{ \color{blue}{70} }x- \frac{200}{ \color{blue}{70} })& = & (\frac{-210}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 560x \color{red}{-200} & = & \color{red}{-210x} +49 \\\Leftrightarrow & 560x \color{red}{-200} \color{blue}{+200} \color{blue}{+210x} & = & \color{red}{-210x} +49 \color{blue}{+210x} \color{blue}{+200} \\\Leftrightarrow & 560x+210x& = & 49+200 \\\Leftrightarrow & \color{red}{770} x& = & 249 \\\Leftrightarrow & x = \frac{249}{770} & & \\ & V = \left\{ \frac{249}{770} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{2}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -20x+\frac{8}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{+24} & = & \color{red}{147x} +14 \\\Leftrightarrow & -420x \color{red}{+24} \color{blue}{-24} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{-24} \\\Leftrightarrow & -420x-147x& = & 14-24 \\\Leftrightarrow & \color{red}{-567} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-567} & & \\\Leftrightarrow & x = \frac{10}{567} & & \\ & V = \left\{ \frac{10}{567} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{5}{11})& = & 7x+\frac{8}{5} \\\Leftrightarrow & 4x-\frac{10}{11}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{220}{ \color{blue}{55} }x- \frac{50}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 220x \color{red}{-50} & = & \color{red}{385x} +88 \\\Leftrightarrow & 220x \color{red}{-50} \color{blue}{+50} \color{blue}{-385x} & = & \color{red}{385x} +88 \color{blue}{-385x} \color{blue}{+50} \\\Leftrightarrow & 220x-385x& = & 88+50 \\\Leftrightarrow & \color{red}{-165} x& = & 138 \\\Leftrightarrow & x = \frac{138}{-165} & & \\\Leftrightarrow & x = \frac{-46}{55} & & \\ & V = \left\{ \frac{-46}{55} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{2}{5})& = & -3x+\frac{6}{5} \\\Leftrightarrow & -18x+\frac{12}{5}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-90}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-15}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -90x \color{red}{+12} & = & \color{red}{-15x} +6 \\\Leftrightarrow & -90x \color{red}{+12} \color{blue}{-12} \color{blue}{+15x} & = & \color{red}{-15x} +6 \color{blue}{+15x} \color{blue}{-12} \\\Leftrightarrow & -90x+15x& = & 6-12 \\\Leftrightarrow & \color{red}{-75} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-75} & & \\\Leftrightarrow & x = \frac{2}{25} & & \\ & V = \left\{ \frac{2}{25} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{4}{7})& = & 7x+\frac{9}{4} \\\Leftrightarrow & 20x-\frac{16}{7}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{560}{ \color{blue}{28} }x- \frac{64}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 560x \color{red}{-64} & = & \color{red}{196x} +63 \\\Leftrightarrow & 560x \color{red}{-64} \color{blue}{+64} \color{blue}{-196x} & = & \color{red}{196x} +63 \color{blue}{-196x} \color{blue}{+64} \\\Leftrightarrow & 560x-196x& = & 63+64 \\\Leftrightarrow & \color{red}{364} x& = & 127 \\\Leftrightarrow & x = \frac{127}{364} & & \\ & V = \left\{ \frac{127}{364} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{2}{11})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -24x-\frac{12}{11}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-792}{ \color{blue}{33} }x- \frac{36}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -792x \color{red}{-36} & = & \color{red}{-165x} +44 \\\Leftrightarrow & -792x \color{red}{-36} \color{blue}{+36} \color{blue}{+165x} & = & \color{red}{-165x} +44 \color{blue}{+165x} \color{blue}{+36} \\\Leftrightarrow & -792x+165x& = & 44+36 \\\Leftrightarrow & \color{red}{-627} x& = & 80 \\\Leftrightarrow & x = \frac{80}{-627} & & \\\Leftrightarrow & x = \frac{-80}{627} & & \\ & V = \left\{ \frac{-80}{627} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{2}{3})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 16x-\frac{8}{3}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{240}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 240x \color{red}{-40} & = & \color{red}{-105x} +18 \\\Leftrightarrow & 240x \color{red}{-40} \color{blue}{+40} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{+40} \\\Leftrightarrow & 240x+105x& = & 18+40 \\\Leftrightarrow & \color{red}{345} x& = & 58 \\\Leftrightarrow & x = \frac{58}{345} & & \\ & V = \left\{ \frac{58}{345} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{3}{7})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 4x-\frac{6}{7}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{-30} & = & \color{red}{175x} +42 \\\Leftrightarrow & 140x \color{red}{-30} \color{blue}{+30} \color{blue}{-175x} & = & \color{red}{175x} +42 \color{blue}{-175x} \color{blue}{+30} \\\Leftrightarrow & 140x-175x& = & 42+30 \\\Leftrightarrow & \color{red}{-35} x& = & 72 \\\Leftrightarrow & x = \frac{72}{-35} & & \\\Leftrightarrow & x = \frac{-72}{35} & & \\ & V = \left\{ \frac{-72}{35} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{3})& = & 3x+\frac{10}{3} \\\Leftrightarrow & 14x+\frac{14}{3}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{42}{ \color{blue}{3} }x+ \frac{14}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 42x \color{red}{+14} & = & \color{red}{9x} +10 \\\Leftrightarrow & 42x \color{red}{+14} \color{blue}{-14} \color{blue}{-9x} & = & \color{red}{9x} +10 \color{blue}{-9x} \color{blue}{-14} \\\Leftrightarrow & 42x-9x& = & 10-14 \\\Leftrightarrow & \color{red}{33} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{33} & & \\ & V = \left\{ \frac{-4}{33} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{2}{3})& = & 6x+\frac{5}{8} \\\Leftrightarrow & 35x-\frac{14}{3}& = & 6x+\frac{5}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{840}{ \color{blue}{24} }x- \frac{112}{ \color{blue}{24} })& = & (\frac{144}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 840x \color{red}{-112} & = & \color{red}{144x} +15 \\\Leftrightarrow & 840x \color{red}{-112} \color{blue}{+112} \color{blue}{-144x} & = & \color{red}{144x} +15 \color{blue}{-144x} \color{blue}{+112} \\\Leftrightarrow & 840x-144x& = & 15+112 \\\Leftrightarrow & \color{red}{696} x& = & 127 \\\Leftrightarrow & x = \frac{127}{696} & & \\ & V = \left\{ \frac{127}{696} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{5}{2})& = & -5x+\frac{9}{10} \\\Leftrightarrow & -9x-\frac{15}{2}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 2 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-90}{ \color{blue}{10} }x- \frac{75}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -90x \color{red}{-75} & = & \color{red}{-50x} +9 \\\Leftrightarrow & -90x \color{red}{-75} \color{blue}{+75} \color{blue}{+50x} & = & \color{red}{-50x} +9 \color{blue}{+50x} \color{blue}{+75} \\\Leftrightarrow & -90x+50x& = & 9+75 \\\Leftrightarrow & \color{red}{-40} x& = & 84 \\\Leftrightarrow & x = \frac{84}{-40} & & \\\Leftrightarrow & x = \frac{-21}{10} & & \\ & V = \left\{ \frac{-21}{10} \right\} & \\\end{align}\)
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