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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{5}{7})& = & 5x+\frac{9}{4} \\\Leftrightarrow & 24x+\frac{30}{7}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{672}{ \color{blue}{28} }x+ \frac{120}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 672x \color{red}{+120} & = & \color{red}{140x} +63 \\\Leftrightarrow & 672x \color{red}{+120} \color{blue}{-120} \color{blue}{-140x} & = & \color{red}{140x} +63 \color{blue}{-140x} \color{blue}{-120} \\\Leftrightarrow & 672x-140x& = & 63-120 \\\Leftrightarrow & \color{red}{532} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{532} & & \\\Leftrightarrow & x = \frac{-3}{28} & & \\ & V = \left\{ \frac{-3}{28} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{3}{10})& = & 7x+\frac{3}{7} \\\Leftrightarrow & -6x-\frac{9}{10}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 10 en 7 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-420}{ \color{blue}{70} }x- \frac{63}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{30}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -420x \color{red}{-63} & = & \color{red}{490x} +30 \\\Leftrightarrow & -420x \color{red}{-63} \color{blue}{+63} \color{blue}{-490x} & = & \color{red}{490x} +30 \color{blue}{-490x} \color{blue}{+63} \\\Leftrightarrow & -420x-490x& = & 30+63 \\\Leftrightarrow & \color{red}{-910} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-910} & & \\\Leftrightarrow & x = \frac{-93}{910} & & \\ & V = \left\{ \frac{-93}{910} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{4}{5})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -9x-\frac{12}{5}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{-84} & = & \color{red}{-175x} +50 \\\Leftrightarrow & -315x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +50 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & -315x+175x& = & 50+84 \\\Leftrightarrow & \color{red}{-140} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-140} & & \\\Leftrightarrow & x = \frac{-67}{70} & & \\ & V = \left\{ \frac{-67}{70} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{3}{7})& = & -2x+\frac{7}{6} \\\Leftrightarrow & -18x-\frac{18}{7}& = & -2x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-756}{ \color{blue}{42} }x- \frac{108}{ \color{blue}{42} })& = & (\frac{-84}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -756x \color{red}{-108} & = & \color{red}{-84x} +49 \\\Leftrightarrow & -756x \color{red}{-108} \color{blue}{+108} \color{blue}{+84x} & = & \color{red}{-84x} +49 \color{blue}{+84x} \color{blue}{+108} \\\Leftrightarrow & -756x+84x& = & 49+108 \\\Leftrightarrow & \color{red}{-672} x& = & 157 \\\Leftrightarrow & x = \frac{157}{-672} & & \\\Leftrightarrow & x = \frac{-157}{672} & & \\ & V = \left\{ \frac{-157}{672} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{3}{4})& = & 9x+\frac{5}{2} \\\Leftrightarrow & 28x+\frac{21}{4}& = & 9x+\frac{5}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{112}{ \color{blue}{4} }x+ \frac{21}{ \color{blue}{4} })& = & (\frac{36}{ \color{blue}{4} }x+ \frac{10}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 112x \color{red}{+21} & = & \color{red}{36x} +10 \\\Leftrightarrow & 112x \color{red}{+21} \color{blue}{-21} \color{blue}{-36x} & = & \color{red}{36x} +10 \color{blue}{-36x} \color{blue}{-21} \\\Leftrightarrow & 112x-36x& = & 10-21 \\\Leftrightarrow & \color{red}{76} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{76} & & \\ & V = \left\{ \frac{-11}{76} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{11})& = & -3x+\frac{6}{11} \\\Leftrightarrow & -14x-\frac{21}{11}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-154}{ \color{blue}{11} }x- \frac{21}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -154x \color{red}{-21} & = & \color{red}{-33x} +6 \\\Leftrightarrow & -154x \color{red}{-21} \color{blue}{+21} \color{blue}{+33x} & = & \color{red}{-33x} +6 \color{blue}{+33x} \color{blue}{+21} \\\Leftrightarrow & -154x+33x& = & 6+21 \\\Leftrightarrow & \color{red}{-121} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-121} & & \\\Leftrightarrow & x = \frac{-27}{121} & & \\ & V = \left\{ \frac{-27}{121} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{2}{3})& = & 8x+\frac{9}{2} \\\Leftrightarrow & -21x-\frac{14}{3}& = & 8x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-126}{ \color{blue}{6} }x- \frac{28}{ \color{blue}{6} })& = & (\frac{48}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -126x \color{red}{-28} & = & \color{red}{48x} +27 \\\Leftrightarrow & -126x \color{red}{-28} \color{blue}{+28} \color{blue}{-48x} & = & \color{red}{48x} +27 \color{blue}{-48x} \color{blue}{+28} \\\Leftrightarrow & -126x-48x& = & 27+28 \\\Leftrightarrow & \color{red}{-174} x& = & 55 \\\Leftrightarrow & x = \frac{55}{-174} & & \\\Leftrightarrow & x = \frac{-55}{174} & & \\ & V = \left\{ \frac{-55}{174} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{2}{9})& = & -3x+\frac{6}{11} \\\Leftrightarrow & -8x-\frac{4}{9}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-792}{ \color{blue}{99} }x- \frac{44}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -792x \color{red}{-44} & = & \color{red}{-297x} +54 \\\Leftrightarrow & -792x \color{red}{-44} \color{blue}{+44} \color{blue}{+297x} & = & \color{red}{-297x} +54 \color{blue}{+297x} \color{blue}{+44} \\\Leftrightarrow & -792x+297x& = & 54+44 \\\Leftrightarrow & \color{red}{-495} x& = & 98 \\\Leftrightarrow & x = \frac{98}{-495} & & \\\Leftrightarrow & x = \frac{-98}{495} & & \\ & V = \left\{ \frac{-98}{495} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{3}{7})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-84}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -84x \color{red}{+12} & = & \color{red}{98x} +63 \\\Leftrightarrow & -84x \color{red}{+12} \color{blue}{-12} \color{blue}{-98x} & = & \color{red}{98x} +63 \color{blue}{-98x} \color{blue}{-12} \\\Leftrightarrow & -84x-98x& = & 63-12 \\\Leftrightarrow & \color{red}{-182} x& = & 51 \\\Leftrightarrow & x = \frac{51}{-182} & & \\\Leftrightarrow & x = \frac{-51}{182} & & \\ & V = \left\{ \frac{-51}{182} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{4}{5})& = & -7x+\frac{7}{9} \\\Leftrightarrow & 24x+\frac{24}{5}& = & -7x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1080}{ \color{blue}{45} }x+ \frac{216}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1080x \color{red}{+216} & = & \color{red}{-315x} +35 \\\Leftrightarrow & 1080x \color{red}{+216} \color{blue}{-216} \color{blue}{+315x} & = & \color{red}{-315x} +35 \color{blue}{+315x} \color{blue}{-216} \\\Leftrightarrow & 1080x+315x& = & 35-216 \\\Leftrightarrow & \color{red}{1395} x& = & -181 \\\Leftrightarrow & x = \frac{-181}{1395} & & \\ & V = \left\{ \frac{-181}{1395} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{2}{7})& = & -7x+\frac{10}{11} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-66} & = & \color{red}{-539x} +70 \\\Leftrightarrow & -462x \color{red}{-66} \color{blue}{+66} \color{blue}{+539x} & = & \color{red}{-539x} +70 \color{blue}{+539x} \color{blue}{+66} \\\Leftrightarrow & -462x+539x& = & 70+66 \\\Leftrightarrow & \color{red}{77} x& = & 136 \\\Leftrightarrow & x = \frac{136}{77} & & \\ & V = \left\{ \frac{136}{77} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{3}{7})& = & 5x+\frac{5}{9} \\\Leftrightarrow & 4x+\frac{6}{7}& = & 5x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{252}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 252x \color{red}{+54} & = & \color{red}{315x} +35 \\\Leftrightarrow & 252x \color{red}{+54} \color{blue}{-54} \color{blue}{-315x} & = & \color{red}{315x} +35 \color{blue}{-315x} \color{blue}{-54} \\\Leftrightarrow & 252x-315x& = & 35-54 \\\Leftrightarrow & \color{red}{-63} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{-63} & & \\\Leftrightarrow & x = \frac{19}{63} & & \\ & V = \left\{ \frac{19}{63} \right\} & \\\end{align}\)
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