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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{3})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -20x-\frac{8}{3}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-88} & = & \color{red}{-231x} +15 \\\Leftrightarrow & -660x \color{red}{-88} \color{blue}{+88} \color{blue}{+231x} & = & \color{red}{-231x} +15 \color{blue}{+231x} \color{blue}{+88} \\\Leftrightarrow & -660x+231x& = & 15+88 \\\Leftrightarrow & \color{red}{-429} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-429} & & \\\Leftrightarrow & x = \frac{-103}{429} & & \\ & V = \left\{ \frac{-103}{429} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{5}{7})& = & 5x+\frac{7}{12} \\\Leftrightarrow & 18x-\frac{30}{7}& = & 5x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{1512}{ \color{blue}{84} }x- \frac{360}{ \color{blue}{84} })& = & (\frac{420}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 1512x \color{red}{-360} & = & \color{red}{420x} +49 \\\Leftrightarrow & 1512x \color{red}{-360} \color{blue}{+360} \color{blue}{-420x} & = & \color{red}{420x} +49 \color{blue}{-420x} \color{blue}{+360} \\\Leftrightarrow & 1512x-420x& = & 49+360 \\\Leftrightarrow & \color{red}{1092} x& = & 409 \\\Leftrightarrow & x = \frac{409}{1092} & & \\ & V = \left\{ \frac{409}{1092} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{3}{5})& = & 9x+\frac{3}{7} \\\Leftrightarrow & 16x-\frac{12}{5}& = & 9x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{560}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 560x \color{red}{-84} & = & \color{red}{315x} +15 \\\Leftrightarrow & 560x \color{red}{-84} \color{blue}{+84} \color{blue}{-315x} & = & \color{red}{315x} +15 \color{blue}{-315x} \color{blue}{+84} \\\Leftrightarrow & 560x-315x& = & 15+84 \\\Leftrightarrow & \color{red}{245} x& = & 99 \\\Leftrightarrow & x = \frac{99}{245} & & \\ & V = \left\{ \frac{99}{245} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{3}{7})& = & -5x+\frac{5}{2} \\\Leftrightarrow & -9x+\frac{9}{7}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-126}{ \color{blue}{14} }x+ \frac{18}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -126x \color{red}{+18} & = & \color{red}{-70x} +35 \\\Leftrightarrow & -126x \color{red}{+18} \color{blue}{-18} \color{blue}{+70x} & = & \color{red}{-70x} +35 \color{blue}{+70x} \color{blue}{-18} \\\Leftrightarrow & -126x+70x& = & 35-18 \\\Leftrightarrow & \color{red}{-56} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-56} & & \\\Leftrightarrow & x = \frac{-17}{56} & & \\ & V = \left\{ \frac{-17}{56} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{4}{5})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+132} & = & \color{red}{275x} +10 \\\Leftrightarrow & -660x \color{red}{+132} \color{blue}{-132} \color{blue}{-275x} & = & \color{red}{275x} +10 \color{blue}{-275x} \color{blue}{-132} \\\Leftrightarrow & -660x-275x& = & 10-132 \\\Leftrightarrow & \color{red}{-935} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{-935} & & \\\Leftrightarrow & x = \frac{122}{935} & & \\ & V = \left\{ \frac{122}{935} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{3}{11})& = & 3x+\frac{8}{9} \\\Leftrightarrow & -8x-\frac{6}{11}& = & 3x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-792}{ \color{blue}{99} }x- \frac{54}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -792x \color{red}{-54} & = & \color{red}{297x} +88 \\\Leftrightarrow & -792x \color{red}{-54} \color{blue}{+54} \color{blue}{-297x} & = & \color{red}{297x} +88 \color{blue}{-297x} \color{blue}{+54} \\\Leftrightarrow & -792x-297x& = & 88+54 \\\Leftrightarrow & \color{red}{-1089} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-1089} & & \\\Leftrightarrow & x = \frac{-142}{1089} & & \\ & V = \left\{ \frac{-142}{1089} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{4}{7})& = & 9x+\frac{10}{9} \\\Leftrightarrow & -8x+\frac{16}{7}& = & 9x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-504}{ \color{blue}{63} }x+ \frac{144}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{+144} & = & \color{red}{567x} +70 \\\Leftrightarrow & -504x \color{red}{+144} \color{blue}{-144} \color{blue}{-567x} & = & \color{red}{567x} +70 \color{blue}{-567x} \color{blue}{-144} \\\Leftrightarrow & -504x-567x& = & 70-144 \\\Leftrightarrow & \color{red}{-1071} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{-1071} & & \\\Leftrightarrow & x = \frac{74}{1071} & & \\ & V = \left\{ \frac{74}{1071} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{2}{5})& = & 7x+\frac{2}{11} \\\Leftrightarrow & 24x+\frac{12}{5}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{+132} & = & \color{red}{385x} +10 \\\Leftrightarrow & 1320x \color{red}{+132} \color{blue}{-132} \color{blue}{-385x} & = & \color{red}{385x} +10 \color{blue}{-385x} \color{blue}{-132} \\\Leftrightarrow & 1320x-385x& = & 10-132 \\\Leftrightarrow & \color{red}{935} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{935} & & \\ & V = \left\{ \frac{-122}{935} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{5}{7})& = & -9x+\frac{6}{5} \\\Leftrightarrow & 10x+\frac{10}{7}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{+50} & = & \color{red}{-315x} +42 \\\Leftrightarrow & 350x \color{red}{+50} \color{blue}{-50} \color{blue}{+315x} & = & \color{red}{-315x} +42 \color{blue}{+315x} \color{blue}{-50} \\\Leftrightarrow & 350x+315x& = & 42-50 \\\Leftrightarrow & \color{red}{665} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{665} & & \\ & V = \left\{ \frac{-8}{665} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{5}{9})& = & 9x+\frac{7}{12} \\\Leftrightarrow & 20x+\frac{25}{9}& = & 9x+\frac{7}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{720}{ \color{blue}{36} }x+ \frac{100}{ \color{blue}{36} })& = & (\frac{324}{ \color{blue}{36} }x+ \frac{21}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 720x \color{red}{+100} & = & \color{red}{324x} +21 \\\Leftrightarrow & 720x \color{red}{+100} \color{blue}{-100} \color{blue}{-324x} & = & \color{red}{324x} +21 \color{blue}{-324x} \color{blue}{-100} \\\Leftrightarrow & 720x-324x& = & 21-100 \\\Leftrightarrow & \color{red}{396} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{396} & & \\ & V = \left\{ \frac{-79}{396} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{3}{5})& = & 9x+\frac{5}{9} \\\Leftrightarrow & 16x-\frac{12}{5}& = & 9x+\frac{5}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{720}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{25}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 720x \color{red}{-108} & = & \color{red}{405x} +25 \\\Leftrightarrow & 720x \color{red}{-108} \color{blue}{+108} \color{blue}{-405x} & = & \color{red}{405x} +25 \color{blue}{-405x} \color{blue}{+108} \\\Leftrightarrow & 720x-405x& = & 25+108 \\\Leftrightarrow & \color{red}{315} x& = & 133 \\\Leftrightarrow & x = \frac{133}{315} & & \\\Leftrightarrow & x = \frac{19}{45} & & \\ & V = \left\{ \frac{19}{45} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{2}{5})& = & -7x+\frac{3}{10} \\\Leftrightarrow & 18x+\frac{12}{5}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{180}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 180x \color{red}{+24} & = & \color{red}{-70x} +3 \\\Leftrightarrow & 180x \color{red}{+24} \color{blue}{-24} \color{blue}{+70x} & = & \color{red}{-70x} +3 \color{blue}{+70x} \color{blue}{-24} \\\Leftrightarrow & 180x+70x& = & 3-24 \\\Leftrightarrow & \color{red}{250} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{250} & & \\ & V = \left\{ \frac{-21}{250} \right\} & \\\end{align}\)
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