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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{2}{7})& = & -5x+\frac{10}{3} \\\Leftrightarrow & -12x+\frac{6}{7}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+18} & = & \color{red}{-105x} +70 \\\Leftrightarrow & -252x \color{red}{+18} \color{blue}{-18} \color{blue}{+105x} & = & \color{red}{-105x} +70 \color{blue}{+105x} \color{blue}{-18} \\\Leftrightarrow & -252x+105x& = & 70-18 \\\Leftrightarrow & \color{red}{-147} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-147} & & \\\Leftrightarrow & x = \frac{-52}{147} & & \\ & V = \left\{ \frac{-52}{147} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -24x-\frac{18}{11}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-792}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -792x \color{red}{-54} & = & \color{red}{-165x} +88 \\\Leftrightarrow & -792x \color{red}{-54} \color{blue}{+54} \color{blue}{+165x} & = & \color{red}{-165x} +88 \color{blue}{+165x} \color{blue}{+54} \\\Leftrightarrow & -792x+165x& = & 88+54 \\\Leftrightarrow & \color{red}{-627} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-627} & & \\\Leftrightarrow & x = \frac{-142}{627} & & \\ & V = \left\{ \frac{-142}{627} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{3})& = & -3x+\frac{9}{5} \\\Leftrightarrow & 16x+\frac{20}{3}& = & -3x+\frac{9}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{240}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 240x \color{red}{+100} & = & \color{red}{-45x} +27 \\\Leftrightarrow & 240x \color{red}{+100} \color{blue}{-100} \color{blue}{+45x} & = & \color{red}{-45x} +27 \color{blue}{+45x} \color{blue}{-100} \\\Leftrightarrow & 240x+45x& = & 27-100 \\\Leftrightarrow & \color{red}{285} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{285} & & \\ & V = \left\{ \frac{-73}{285} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{3})& = & -4x+\frac{9}{4} \\\Leftrightarrow & 15x+\frac{20}{3}& = & -4x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x+ \frac{80}{ \color{blue}{12} })& = & (\frac{-48}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{+80} & = & \color{red}{-48x} +27 \\\Leftrightarrow & 180x \color{red}{+80} \color{blue}{-80} \color{blue}{+48x} & = & \color{red}{-48x} +27 \color{blue}{+48x} \color{blue}{-80} \\\Leftrightarrow & 180x+48x& = & 27-80 \\\Leftrightarrow & \color{red}{228} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{228} & & \\ & V = \left\{ \frac{-53}{228} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{5}{9})& = & -6x+\frac{10}{3} \\\Leftrightarrow & 25x+\frac{25}{9}& = & -6x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{225}{ \color{blue}{9} }x+ \frac{25}{ \color{blue}{9} })& = & (\frac{-54}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 225x \color{red}{+25} & = & \color{red}{-54x} +30 \\\Leftrightarrow & 225x \color{red}{+25} \color{blue}{-25} \color{blue}{+54x} & = & \color{red}{-54x} +30 \color{blue}{+54x} \color{blue}{-25} \\\Leftrightarrow & 225x+54x& = & 30-25 \\\Leftrightarrow & \color{red}{279} x& = & 5 \\\Leftrightarrow & x = \frac{5}{279} & & \\ & V = \left\{ \frac{5}{279} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{4}{9})& = & -7x+\frac{8}{5} \\\Leftrightarrow & -10x+\frac{20}{9}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-450}{ \color{blue}{45} }x+ \frac{100}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{72}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -450x \color{red}{+100} & = & \color{red}{-315x} +72 \\\Leftrightarrow & -450x \color{red}{+100} \color{blue}{-100} \color{blue}{+315x} & = & \color{red}{-315x} +72 \color{blue}{+315x} \color{blue}{-100} \\\Leftrightarrow & -450x+315x& = & 72-100 \\\Leftrightarrow & \color{red}{-135} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{-135} & & \\\Leftrightarrow & x = \frac{28}{135} & & \\ & V = \left\{ \frac{28}{135} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{3}{2})& = & 7x+\frac{5}{6} \\\Leftrightarrow & -10x+\frac{15}{2}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 2 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-60}{ \color{blue}{6} }x+ \frac{45}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -60x \color{red}{+45} & = & \color{red}{42x} +5 \\\Leftrightarrow & -60x \color{red}{+45} \color{blue}{-45} \color{blue}{-42x} & = & \color{red}{42x} +5 \color{blue}{-42x} \color{blue}{-45} \\\Leftrightarrow & -60x-42x& = & 5-45 \\\Leftrightarrow & \color{red}{-102} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{-102} & & \\\Leftrightarrow & x = \frac{20}{51} & & \\ & V = \left\{ \frac{20}{51} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{2}{5})& = & 5x+\frac{9}{10} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-24} & = & \color{red}{50x} +9 \\\Leftrightarrow & 120x \color{red}{-24} \color{blue}{+24} \color{blue}{-50x} & = & \color{red}{50x} +9 \color{blue}{-50x} \color{blue}{+24} \\\Leftrightarrow & 120x-50x& = & 9+24 \\\Leftrightarrow & \color{red}{70} x& = & 33 \\\Leftrightarrow & x = \frac{33}{70} & & \\ & V = \left\{ \frac{33}{70} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{7})& = & 9x+\frac{5}{9} \\\Leftrightarrow & -8x+\frac{8}{7}& = & 9x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-504}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{+72} & = & \color{red}{567x} +35 \\\Leftrightarrow & -504x \color{red}{+72} \color{blue}{-72} \color{blue}{-567x} & = & \color{red}{567x} +35 \color{blue}{-567x} \color{blue}{-72} \\\Leftrightarrow & -504x-567x& = & 35-72 \\\Leftrightarrow & \color{red}{-1071} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-1071} & & \\\Leftrightarrow & x = \frac{37}{1071} & & \\ & V = \left\{ \frac{37}{1071} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{2}{5})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 9x+\frac{6}{5}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{495}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 495x \color{red}{+66} & = & \color{red}{275x} +40 \\\Leftrightarrow & 495x \color{red}{+66} \color{blue}{-66} \color{blue}{-275x} & = & \color{red}{275x} +40 \color{blue}{-275x} \color{blue}{-66} \\\Leftrightarrow & 495x-275x& = & 40-66 \\\Leftrightarrow & \color{red}{220} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{220} & & \\\Leftrightarrow & x = \frac{-13}{110} & & \\ & V = \left\{ \frac{-13}{110} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{8})& = & -2x+\frac{3}{8} \\\Leftrightarrow & 21x+\frac{21}{8}& = & -2x+\frac{3}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{168}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{-16}{ \color{blue}{8} }x+ \frac{3}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 168x \color{red}{+21} & = & \color{red}{-16x} +3 \\\Leftrightarrow & 168x \color{red}{+21} \color{blue}{-21} \color{blue}{+16x} & = & \color{red}{-16x} +3 \color{blue}{+16x} \color{blue}{-21} \\\Leftrightarrow & 168x+16x& = & 3-21 \\\Leftrightarrow & \color{red}{184} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{184} & & \\\Leftrightarrow & x = \frac{-9}{92} & & \\ & V = \left\{ \frac{-9}{92} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{3}{5})& = & -7x+\frac{5}{11} \\\Leftrightarrow & 16x+\frac{12}{5}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{880}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 880x \color{red}{+132} & = & \color{red}{-385x} +25 \\\Leftrightarrow & 880x \color{red}{+132} \color{blue}{-132} \color{blue}{+385x} & = & \color{red}{-385x} +25 \color{blue}{+385x} \color{blue}{-132} \\\Leftrightarrow & 880x+385x& = & 25-132 \\\Leftrightarrow & \color{red}{1265} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{1265} & & \\ & V = \left\{ \frac{-107}{1265} \right\} & \\\end{align}\)
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