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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{3}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 12x+\frac{9}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+27} & = & \color{red}{-147x} +14 \\\Leftrightarrow & 252x \color{red}{+27} \color{blue}{-27} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{-27} \\\Leftrightarrow & 252x+147x& = & 14-27 \\\Leftrightarrow & \color{red}{399} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{399} & & \\ & V = \left\{ \frac{-13}{399} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{2}{9})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 6x-\frac{4}{9}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{594}{ \color{blue}{99} }x- \frac{44}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 594x \color{red}{-44} & = & \color{red}{-495x} +45 \\\Leftrightarrow & 594x \color{red}{-44} \color{blue}{+44} \color{blue}{+495x} & = & \color{red}{-495x} +45 \color{blue}{+495x} \color{blue}{+44} \\\Leftrightarrow & 594x+495x& = & 45+44 \\\Leftrightarrow & \color{red}{1089} x& = & 89 \\\Leftrightarrow & x = \frac{89}{1089} & & \\ & V = \left\{ \frac{89}{1089} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{4}{5})& = & 5x+\frac{10}{11} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+132} & = & \color{red}{275x} +50 \\\Leftrightarrow & -660x \color{red}{+132} \color{blue}{-132} \color{blue}{-275x} & = & \color{red}{275x} +50 \color{blue}{-275x} \color{blue}{-132} \\\Leftrightarrow & -660x-275x& = & 50-132 \\\Leftrightarrow & \color{red}{-935} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-935} & & \\\Leftrightarrow & x = \frac{82}{935} & & \\ & V = \left\{ \frac{82}{935} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{5}{7})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 18x-\frac{30}{7}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{-150} & = & \color{red}{245x} +42 \\\Leftrightarrow & 630x \color{red}{-150} \color{blue}{+150} \color{blue}{-245x} & = & \color{red}{245x} +42 \color{blue}{-245x} \color{blue}{+150} \\\Leftrightarrow & 630x-245x& = & 42+150 \\\Leftrightarrow & \color{red}{385} x& = & 192 \\\Leftrightarrow & x = \frac{192}{385} & & \\ & V = \left\{ \frac{192}{385} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{5}{3})& = & -3x+\frac{9}{7} \\\Leftrightarrow & 16x-\frac{20}{3}& = & -3x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{-140} & = & \color{red}{-63x} +27 \\\Leftrightarrow & 336x \color{red}{-140} \color{blue}{+140} \color{blue}{+63x} & = & \color{red}{-63x} +27 \color{blue}{+63x} \color{blue}{+140} \\\Leftrightarrow & 336x+63x& = & 27+140 \\\Leftrightarrow & \color{red}{399} x& = & 167 \\\Leftrightarrow & x = \frac{167}{399} & & \\ & V = \left\{ \frac{167}{399} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{2}{3})& = & 9x+\frac{4}{9} \\\Leftrightarrow & 35x+\frac{14}{3}& = & 9x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{315}{ \color{blue}{9} }x+ \frac{42}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 315x \color{red}{+42} & = & \color{red}{81x} +4 \\\Leftrightarrow & 315x \color{red}{+42} \color{blue}{-42} \color{blue}{-81x} & = & \color{red}{81x} +4 \color{blue}{-81x} \color{blue}{-42} \\\Leftrightarrow & 315x-81x& = & 4-42 \\\Leftrightarrow & \color{red}{234} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{234} & & \\\Leftrightarrow & x = \frac{-19}{117} & & \\ & V = \left\{ \frac{-19}{117} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{4}{9})& = & -3x+\frac{7}{2} \\\Leftrightarrow & 8x+\frac{8}{9}& = & -3x+\frac{7}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{144}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{-54}{ \color{blue}{18} }x+ \frac{63}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 144x \color{red}{+16} & = & \color{red}{-54x} +63 \\\Leftrightarrow & 144x \color{red}{+16} \color{blue}{-16} \color{blue}{+54x} & = & \color{red}{-54x} +63 \color{blue}{+54x} \color{blue}{-16} \\\Leftrightarrow & 144x+54x& = & 63-16 \\\Leftrightarrow & \color{red}{198} x& = & 47 \\\Leftrightarrow & x = \frac{47}{198} & & \\ & V = \left\{ \frac{47}{198} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & -5x+\frac{7}{2} \\\Leftrightarrow & -28x+\frac{21}{8}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-224}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{-40}{ \color{blue}{8} }x+ \frac{28}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -224x \color{red}{+21} & = & \color{red}{-40x} +28 \\\Leftrightarrow & -224x \color{red}{+21} \color{blue}{-21} \color{blue}{+40x} & = & \color{red}{-40x} +28 \color{blue}{+40x} \color{blue}{-21} \\\Leftrightarrow & -224x+40x& = & 28-21 \\\Leftrightarrow & \color{red}{-184} x& = & 7 \\\Leftrightarrow & x = \frac{7}{-184} & & \\\Leftrightarrow & x = \frac{-7}{184} & & \\ & V = \left\{ \frac{-7}{184} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{5}{3})& = & -5x+\frac{3}{5} \\\Leftrightarrow & 8x+\frac{20}{3}& = & -5x+\frac{3}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{9}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+100} & = & \color{red}{-75x} +9 \\\Leftrightarrow & 120x \color{red}{+100} \color{blue}{-100} \color{blue}{+75x} & = & \color{red}{-75x} +9 \color{blue}{+75x} \color{blue}{-100} \\\Leftrightarrow & 120x+75x& = & 9-100 \\\Leftrightarrow & \color{red}{195} x& = & -91 \\\Leftrightarrow & x = \frac{-91}{195} & & \\\Leftrightarrow & x = \frac{-7}{15} & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{3}{5})& = & -9x+\frac{3}{11} \\\Leftrightarrow & 20x-\frac{12}{5}& = & -9x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1100}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1100x \color{red}{-132} & = & \color{red}{-495x} +15 \\\Leftrightarrow & 1100x \color{red}{-132} \color{blue}{+132} \color{blue}{+495x} & = & \color{red}{-495x} +15 \color{blue}{+495x} \color{blue}{+132} \\\Leftrightarrow & 1100x+495x& = & 15+132 \\\Leftrightarrow & \color{red}{1595} x& = & 147 \\\Leftrightarrow & x = \frac{147}{1595} & & \\ & V = \left\{ \frac{147}{1595} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{2}{3})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -10x+\frac{10}{3}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-60}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -60x \color{red}{+20} & = & \color{red}{-42x} +15 \\\Leftrightarrow & -60x \color{red}{+20} \color{blue}{-20} \color{blue}{+42x} & = & \color{red}{-42x} +15 \color{blue}{+42x} \color{blue}{-20} \\\Leftrightarrow & -60x+42x& = & 15-20 \\\Leftrightarrow & \color{red}{-18} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-18} & & \\\Leftrightarrow & x = \frac{5}{18} & & \\ & V = \left\{ \frac{5}{18} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{3}{7})& = & 9x+\frac{6}{11} \\\Leftrightarrow & -8x-\frac{6}{7}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{-66} & = & \color{red}{693x} +42 \\\Leftrightarrow & -616x \color{red}{-66} \color{blue}{+66} \color{blue}{-693x} & = & \color{red}{693x} +42 \color{blue}{-693x} \color{blue}{+66} \\\Leftrightarrow & -616x-693x& = & 42+66 \\\Leftrightarrow & \color{red}{-1309} x& = & 108 \\\Leftrightarrow & x = \frac{108}{-1309} & & \\\Leftrightarrow & x = \frac{-108}{1309} & & \\ & V = \left\{ \frac{-108}{1309} \right\} & \\\end{align}\)
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