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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{3}{10})& = & -7x+\frac{8}{9} \\\Leftrightarrow & 6x+\frac{9}{10}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 10 en 9 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{540}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} })& = & (\frac{-630}{ \color{blue}{90} }x+ \frac{80}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 540x \color{red}{+81} & = & \color{red}{-630x} +80 \\\Leftrightarrow & 540x \color{red}{+81} \color{blue}{-81} \color{blue}{+630x} & = & \color{red}{-630x} +80 \color{blue}{+630x} \color{blue}{-81} \\\Leftrightarrow & 540x+630x& = & 80-81 \\\Leftrightarrow & \color{red}{1170} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{1170} & & \\ & V = \left\{ \frac{-1}{1170} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{8})& = & -8x+\frac{4}{5} \\\Leftrightarrow & 21x-\frac{21}{8}& = & -8x+\frac{4}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{840}{ \color{blue}{40} }x- \frac{105}{ \color{blue}{40} })& = & (\frac{-320}{ \color{blue}{40} }x+ \frac{32}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 840x \color{red}{-105} & = & \color{red}{-320x} +32 \\\Leftrightarrow & 840x \color{red}{-105} \color{blue}{+105} \color{blue}{+320x} & = & \color{red}{-320x} +32 \color{blue}{+320x} \color{blue}{+105} \\\Leftrightarrow & 840x+320x& = & 32+105 \\\Leftrightarrow & \color{red}{1160} x& = & 137 \\\Leftrightarrow & x = \frac{137}{1160} & & \\ & V = \left\{ \frac{137}{1160} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{7})& = & -5x+\frac{9}{2} \\\Leftrightarrow & -12x-\frac{15}{7}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-168}{ \color{blue}{14} }x- \frac{30}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -168x \color{red}{-30} & = & \color{red}{-70x} +63 \\\Leftrightarrow & -168x \color{red}{-30} \color{blue}{+30} \color{blue}{+70x} & = & \color{red}{-70x} +63 \color{blue}{+70x} \color{blue}{+30} \\\Leftrightarrow & -168x+70x& = & 63+30 \\\Leftrightarrow & \color{red}{-98} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-98} & & \\\Leftrightarrow & x = \frac{-93}{98} & & \\ & V = \left\{ \frac{-93}{98} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{4})& = & -4x+\frac{3}{2} \\\Leftrightarrow & -15x-\frac{15}{4}& = & -4x+\frac{3}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-60}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{-16}{ \color{blue}{4} }x+ \frac{6}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -60x \color{red}{-15} & = & \color{red}{-16x} +6 \\\Leftrightarrow & -60x \color{red}{-15} \color{blue}{+15} \color{blue}{+16x} & = & \color{red}{-16x} +6 \color{blue}{+16x} \color{blue}{+15} \\\Leftrightarrow & -60x+16x& = & 6+15 \\\Leftrightarrow & \color{red}{-44} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-44} & & \\\Leftrightarrow & x = \frac{-21}{44} & & \\ & V = \left\{ \frac{-21}{44} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{2}{11})& = & -5x+\frac{5}{12} \\\Leftrightarrow & -12x-\frac{6}{11}& = & -5x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-1584}{ \color{blue}{132} }x- \frac{72}{ \color{blue}{132} })& = & (\frac{-660}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -1584x \color{red}{-72} & = & \color{red}{-660x} +55 \\\Leftrightarrow & -1584x \color{red}{-72} \color{blue}{+72} \color{blue}{+660x} & = & \color{red}{-660x} +55 \color{blue}{+660x} \color{blue}{+72} \\\Leftrightarrow & -1584x+660x& = & 55+72 \\\Leftrightarrow & \color{red}{-924} x& = & 127 \\\Leftrightarrow & x = \frac{127}{-924} & & \\\Leftrightarrow & x = \frac{-127}{924} & & \\ & V = \left\{ \frac{-127}{924} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{3})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -10x-\frac{10}{3}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-60}{ \color{blue}{6} }x- \frac{20}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -60x \color{red}{-20} & = & \color{red}{-42x} +15 \\\Leftrightarrow & -60x \color{red}{-20} \color{blue}{+20} \color{blue}{+42x} & = & \color{red}{-42x} +15 \color{blue}{+42x} \color{blue}{+20} \\\Leftrightarrow & -60x+42x& = & 15+20 \\\Leftrightarrow & \color{red}{-18} x& = & 35 \\\Leftrightarrow & x = \frac{35}{-18} & & \\\Leftrightarrow & x = \frac{-35}{18} & & \\ & V = \left\{ \frac{-35}{18} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{2}{3})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 10x+\frac{4}{3}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{+44} & = & \color{red}{-231x} +18 \\\Leftrightarrow & 330x \color{red}{+44} \color{blue}{-44} \color{blue}{+231x} & = & \color{red}{-231x} +18 \color{blue}{+231x} \color{blue}{-44} \\\Leftrightarrow & 330x+231x& = & 18-44 \\\Leftrightarrow & \color{red}{561} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{561} & & \\ & V = \left\{ \frac{-26}{561} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{2}{7})& = & 2x+\frac{4}{3} \\\Leftrightarrow & 9x+\frac{6}{7}& = & 2x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{189}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{42}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 189x \color{red}{+18} & = & \color{red}{42x} +28 \\\Leftrightarrow & 189x \color{red}{+18} \color{blue}{-18} \color{blue}{-42x} & = & \color{red}{42x} +28 \color{blue}{-42x} \color{blue}{-18} \\\Leftrightarrow & 189x-42x& = & 28-18 \\\Leftrightarrow & \color{red}{147} x& = & 10 \\\Leftrightarrow & x = \frac{10}{147} & & \\ & V = \left\{ \frac{10}{147} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{5}{11})& = & -3x+\frac{2}{7} \\\Leftrightarrow & 35x-\frac{35}{11}& = & -3x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2695}{ \color{blue}{77} }x- \frac{245}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2695x \color{red}{-245} & = & \color{red}{-231x} +22 \\\Leftrightarrow & 2695x \color{red}{-245} \color{blue}{+245} \color{blue}{+231x} & = & \color{red}{-231x} +22 \color{blue}{+231x} \color{blue}{+245} \\\Leftrightarrow & 2695x+231x& = & 22+245 \\\Leftrightarrow & \color{red}{2926} x& = & 267 \\\Leftrightarrow & x = \frac{267}{2926} & & \\ & V = \left\{ \frac{267}{2926} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{5}{7})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 4x-\frac{10}{7}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{-50} & = & \color{red}{-175x} +42 \\\Leftrightarrow & 140x \color{red}{-50} \color{blue}{+50} \color{blue}{+175x} & = & \color{red}{-175x} +42 \color{blue}{+175x} \color{blue}{+50} \\\Leftrightarrow & 140x+175x& = & 42+50 \\\Leftrightarrow & \color{red}{315} x& = & 92 \\\Leftrightarrow & x = \frac{92}{315} & & \\ & V = \left\{ \frac{92}{315} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{4}{7})& = & -9x+\frac{7}{6} \\\Leftrightarrow & -8x+\frac{16}{7}& = & -9x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-336}{ \color{blue}{42} }x+ \frac{96}{ \color{blue}{42} })& = & (\frac{-378}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -336x \color{red}{+96} & = & \color{red}{-378x} +49 \\\Leftrightarrow & -336x \color{red}{+96} \color{blue}{-96} \color{blue}{+378x} & = & \color{red}{-378x} +49 \color{blue}{+378x} \color{blue}{-96} \\\Leftrightarrow & -336x+378x& = & 49-96 \\\Leftrightarrow & \color{red}{42} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{42} & & \\ & V = \left\{ \frac{-47}{42} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{5}{9})& = & -5x+\frac{7}{12} \\\Leftrightarrow & 12x+\frac{20}{9}& = & -5x+\frac{7}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{432}{ \color{blue}{36} }x+ \frac{80}{ \color{blue}{36} })& = & (\frac{-180}{ \color{blue}{36} }x+ \frac{21}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 432x \color{red}{+80} & = & \color{red}{-180x} +21 \\\Leftrightarrow & 432x \color{red}{+80} \color{blue}{-80} \color{blue}{+180x} & = & \color{red}{-180x} +21 \color{blue}{+180x} \color{blue}{-80} \\\Leftrightarrow & 432x+180x& = & 21-80 \\\Leftrightarrow & \color{red}{612} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{612} & & \\ & V = \left\{ \frac{-59}{612} \right\} & \\\end{align}\)
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