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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{5}{11})& = & -4x+\frac{9}{7} \\\Leftrightarrow & 35x-\frac{35}{11}& = & -4x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2695}{ \color{blue}{77} }x- \frac{245}{ \color{blue}{77} })& = & (\frac{-308}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2695x \color{red}{-245} & = & \color{red}{-308x} +99 \\\Leftrightarrow & 2695x \color{red}{-245} \color{blue}{+245} \color{blue}{+308x} & = & \color{red}{-308x} +99 \color{blue}{+308x} \color{blue}{+245} \\\Leftrightarrow & 2695x+308x& = & 99+245 \\\Leftrightarrow & \color{red}{3003} x& = & 344 \\\Leftrightarrow & x = \frac{344}{3003} & & \\ & V = \left\{ \frac{344}{3003} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{2}{9})& = & 7x+\frac{9}{5} \\\Leftrightarrow & 8x-\frac{8}{9}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{360}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{81}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 360x \color{red}{-40} & = & \color{red}{315x} +81 \\\Leftrightarrow & 360x \color{red}{-40} \color{blue}{+40} \color{blue}{-315x} & = & \color{red}{315x} +81 \color{blue}{-315x} \color{blue}{+40} \\\Leftrightarrow & 360x-315x& = & 81+40 \\\Leftrightarrow & \color{red}{45} x& = & 121 \\\Leftrightarrow & x = \frac{121}{45} & & \\ & V = \left\{ \frac{121}{45} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{3})& = & -7x+\frac{8}{11} \\\Leftrightarrow & -10x-\frac{8}{3}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{-88} & = & \color{red}{-231x} +24 \\\Leftrightarrow & -330x \color{red}{-88} \color{blue}{+88} \color{blue}{+231x} & = & \color{red}{-231x} +24 \color{blue}{+231x} \color{blue}{+88} \\\Leftrightarrow & -330x+231x& = & 24+88 \\\Leftrightarrow & \color{red}{-99} x& = & 112 \\\Leftrightarrow & x = \frac{112}{-99} & & \\\Leftrightarrow & x = \frac{-112}{99} & & \\ & V = \left\{ \frac{-112}{99} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{3}{7})& = & 5x+\frac{7}{2} \\\Leftrightarrow & 12x+\frac{9}{7}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x+ \frac{18}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{+18} & = & \color{red}{70x} +49 \\\Leftrightarrow & 168x \color{red}{+18} \color{blue}{-18} \color{blue}{-70x} & = & \color{red}{70x} +49 \color{blue}{-70x} \color{blue}{-18} \\\Leftrightarrow & 168x-70x& = & 49-18 \\\Leftrightarrow & \color{red}{98} x& = & 31 \\\Leftrightarrow & x = \frac{31}{98} & & \\ & V = \left\{ \frac{31}{98} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{5}{11})& = & -3x+\frac{5}{6} \\\Leftrightarrow & -20x+\frac{20}{11}& = & -3x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1320}{ \color{blue}{66} }x+ \frac{120}{ \color{blue}{66} })& = & (\frac{-198}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1320x \color{red}{+120} & = & \color{red}{-198x} +55 \\\Leftrightarrow & -1320x \color{red}{+120} \color{blue}{-120} \color{blue}{+198x} & = & \color{red}{-198x} +55 \color{blue}{+198x} \color{blue}{-120} \\\Leftrightarrow & -1320x+198x& = & 55-120 \\\Leftrightarrow & \color{red}{-1122} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{-1122} & & \\\Leftrightarrow & x = \frac{65}{1122} & & \\ & V = \left\{ \frac{65}{1122} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{3}{5})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -6x-\frac{6}{5}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{-12} & = & \color{red}{70x} +15 \\\Leftrightarrow & -60x \color{red}{-12} \color{blue}{+12} \color{blue}{-70x} & = & \color{red}{70x} +15 \color{blue}{-70x} \color{blue}{+12} \\\Leftrightarrow & -60x-70x& = & 15+12 \\\Leftrightarrow & \color{red}{-130} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-130} & & \\\Leftrightarrow & x = \frac{-27}{130} & & \\ & V = \left\{ \frac{-27}{130} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{5}{11})& = & -8x+\frac{3}{8} \\\Leftrightarrow & 15x-\frac{15}{11}& = & -8x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1320}{ \color{blue}{88} }x- \frac{120}{ \color{blue}{88} })& = & (\frac{-704}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1320x \color{red}{-120} & = & \color{red}{-704x} +33 \\\Leftrightarrow & 1320x \color{red}{-120} \color{blue}{+120} \color{blue}{+704x} & = & \color{red}{-704x} +33 \color{blue}{+704x} \color{blue}{+120} \\\Leftrightarrow & 1320x+704x& = & 33+120 \\\Leftrightarrow & \color{red}{2024} x& = & 153 \\\Leftrightarrow & x = \frac{153}{2024} & & \\ & V = \left\{ \frac{153}{2024} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{2}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 24x-\frac{12}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{-60} & = & \color{red}{-275x} +66 \\\Leftrightarrow & 1320x \color{red}{-60} \color{blue}{+60} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{+60} \\\Leftrightarrow & 1320x+275x& = & 66+60 \\\Leftrightarrow & \color{red}{1595} x& = & 126 \\\Leftrightarrow & x = \frac{126}{1595} & & \\ & V = \left\{ \frac{126}{1595} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{4}{11})& = & 9x+\frac{2}{9} \\\Leftrightarrow & 8x+\frac{16}{11}& = & 9x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{792}{ \color{blue}{99} }x+ \frac{144}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 792x \color{red}{+144} & = & \color{red}{891x} +22 \\\Leftrightarrow & 792x \color{red}{+144} \color{blue}{-144} \color{blue}{-891x} & = & \color{red}{891x} +22 \color{blue}{-891x} \color{blue}{-144} \\\Leftrightarrow & 792x-891x& = & 22-144 \\\Leftrightarrow & \color{red}{-99} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{-99} & & \\\Leftrightarrow & x = \frac{122}{99} & & \\ & V = \left\{ \frac{122}{99} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{2}{5})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-132} & = & \color{red}{-275x} +25 \\\Leftrightarrow & 660x \color{red}{-132} \color{blue}{+132} \color{blue}{+275x} & = & \color{red}{-275x} +25 \color{blue}{+275x} \color{blue}{+132} \\\Leftrightarrow & 660x+275x& = & 25+132 \\\Leftrightarrow & \color{red}{935} x& = & 157 \\\Leftrightarrow & x = \frac{157}{935} & & \\ & V = \left\{ \frac{157}{935} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{3}{7})& = & 3x+\frac{9}{2} \\\Leftrightarrow & 10x+\frac{15}{7}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{140}{ \color{blue}{14} }x+ \frac{30}{ \color{blue}{14} })& = & (\frac{42}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 140x \color{red}{+30} & = & \color{red}{42x} +63 \\\Leftrightarrow & 140x \color{red}{+30} \color{blue}{-30} \color{blue}{-42x} & = & \color{red}{42x} +63 \color{blue}{-42x} \color{blue}{-30} \\\Leftrightarrow & 140x-42x& = & 63-30 \\\Leftrightarrow & \color{red}{98} x& = & 33 \\\Leftrightarrow & x = \frac{33}{98} & & \\ & V = \left\{ \frac{33}{98} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{4}{7})& = & 6x+\frac{8}{3} \\\Leftrightarrow & -25x+\frac{20}{7}& = & 6x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-525}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{126}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -525x \color{red}{+60} & = & \color{red}{126x} +56 \\\Leftrightarrow & -525x \color{red}{+60} \color{blue}{-60} \color{blue}{-126x} & = & \color{red}{126x} +56 \color{blue}{-126x} \color{blue}{-60} \\\Leftrightarrow & -525x-126x& = & 56-60 \\\Leftrightarrow & \color{red}{-651} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-651} & & \\\Leftrightarrow & x = \frac{4}{651} & & \\ & V = \left\{ \frac{4}{651} \right\} & \\\end{align}\)
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