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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{4}{9})& = & -9x+\frac{6}{5} \\\Leftrightarrow & 14x+\frac{28}{9}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{630}{ \color{blue}{45} }x+ \frac{140}{ \color{blue}{45} })& = & (\frac{-405}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 630x \color{red}{+140} & = & \color{red}{-405x} +54 \\\Leftrightarrow & 630x \color{red}{+140} \color{blue}{-140} \color{blue}{+405x} & = & \color{red}{-405x} +54 \color{blue}{+405x} \color{blue}{-140} \\\Leftrightarrow & 630x+405x& = & 54-140 \\\Leftrightarrow & \color{red}{1035} x& = & -86 \\\Leftrightarrow & x = \frac{-86}{1035} & & \\ & V = \left\{ \frac{-86}{1035} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{5}{3})& = & -2x+\frac{8}{11} \\\Leftrightarrow & 15x+\frac{25}{3}& = & -2x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x+ \frac{275}{ \color{blue}{33} })& = & (\frac{-66}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{+275} & = & \color{red}{-66x} +24 \\\Leftrightarrow & 495x \color{red}{+275} \color{blue}{-275} \color{blue}{+66x} & = & \color{red}{-66x} +24 \color{blue}{+66x} \color{blue}{-275} \\\Leftrightarrow & 495x+66x& = & 24-275 \\\Leftrightarrow & \color{red}{561} x& = & -251 \\\Leftrightarrow & x = \frac{-251}{561} & & \\ & V = \left\{ \frac{-251}{561} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{5}{8})& = & 3x+\frac{3}{5} \\\Leftrightarrow & -35x+\frac{35}{8}& = & 3x+\frac{3}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1400}{ \color{blue}{40} }x+ \frac{175}{ \color{blue}{40} })& = & (\frac{120}{ \color{blue}{40} }x+ \frac{24}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1400x \color{red}{+175} & = & \color{red}{120x} +24 \\\Leftrightarrow & -1400x \color{red}{+175} \color{blue}{-175} \color{blue}{-120x} & = & \color{red}{120x} +24 \color{blue}{-120x} \color{blue}{-175} \\\Leftrightarrow & -1400x-120x& = & 24-175 \\\Leftrightarrow & \color{red}{-1520} x& = & -151 \\\Leftrightarrow & x = \frac{-151}{-1520} & & \\\Leftrightarrow & x = \frac{151}{1520} & & \\ & V = \left\{ \frac{151}{1520} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{5})& = & 7x+\frac{7}{12} \\\Leftrightarrow & -6x+\frac{12}{5}& = & 7x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-360}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{420}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -360x \color{red}{+144} & = & \color{red}{420x} +35 \\\Leftrightarrow & -360x \color{red}{+144} \color{blue}{-144} \color{blue}{-420x} & = & \color{red}{420x} +35 \color{blue}{-420x} \color{blue}{-144} \\\Leftrightarrow & -360x-420x& = & 35-144 \\\Leftrightarrow & \color{red}{-780} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{-780} & & \\\Leftrightarrow & x = \frac{109}{780} & & \\ & V = \left\{ \frac{109}{780} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{3}{8})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 10x+\frac{15}{8}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{560}{ \color{blue}{56} }x+ \frac{105}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 560x \color{red}{+105} & = & \color{red}{392x} +80 \\\Leftrightarrow & 560x \color{red}{+105} \color{blue}{-105} \color{blue}{-392x} & = & \color{red}{392x} +80 \color{blue}{-392x} \color{blue}{-105} \\\Leftrightarrow & 560x-392x& = & 80-105 \\\Leftrightarrow & \color{red}{168} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{168} & & \\ & V = \left\{ \frac{-25}{168} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{4}{5})& = & 4x+\frac{3}{4} \\\Leftrightarrow & 21x-\frac{28}{5}& = & 4x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{420}{ \color{blue}{20} }x- \frac{112}{ \color{blue}{20} })& = & (\frac{80}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 420x \color{red}{-112} & = & \color{red}{80x} +15 \\\Leftrightarrow & 420x \color{red}{-112} \color{blue}{+112} \color{blue}{-80x} & = & \color{red}{80x} +15 \color{blue}{-80x} \color{blue}{+112} \\\Leftrightarrow & 420x-80x& = & 15+112 \\\Leftrightarrow & \color{red}{340} x& = & 127 \\\Leftrightarrow & x = \frac{127}{340} & & \\ & V = \left\{ \frac{127}{340} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{2}{3})& = & -9x+\frac{4}{9} \\\Leftrightarrow & 35x+\frac{14}{3}& = & -9x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{315}{ \color{blue}{9} }x+ \frac{42}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 315x \color{red}{+42} & = & \color{red}{-81x} +4 \\\Leftrightarrow & 315x \color{red}{+42} \color{blue}{-42} \color{blue}{+81x} & = & \color{red}{-81x} +4 \color{blue}{+81x} \color{blue}{-42} \\\Leftrightarrow & 315x+81x& = & 4-42 \\\Leftrightarrow & \color{red}{396} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{396} & & \\\Leftrightarrow & x = \frac{-19}{198} & & \\ & V = \left\{ \frac{-19}{198} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{5}{11})& = & 9x+\frac{7}{2} \\\Leftrightarrow & -8x+\frac{10}{11}& = & 9x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-176}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} })& = & (\frac{198}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -176x \color{red}{+20} & = & \color{red}{198x} +77 \\\Leftrightarrow & -176x \color{red}{+20} \color{blue}{-20} \color{blue}{-198x} & = & \color{red}{198x} +77 \color{blue}{-198x} \color{blue}{-20} \\\Leftrightarrow & -176x-198x& = & 77-20 \\\Leftrightarrow & \color{red}{-374} x& = & 57 \\\Leftrightarrow & x = \frac{57}{-374} & & \\\Leftrightarrow & x = \frac{-57}{374} & & \\ & V = \left\{ \frac{-57}{374} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{4}{9})& = & -3x+\frac{9}{4} \\\Leftrightarrow & -8x-\frac{8}{9}& = & -3x+\frac{9}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-288}{ \color{blue}{36} }x- \frac{32}{ \color{blue}{36} })& = & (\frac{-108}{ \color{blue}{36} }x+ \frac{81}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -288x \color{red}{-32} & = & \color{red}{-108x} +81 \\\Leftrightarrow & -288x \color{red}{-32} \color{blue}{+32} \color{blue}{+108x} & = & \color{red}{-108x} +81 \color{blue}{+108x} \color{blue}{+32} \\\Leftrightarrow & -288x+108x& = & 81+32 \\\Leftrightarrow & \color{red}{-180} x& = & 113 \\\Leftrightarrow & x = \frac{113}{-180} & & \\\Leftrightarrow & x = \frac{-113}{180} & & \\ & V = \left\{ \frac{-113}{180} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{11})& = & 3x+\frac{6}{11} \\\Leftrightarrow & 10x+\frac{25}{11}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{110}{ \color{blue}{11} }x+ \frac{25}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 110x \color{red}{+25} & = & \color{red}{33x} +6 \\\Leftrightarrow & 110x \color{red}{+25} \color{blue}{-25} \color{blue}{-33x} & = & \color{red}{33x} +6 \color{blue}{-33x} \color{blue}{-25} \\\Leftrightarrow & 110x-33x& = & 6-25 \\\Leftrightarrow & \color{red}{77} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{77} & & \\ & V = \left\{ \frac{-19}{77} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{3})& = & 3x+\frac{2}{9} \\\Leftrightarrow & 20x+\frac{25}{3}& = & 3x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{75}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+75} & = & \color{red}{27x} +2 \\\Leftrightarrow & 180x \color{red}{+75} \color{blue}{-75} \color{blue}{-27x} & = & \color{red}{27x} +2 \color{blue}{-27x} \color{blue}{-75} \\\Leftrightarrow & 180x-27x& = & 2-75 \\\Leftrightarrow & \color{red}{153} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{153} & & \\ & V = \left\{ \frac{-73}{153} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{4}{11})& = & 9x+\frac{9}{4} \\\Leftrightarrow & -8x+\frac{16}{11}& = & 9x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-352}{ \color{blue}{44} }x+ \frac{64}{ \color{blue}{44} })& = & (\frac{396}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -352x \color{red}{+64} & = & \color{red}{396x} +99 \\\Leftrightarrow & -352x \color{red}{+64} \color{blue}{-64} \color{blue}{-396x} & = & \color{red}{396x} +99 \color{blue}{-396x} \color{blue}{-64} \\\Leftrightarrow & -352x-396x& = & 99-64 \\\Leftrightarrow & \color{red}{-748} x& = & 35 \\\Leftrightarrow & x = \frac{35}{-748} & & \\\Leftrightarrow & x = \frac{-35}{748} & & \\ & V = \left\{ \frac{-35}{748} \right\} & \\\end{align}\)
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