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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{2}{11})& = & -3x+\frac{6}{11} \\\Leftrightarrow & -35x-\frac{14}{11}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-385}{ \color{blue}{11} }x- \frac{14}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -385x \color{red}{-14} & = & \color{red}{-33x} +6 \\\Leftrightarrow & -385x \color{red}{-14} \color{blue}{+14} \color{blue}{+33x} & = & \color{red}{-33x} +6 \color{blue}{+33x} \color{blue}{+14} \\\Leftrightarrow & -385x+33x& = & 6+14 \\\Leftrightarrow & \color{red}{-352} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-352} & & \\\Leftrightarrow & x = \frac{-5}{88} & & \\ & V = \left\{ \frac{-5}{88} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{5}{7})& = & -7x+\frac{9}{10} \\\Leftrightarrow & -16x-\frac{20}{7}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1120}{ \color{blue}{70} }x- \frac{200}{ \color{blue}{70} })& = & (\frac{-490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1120x \color{red}{-200} & = & \color{red}{-490x} +63 \\\Leftrightarrow & -1120x \color{red}{-200} \color{blue}{+200} \color{blue}{+490x} & = & \color{red}{-490x} +63 \color{blue}{+490x} \color{blue}{+200} \\\Leftrightarrow & -1120x+490x& = & 63+200 \\\Leftrightarrow & \color{red}{-630} x& = & 263 \\\Leftrightarrow & x = \frac{263}{-630} & & \\\Leftrightarrow & x = \frac{-263}{630} & & \\ & V = \left\{ \frac{-263}{630} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{5})& = & 9x+\frac{2}{3} \\\Leftrightarrow & 4x-\frac{4}{5}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{60}{ \color{blue}{15} }x- \frac{12}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 60x \color{red}{-12} & = & \color{red}{135x} +10 \\\Leftrightarrow & 60x \color{red}{-12} \color{blue}{+12} \color{blue}{-135x} & = & \color{red}{135x} +10 \color{blue}{-135x} \color{blue}{+12} \\\Leftrightarrow & 60x-135x& = & 10+12 \\\Leftrightarrow & \color{red}{-75} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-75} & & \\\Leftrightarrow & x = \frac{-22}{75} & & \\ & V = \left\{ \frac{-22}{75} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{5}{9})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 20x+\frac{25}{9}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{900}{ \color{blue}{45} }x+ \frac{125}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 900x \color{red}{+125} & = & \color{red}{315x} +54 \\\Leftrightarrow & 900x \color{red}{+125} \color{blue}{-125} \color{blue}{-315x} & = & \color{red}{315x} +54 \color{blue}{-315x} \color{blue}{-125} \\\Leftrightarrow & 900x-315x& = & 54-125 \\\Leftrightarrow & \color{red}{585} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{585} & & \\ & V = \left\{ \frac{-71}{585} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{5}{11})& = & 9x+\frac{5}{7} \\\Leftrightarrow & -35x+\frac{35}{11}& = & 9x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2695}{ \color{blue}{77} }x+ \frac{245}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2695x \color{red}{+245} & = & \color{red}{693x} +55 \\\Leftrightarrow & -2695x \color{red}{+245} \color{blue}{-245} \color{blue}{-693x} & = & \color{red}{693x} +55 \color{blue}{-693x} \color{blue}{-245} \\\Leftrightarrow & -2695x-693x& = & 55-245 \\\Leftrightarrow & \color{red}{-3388} x& = & -190 \\\Leftrightarrow & x = \frac{-190}{-3388} & & \\\Leftrightarrow & x = \frac{95}{1694} & & \\ & V = \left\{ \frac{95}{1694} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{2}{5})& = & 4x+\frac{5}{2} \\\Leftrightarrow & 35x+\frac{14}{5}& = & 4x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{350}{ \color{blue}{10} }x+ \frac{28}{ \color{blue}{10} })& = & (\frac{40}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 350x \color{red}{+28} & = & \color{red}{40x} +25 \\\Leftrightarrow & 350x \color{red}{+28} \color{blue}{-28} \color{blue}{-40x} & = & \color{red}{40x} +25 \color{blue}{-40x} \color{blue}{-28} \\\Leftrightarrow & 350x-40x& = & 25-28 \\\Leftrightarrow & \color{red}{310} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{310} & & \\ & V = \left\{ \frac{-3}{310} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{3}{4})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 20x-\frac{15}{4}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{400}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 400x \color{red}{-75} & = & \color{red}{140x} +24 \\\Leftrightarrow & 400x \color{red}{-75} \color{blue}{+75} \color{blue}{-140x} & = & \color{red}{140x} +24 \color{blue}{-140x} \color{blue}{+75} \\\Leftrightarrow & 400x-140x& = & 24+75 \\\Leftrightarrow & \color{red}{260} x& = & 99 \\\Leftrightarrow & x = \frac{99}{260} & & \\ & V = \left\{ \frac{99}{260} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{4}{5})& = & 7x+\frac{7}{9} \\\Leftrightarrow & -30x-\frac{24}{5}& = & 7x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1350}{ \color{blue}{45} }x- \frac{216}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1350x \color{red}{-216} & = & \color{red}{315x} +35 \\\Leftrightarrow & -1350x \color{red}{-216} \color{blue}{+216} \color{blue}{-315x} & = & \color{red}{315x} +35 \color{blue}{-315x} \color{blue}{+216} \\\Leftrightarrow & -1350x-315x& = & 35+216 \\\Leftrightarrow & \color{red}{-1665} x& = & 251 \\\Leftrightarrow & x = \frac{251}{-1665} & & \\\Leftrightarrow & x = \frac{-251}{1665} & & \\ & V = \left\{ \frac{-251}{1665} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{3}{4})& = & -7x+\frac{4}{11} \\\Leftrightarrow & -10x+\frac{15}{4}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-440}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{16}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -440x \color{red}{+165} & = & \color{red}{-308x} +16 \\\Leftrightarrow & -440x \color{red}{+165} \color{blue}{-165} \color{blue}{+308x} & = & \color{red}{-308x} +16 \color{blue}{+308x} \color{blue}{-165} \\\Leftrightarrow & -440x+308x& = & 16-165 \\\Leftrightarrow & \color{red}{-132} x& = & -149 \\\Leftrightarrow & x = \frac{-149}{-132} & & \\\Leftrightarrow & x = \frac{149}{132} & & \\ & V = \left\{ \frac{149}{132} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{3}{7})& = & 7x+\frac{9}{10} \\\Leftrightarrow & 15x-\frac{15}{7}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1050}{ \color{blue}{70} }x- \frac{150}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1050x \color{red}{-150} & = & \color{red}{490x} +63 \\\Leftrightarrow & 1050x \color{red}{-150} \color{blue}{+150} \color{blue}{-490x} & = & \color{red}{490x} +63 \color{blue}{-490x} \color{blue}{+150} \\\Leftrightarrow & 1050x-490x& = & 63+150 \\\Leftrightarrow & \color{red}{560} x& = & 213 \\\Leftrightarrow & x = \frac{213}{560} & & \\ & V = \left\{ \frac{213}{560} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{4}{11})& = & 9x+\frac{5}{2} \\\Leftrightarrow & 10x-\frac{8}{11}& = & 9x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{220}{ \color{blue}{22} }x- \frac{16}{ \color{blue}{22} })& = & (\frac{198}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 220x \color{red}{-16} & = & \color{red}{198x} +55 \\\Leftrightarrow & 220x \color{red}{-16} \color{blue}{+16} \color{blue}{-198x} & = & \color{red}{198x} +55 \color{blue}{-198x} \color{blue}{+16} \\\Leftrightarrow & 220x-198x& = & 55+16 \\\Leftrightarrow & \color{red}{22} x& = & 71 \\\Leftrightarrow & x = \frac{71}{22} & & \\ & V = \left\{ \frac{71}{22} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{11})& = & 7x+\frac{5}{7} \\\Leftrightarrow & -6x+\frac{15}{11}& = & 7x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{105}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+105} & = & \color{red}{539x} +55 \\\Leftrightarrow & -462x \color{red}{+105} \color{blue}{-105} \color{blue}{-539x} & = & \color{red}{539x} +55 \color{blue}{-539x} \color{blue}{-105} \\\Leftrightarrow & -462x-539x& = & 55-105 \\\Leftrightarrow & \color{red}{-1001} x& = & -50 \\\Leftrightarrow & x = \frac{-50}{-1001} & & \\\Leftrightarrow & x = \frac{50}{1001} & & \\ & V = \left\{ \frac{50}{1001} \right\} & \\\end{align}\)
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