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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{4}{7})& = & -9x+\frac{7}{2} \\\Leftrightarrow & -8x+\frac{16}{7}& = & -9x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-112}{ \color{blue}{14} }x+ \frac{32}{ \color{blue}{14} })& = & (\frac{-126}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -112x \color{red}{+32} & = & \color{red}{-126x} +49 \\\Leftrightarrow & -112x \color{red}{+32} \color{blue}{-32} \color{blue}{+126x} & = & \color{red}{-126x} +49 \color{blue}{+126x} \color{blue}{-32} \\\Leftrightarrow & -112x+126x& = & 49-32 \\\Leftrightarrow & \color{red}{14} x& = & 17 \\\Leftrightarrow & x = \frac{17}{14} & & \\ & V = \left\{ \frac{17}{14} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{3}{7})& = & 3x+\frac{9}{11} \\\Leftrightarrow & 16x-\frac{12}{7}& = & 3x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1232}{ \color{blue}{77} }x- \frac{132}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1232x \color{red}{-132} & = & \color{red}{231x} +63 \\\Leftrightarrow & 1232x \color{red}{-132} \color{blue}{+132} \color{blue}{-231x} & = & \color{red}{231x} +63 \color{blue}{-231x} \color{blue}{+132} \\\Leftrightarrow & 1232x-231x& = & 63+132 \\\Leftrightarrow & \color{red}{1001} x& = & 195 \\\Leftrightarrow & x = \frac{195}{1001} & & \\\Leftrightarrow & x = \frac{15}{77} & & \\ & V = \left\{ \frac{15}{77} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{8})& = & -8x+\frac{2}{3} \\\Leftrightarrow & 21x+\frac{21}{8}& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{504}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{-192}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 504x \color{red}{+63} & = & \color{red}{-192x} +16 \\\Leftrightarrow & 504x \color{red}{+63} \color{blue}{-63} \color{blue}{+192x} & = & \color{red}{-192x} +16 \color{blue}{+192x} \color{blue}{-63} \\\Leftrightarrow & 504x+192x& = & 16-63 \\\Leftrightarrow & \color{red}{696} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{696} & & \\ & V = \left\{ \frac{-47}{696} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{2}{11})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -12x-\frac{6}{11}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{18}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-18} & = & \color{red}{165x} +22 \\\Leftrightarrow & -396x \color{red}{-18} \color{blue}{+18} \color{blue}{-165x} & = & \color{red}{165x} +22 \color{blue}{-165x} \color{blue}{+18} \\\Leftrightarrow & -396x-165x& = & 22+18 \\\Leftrightarrow & \color{red}{-561} x& = & 40 \\\Leftrightarrow & x = \frac{40}{-561} & & \\\Leftrightarrow & x = \frac{-40}{561} & & \\ & V = \left\{ \frac{-40}{561} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{2}{11})& = & -7x+\frac{10}{9} \\\Leftrightarrow & 4x-\frac{4}{11}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{396}{ \color{blue}{99} }x- \frac{36}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 396x \color{red}{-36} & = & \color{red}{-693x} +110 \\\Leftrightarrow & 396x \color{red}{-36} \color{blue}{+36} \color{blue}{+693x} & = & \color{red}{-693x} +110 \color{blue}{+693x} \color{blue}{+36} \\\Leftrightarrow & 396x+693x& = & 110+36 \\\Leftrightarrow & \color{red}{1089} x& = & 146 \\\Leftrightarrow & x = \frac{146}{1089} & & \\ & V = \left\{ \frac{146}{1089} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{4}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 12x+\frac{24}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{48}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+48} & = & \color{red}{50x} +45 \\\Leftrightarrow & 120x \color{red}{+48} \color{blue}{-48} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{-48} \\\Leftrightarrow & 120x-50x& = & 45-48 \\\Leftrightarrow & \color{red}{70} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{70} & & \\ & V = \left\{ \frac{-3}{70} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{2}{5})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 30x-\frac{12}{5}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{300}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 300x \color{red}{-24} & = & \color{red}{70x} +45 \\\Leftrightarrow & 300x \color{red}{-24} \color{blue}{+24} \color{blue}{-70x} & = & \color{red}{70x} +45 \color{blue}{-70x} \color{blue}{+24} \\\Leftrightarrow & 300x-70x& = & 45+24 \\\Leftrightarrow & \color{red}{230} x& = & 69 \\\Leftrightarrow & x = \frac{69}{230} & & \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{3}{7})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 18x-\frac{18}{7}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{252}{ \color{blue}{14} }x- \frac{36}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 252x \color{red}{-36} & = & \color{red}{-98x} +49 \\\Leftrightarrow & 252x \color{red}{-36} \color{blue}{+36} \color{blue}{+98x} & = & \color{red}{-98x} +49 \color{blue}{+98x} \color{blue}{+36} \\\Leftrightarrow & 252x+98x& = & 49+36 \\\Leftrightarrow & \color{red}{350} x& = & 85 \\\Leftrightarrow & x = \frac{85}{350} & & \\\Leftrightarrow & x = \frac{17}{70} & & \\ & V = \left\{ \frac{17}{70} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{7})& = & 7x+\frac{9}{5} \\\Leftrightarrow & 24x+\frac{24}{7}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{840}{ \color{blue}{35} }x+ \frac{120}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 840x \color{red}{+120} & = & \color{red}{245x} +63 \\\Leftrightarrow & 840x \color{red}{+120} \color{blue}{-120} \color{blue}{-245x} & = & \color{red}{245x} +63 \color{blue}{-245x} \color{blue}{-120} \\\Leftrightarrow & 840x-245x& = & 63-120 \\\Leftrightarrow & \color{red}{595} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{595} & & \\ & V = \left\{ \frac{-57}{595} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{5})& = & -7x+\frac{9}{10} \\\Leftrightarrow & 12x+\frac{6}{5}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+12} & = & \color{red}{-70x} +9 \\\Leftrightarrow & 120x \color{red}{+12} \color{blue}{-12} \color{blue}{+70x} & = & \color{red}{-70x} +9 \color{blue}{+70x} \color{blue}{-12} \\\Leftrightarrow & 120x+70x& = & 9-12 \\\Leftrightarrow & \color{red}{190} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{190} & & \\ & V = \left\{ \frac{-3}{190} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{3}{8})& = & -8x+\frac{7}{11} \\\Leftrightarrow & -21x+\frac{21}{8}& = & -8x+\frac{7}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1848}{ \color{blue}{88} }x+ \frac{231}{ \color{blue}{88} })& = & (\frac{-704}{ \color{blue}{88} }x+ \frac{56}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1848x \color{red}{+231} & = & \color{red}{-704x} +56 \\\Leftrightarrow & -1848x \color{red}{+231} \color{blue}{-231} \color{blue}{+704x} & = & \color{red}{-704x} +56 \color{blue}{+704x} \color{blue}{-231} \\\Leftrightarrow & -1848x+704x& = & 56-231 \\\Leftrightarrow & \color{red}{-1144} x& = & -175 \\\Leftrightarrow & x = \frac{-175}{-1144} & & \\\Leftrightarrow & x = \frac{175}{1144} & & \\ & V = \left\{ \frac{175}{1144} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{4}{5})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -9x+\frac{12}{5}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-135}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -135x \color{red}{+36} & = & \color{red}{-105x} +10 \\\Leftrightarrow & -135x \color{red}{+36} \color{blue}{-36} \color{blue}{+105x} & = & \color{red}{-105x} +10 \color{blue}{+105x} \color{blue}{-36} \\\Leftrightarrow & -135x+105x& = & 10-36 \\\Leftrightarrow & \color{red}{-30} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-30} & & \\\Leftrightarrow & x = \frac{13}{15} & & \\ & V = \left\{ \frac{13}{15} \right\} & \\\end{align}\)
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