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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{4}{11})& = & 7x+\frac{7}{8} \\\Leftrightarrow & -20x+\frac{20}{11}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1760}{ \color{blue}{88} }x+ \frac{160}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1760x \color{red}{+160} & = & \color{red}{616x} +77 \\\Leftrightarrow & -1760x \color{red}{+160} \color{blue}{-160} \color{blue}{-616x} & = & \color{red}{616x} +77 \color{blue}{-616x} \color{blue}{-160} \\\Leftrightarrow & -1760x-616x& = & 77-160 \\\Leftrightarrow & \color{red}{-2376} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{-2376} & & \\\Leftrightarrow & x = \frac{83}{2376} & & \\ & V = \left\{ \frac{83}{2376} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{3}{11})& = & 8x+\frac{2}{7} \\\Leftrightarrow & 9x-\frac{9}{11}& = & 8x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{693}{ \color{blue}{77} }x- \frac{63}{ \color{blue}{77} })& = & (\frac{616}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 693x \color{red}{-63} & = & \color{red}{616x} +22 \\\Leftrightarrow & 693x \color{red}{-63} \color{blue}{+63} \color{blue}{-616x} & = & \color{red}{616x} +22 \color{blue}{-616x} \color{blue}{+63} \\\Leftrightarrow & 693x-616x& = & 22+63 \\\Leftrightarrow & \color{red}{77} x& = & 85 \\\Leftrightarrow & x = \frac{85}{77} & & \\ & V = \left\{ \frac{85}{77} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{4}{5})& = & -5x+\frac{8}{7} \\\Leftrightarrow & 6x+\frac{12}{5}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{+84} & = & \color{red}{-175x} +40 \\\Leftrightarrow & 210x \color{red}{+84} \color{blue}{-84} \color{blue}{+175x} & = & \color{red}{-175x} +40 \color{blue}{+175x} \color{blue}{-84} \\\Leftrightarrow & 210x+175x& = & 40-84 \\\Leftrightarrow & \color{red}{385} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{385} & & \\\Leftrightarrow & x = \frac{-4}{35} & & \\ & V = \left\{ \frac{-4}{35} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{2}{7})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 6x+\frac{6}{7}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{+30} & = & \color{red}{-175x} +42 \\\Leftrightarrow & 210x \color{red}{+30} \color{blue}{-30} \color{blue}{+175x} & = & \color{red}{-175x} +42 \color{blue}{+175x} \color{blue}{-30} \\\Leftrightarrow & 210x+175x& = & 42-30 \\\Leftrightarrow & \color{red}{385} x& = & 12 \\\Leftrightarrow & x = \frac{12}{385} & & \\ & V = \left\{ \frac{12}{385} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{5}{3})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 8x+\frac{10}{3}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{+110} & = & \color{red}{165x} +18 \\\Leftrightarrow & 264x \color{red}{+110} \color{blue}{-110} \color{blue}{-165x} & = & \color{red}{165x} +18 \color{blue}{-165x} \color{blue}{-110} \\\Leftrightarrow & 264x-165x& = & 18-110 \\\Leftrightarrow & \color{red}{99} x& = & -92 \\\Leftrightarrow & x = \frac{-92}{99} & & \\ & V = \left\{ \frac{-92}{99} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{4}{5})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -6x+\frac{12}{5}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{+132} & = & \color{red}{385x} +30 \\\Leftrightarrow & -330x \color{red}{+132} \color{blue}{-132} \color{blue}{-385x} & = & \color{red}{385x} +30 \color{blue}{-385x} \color{blue}{-132} \\\Leftrightarrow & -330x-385x& = & 30-132 \\\Leftrightarrow & \color{red}{-715} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{-715} & & \\\Leftrightarrow & x = \frac{102}{715} & & \\ & V = \left\{ \frac{102}{715} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{3}{4})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -10x-\frac{15}{4}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-40}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{28}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -40x \color{red}{-15} & = & \color{red}{28x} +3 \\\Leftrightarrow & -40x \color{red}{-15} \color{blue}{+15} \color{blue}{-28x} & = & \color{red}{28x} +3 \color{blue}{-28x} \color{blue}{+15} \\\Leftrightarrow & -40x-28x& = & 3+15 \\\Leftrightarrow & \color{red}{-68} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-68} & & \\\Leftrightarrow & x = \frac{-9}{34} & & \\ & V = \left\{ \frac{-9}{34} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{5}{7})& = & 7x+\frac{5}{12} \\\Leftrightarrow & -6x+\frac{10}{7}& = & 7x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-504}{ \color{blue}{84} }x+ \frac{120}{ \color{blue}{84} })& = & (\frac{588}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -504x \color{red}{+120} & = & \color{red}{588x} +35 \\\Leftrightarrow & -504x \color{red}{+120} \color{blue}{-120} \color{blue}{-588x} & = & \color{red}{588x} +35 \color{blue}{-588x} \color{blue}{-120} \\\Leftrightarrow & -504x-588x& = & 35-120 \\\Leftrightarrow & \color{red}{-1092} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{-1092} & & \\\Leftrightarrow & x = \frac{85}{1092} & & \\ & V = \left\{ \frac{85}{1092} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{5})& = & -7x+\frac{4}{5} \\\Leftrightarrow & 30x+\frac{24}{5}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{150}{ \color{blue}{5} }x+ \frac{24}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 150x \color{red}{+24} & = & \color{red}{-35x} +4 \\\Leftrightarrow & 150x \color{red}{+24} \color{blue}{-24} \color{blue}{+35x} & = & \color{red}{-35x} +4 \color{blue}{+35x} \color{blue}{-24} \\\Leftrightarrow & 150x+35x& = & 4-24 \\\Leftrightarrow & \color{red}{185} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{185} & & \\\Leftrightarrow & x = \frac{-4}{37} & & \\ & V = \left\{ \frac{-4}{37} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{3}{10})& = & 6x+\frac{3}{8} \\\Leftrightarrow & 35x-\frac{21}{10}& = & 6x+\frac{3}{8} \\ & & & \text{kgv van noemers 10 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{1400}{ \color{blue}{40} }x- \frac{84}{ \color{blue}{40} })& = & (\frac{240}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 1400x \color{red}{-84} & = & \color{red}{240x} +15 \\\Leftrightarrow & 1400x \color{red}{-84} \color{blue}{+84} \color{blue}{-240x} & = & \color{red}{240x} +15 \color{blue}{-240x} \color{blue}{+84} \\\Leftrightarrow & 1400x-240x& = & 15+84 \\\Leftrightarrow & \color{red}{1160} x& = & 99 \\\Leftrightarrow & x = \frac{99}{1160} & & \\ & V = \left\{ \frac{99}{1160} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{5}{11})& = & -7x+\frac{10}{11} \\\Leftrightarrow & -9x+\frac{15}{11}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-99}{ \color{blue}{11} }x+ \frac{15}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -99x \color{red}{+15} & = & \color{red}{-77x} +10 \\\Leftrightarrow & -99x \color{red}{+15} \color{blue}{-15} \color{blue}{+77x} & = & \color{red}{-77x} +10 \color{blue}{+77x} \color{blue}{-15} \\\Leftrightarrow & -99x+77x& = & 10-15 \\\Leftrightarrow & \color{red}{-22} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-22} & & \\\Leftrightarrow & x = \frac{5}{22} & & \\ & V = \left\{ \frac{5}{22} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{2}{5})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 18x+\frac{12}{5}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{+36} & = & \color{red}{-75x} +50 \\\Leftrightarrow & 270x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +50 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & 270x+75x& = & 50-36 \\\Leftrightarrow & \color{red}{345} x& = & 14 \\\Leftrightarrow & x = \frac{14}{345} & & \\ & V = \left\{ \frac{14}{345} \right\} & \\\end{align}\)
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