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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{3}{11})& = & -5x+\frac{5}{8} \\\Leftrightarrow & 12x-\frac{12}{11}& = & -5x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1056}{ \color{blue}{88} }x- \frac{96}{ \color{blue}{88} })& = & (\frac{-440}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1056x \color{red}{-96} & = & \color{red}{-440x} +55 \\\Leftrightarrow & 1056x \color{red}{-96} \color{blue}{+96} \color{blue}{+440x} & = & \color{red}{-440x} +55 \color{blue}{+440x} \color{blue}{+96} \\\Leftrightarrow & 1056x+440x& = & 55+96 \\\Leftrightarrow & \color{red}{1496} x& = & 151 \\\Leftrightarrow & x = \frac{151}{1496} & & \\ & V = \left\{ \frac{151}{1496} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{3}{5})& = & -5x+\frac{10}{9} \\\Leftrightarrow & 16x-\frac{12}{5}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{720}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 720x \color{red}{-108} & = & \color{red}{-225x} +50 \\\Leftrightarrow & 720x \color{red}{-108} \color{blue}{+108} \color{blue}{+225x} & = & \color{red}{-225x} +50 \color{blue}{+225x} \color{blue}{+108} \\\Leftrightarrow & 720x+225x& = & 50+108 \\\Leftrightarrow & \color{red}{945} x& = & 158 \\\Leftrightarrow & x = \frac{158}{945} & & \\ & V = \left\{ \frac{158}{945} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{7})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 12x-\frac{30}{7}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{-30} & = & \color{red}{-35x} +3 \\\Leftrightarrow & 84x \color{red}{-30} \color{blue}{+30} \color{blue}{+35x} & = & \color{red}{-35x} +3 \color{blue}{+35x} \color{blue}{+30} \\\Leftrightarrow & 84x+35x& = & 3+30 \\\Leftrightarrow & \color{red}{119} x& = & 33 \\\Leftrightarrow & x = \frac{33}{119} & & \\ & V = \left\{ \frac{33}{119} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{5}{11})& = & 7x+\frac{8}{7} \\\Leftrightarrow & 15x+\frac{15}{11}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x+ \frac{105}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{+105} & = & \color{red}{539x} +88 \\\Leftrightarrow & 1155x \color{red}{+105} \color{blue}{-105} \color{blue}{-539x} & = & \color{red}{539x} +88 \color{blue}{-539x} \color{blue}{-105} \\\Leftrightarrow & 1155x-539x& = & 88-105 \\\Leftrightarrow & \color{red}{616} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{616} & & \\ & V = \left\{ \frac{-17}{616} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{11})& = & -7x+\frac{10}{11} \\\Leftrightarrow & -10x+\frac{4}{11}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-110}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -110x \color{red}{+4} & = & \color{red}{-77x} +10 \\\Leftrightarrow & -110x \color{red}{+4} \color{blue}{-4} \color{blue}{+77x} & = & \color{red}{-77x} +10 \color{blue}{+77x} \color{blue}{-4} \\\Leftrightarrow & -110x+77x& = & 10-4 \\\Leftrightarrow & \color{red}{-33} x& = & 6 \\\Leftrightarrow & x = \frac{6}{-33} & & \\\Leftrightarrow & x = \frac{-2}{11} & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{5})& = & -5x+\frac{3}{8} \\\Leftrightarrow & 6x+\frac{6}{5}& = & -5x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{240}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 240x \color{red}{+48} & = & \color{red}{-200x} +15 \\\Leftrightarrow & 240x \color{red}{+48} \color{blue}{-48} \color{blue}{+200x} & = & \color{red}{-200x} +15 \color{blue}{+200x} \color{blue}{-48} \\\Leftrightarrow & 240x+200x& = & 15-48 \\\Leftrightarrow & \color{red}{440} x& = & -33 \\\Leftrightarrow & x = \frac{-33}{440} & & \\\Leftrightarrow & x = \frac{-3}{40} & & \\ & V = \left\{ \frac{-3}{40} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{2}{11})& = & 5x+\frac{9}{10} \\\Leftrightarrow & -12x+\frac{12}{11}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1320}{ \color{blue}{110} }x+ \frac{120}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1320x \color{red}{+120} & = & \color{red}{550x} +99 \\\Leftrightarrow & -1320x \color{red}{+120} \color{blue}{-120} \color{blue}{-550x} & = & \color{red}{550x} +99 \color{blue}{-550x} \color{blue}{-120} \\\Leftrightarrow & -1320x-550x& = & 99-120 \\\Leftrightarrow & \color{red}{-1870} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-1870} & & \\\Leftrightarrow & x = \frac{21}{1870} & & \\ & V = \left\{ \frac{21}{1870} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{4}{11})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -10x+\frac{8}{11}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-990}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -990x \color{red}{+72} & = & \color{red}{-693x} +110 \\\Leftrightarrow & -990x \color{red}{+72} \color{blue}{-72} \color{blue}{+693x} & = & \color{red}{-693x} +110 \color{blue}{+693x} \color{blue}{-72} \\\Leftrightarrow & -990x+693x& = & 110-72 \\\Leftrightarrow & \color{red}{-297} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-297} & & \\\Leftrightarrow & x = \frac{-38}{297} & & \\ & V = \left\{ \frac{-38}{297} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{3}{5})& = & -8x+\frac{5}{11} \\\Leftrightarrow & -18x+\frac{18}{5}& = & -8x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x+ \frac{198}{ \color{blue}{55} })& = & (\frac{-440}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{+198} & = & \color{red}{-440x} +25 \\\Leftrightarrow & -990x \color{red}{+198} \color{blue}{-198} \color{blue}{+440x} & = & \color{red}{-440x} +25 \color{blue}{+440x} \color{blue}{-198} \\\Leftrightarrow & -990x+440x& = & 25-198 \\\Leftrightarrow & \color{red}{-550} x& = & -173 \\\Leftrightarrow & x = \frac{-173}{-550} & & \\\Leftrightarrow & x = \frac{173}{550} & & \\ & V = \left\{ \frac{173}{550} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{2}{5})& = & 5x+\frac{5}{6} \\\Leftrightarrow & 24x-\frac{12}{5}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{720}{ \color{blue}{30} }x- \frac{72}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 720x \color{red}{-72} & = & \color{red}{150x} +25 \\\Leftrightarrow & 720x \color{red}{-72} \color{blue}{+72} \color{blue}{-150x} & = & \color{red}{150x} +25 \color{blue}{-150x} \color{blue}{+72} \\\Leftrightarrow & 720x-150x& = & 25+72 \\\Leftrightarrow & \color{red}{570} x& = & 97 \\\Leftrightarrow & x = \frac{97}{570} & & \\ & V = \left\{ \frac{97}{570} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{2}{7})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -10x+\frac{10}{7}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{+110} & = & \color{red}{539x} +56 \\\Leftrightarrow & -770x \color{red}{+110} \color{blue}{-110} \color{blue}{-539x} & = & \color{red}{539x} +56 \color{blue}{-539x} \color{blue}{-110} \\\Leftrightarrow & -770x-539x& = & 56-110 \\\Leftrightarrow & \color{red}{-1309} x& = & -54 \\\Leftrightarrow & x = \frac{-54}{-1309} & & \\\Leftrightarrow & x = \frac{54}{1309} & & \\ & V = \left\{ \frac{54}{1309} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{4}{11})& = & -3x+\frac{2}{7} \\\Leftrightarrow & 10x-\frac{20}{11}& = & -3x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{140}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-140} & = & \color{red}{-231x} +22 \\\Leftrightarrow & 770x \color{red}{-140} \color{blue}{+140} \color{blue}{+231x} & = & \color{red}{-231x} +22 \color{blue}{+231x} \color{blue}{+140} \\\Leftrightarrow & 770x+231x& = & 22+140 \\\Leftrightarrow & \color{red}{1001} x& = & 162 \\\Leftrightarrow & x = \frac{162}{1001} & & \\ & V = \left\{ \frac{162}{1001} \right\} & \\\end{align}\)
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