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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{3}{7})& = & -7x+\frac{4}{5} \\\Leftrightarrow & 12x-\frac{9}{7}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{45}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-45} & = & \color{red}{-245x} +28 \\\Leftrightarrow & 420x \color{red}{-45} \color{blue}{+45} \color{blue}{+245x} & = & \color{red}{-245x} +28 \color{blue}{+245x} \color{blue}{+45} \\\Leftrightarrow & 420x+245x& = & 28+45 \\\Leftrightarrow & \color{red}{665} x& = & 73 \\\Leftrightarrow & x = \frac{73}{665} & & \\ & V = \left\{ \frac{73}{665} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{7})& = & 5x+\frac{9}{10} \\\Leftrightarrow & 12x+\frac{6}{7}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{840}{ \color{blue}{70} }x+ \frac{60}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 840x \color{red}{+60} & = & \color{red}{350x} +63 \\\Leftrightarrow & 840x \color{red}{+60} \color{blue}{-60} \color{blue}{-350x} & = & \color{red}{350x} +63 \color{blue}{-350x} \color{blue}{-60} \\\Leftrightarrow & 840x-350x& = & 63-60 \\\Leftrightarrow & \color{red}{490} x& = & 3 \\\Leftrightarrow & x = \frac{3}{490} & & \\ & V = \left\{ \frac{3}{490} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{9})& = & -5x+\frac{3}{5} \\\Leftrightarrow & -4x-\frac{8}{9}& = & -5x+\frac{3}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-180}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{27}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -180x \color{red}{-40} & = & \color{red}{-225x} +27 \\\Leftrightarrow & -180x \color{red}{-40} \color{blue}{+40} \color{blue}{+225x} & = & \color{red}{-225x} +27 \color{blue}{+225x} \color{blue}{+40} \\\Leftrightarrow & -180x+225x& = & 27+40 \\\Leftrightarrow & \color{red}{45} x& = & 67 \\\Leftrightarrow & x = \frac{67}{45} & & \\ & V = \left\{ \frac{67}{45} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{4}{5})& = & -5x+\frac{9}{4} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{-48} & = & \color{red}{-100x} +45 \\\Leftrightarrow & -240x \color{red}{-48} \color{blue}{+48} \color{blue}{+100x} & = & \color{red}{-100x} +45 \color{blue}{+100x} \color{blue}{+48} \\\Leftrightarrow & -240x+100x& = & 45+48 \\\Leftrightarrow & \color{red}{-140} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-140} & & \\\Leftrightarrow & x = \frac{-93}{140} & & \\ & V = \left\{ \frac{-93}{140} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{2}{11})& = & 3x+\frac{3}{11} \\\Leftrightarrow & -8x-\frac{8}{11}& = & 3x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-88}{ \color{blue}{11} }x- \frac{8}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -88x \color{red}{-8} & = & \color{red}{33x} +3 \\\Leftrightarrow & -88x \color{red}{-8} \color{blue}{+8} \color{blue}{-33x} & = & \color{red}{33x} +3 \color{blue}{-33x} \color{blue}{+8} \\\Leftrightarrow & -88x-33x& = & 3+8 \\\Leftrightarrow & \color{red}{-121} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-121} & & \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{3}{4})& = & 8x+\frac{2}{3} \\\Leftrightarrow & 25x-\frac{15}{4}& = & 8x+\frac{2}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{300}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 300x \color{red}{-45} & = & \color{red}{96x} +8 \\\Leftrightarrow & 300x \color{red}{-45} \color{blue}{+45} \color{blue}{-96x} & = & \color{red}{96x} +8 \color{blue}{-96x} \color{blue}{+45} \\\Leftrightarrow & 300x-96x& = & 8+45 \\\Leftrightarrow & \color{red}{204} x& = & 53 \\\Leftrightarrow & x = \frac{53}{204} & & \\ & V = \left\{ \frac{53}{204} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{3}{10})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -6x-\frac{9}{10}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-180}{ \color{blue}{30} }x- \frac{27}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{80}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -180x \color{red}{-27} & = & \color{red}{210x} +80 \\\Leftrightarrow & -180x \color{red}{-27} \color{blue}{+27} \color{blue}{-210x} & = & \color{red}{210x} +80 \color{blue}{-210x} \color{blue}{+27} \\\Leftrightarrow & -180x-210x& = & 80+27 \\\Leftrightarrow & \color{red}{-390} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-390} & & \\\Leftrightarrow & x = \frac{-107}{390} & & \\ & V = \left\{ \frac{-107}{390} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{3}{5})& = & 6x+\frac{2}{3} \\\Leftrightarrow & -35x-\frac{21}{5}& = & 6x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-525}{ \color{blue}{15} }x- \frac{63}{ \color{blue}{15} })& = & (\frac{90}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -525x \color{red}{-63} & = & \color{red}{90x} +10 \\\Leftrightarrow & -525x \color{red}{-63} \color{blue}{+63} \color{blue}{-90x} & = & \color{red}{90x} +10 \color{blue}{-90x} \color{blue}{+63} \\\Leftrightarrow & -525x-90x& = & 10+63 \\\Leftrightarrow & \color{red}{-615} x& = & 73 \\\Leftrightarrow & x = \frac{73}{-615} & & \\\Leftrightarrow & x = \frac{-73}{615} & & \\ & V = \left\{ \frac{-73}{615} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{3}{11})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -18x-\frac{18}{11}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1782}{ \color{blue}{99} }x- \frac{162}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1782x \color{red}{-162} & = & \color{red}{-693x} +110 \\\Leftrightarrow & -1782x \color{red}{-162} \color{blue}{+162} \color{blue}{+693x} & = & \color{red}{-693x} +110 \color{blue}{+693x} \color{blue}{+162} \\\Leftrightarrow & -1782x+693x& = & 110+162 \\\Leftrightarrow & \color{red}{-1089} x& = & 272 \\\Leftrightarrow & x = \frac{272}{-1089} & & \\\Leftrightarrow & x = \frac{-272}{1089} & & \\ & V = \left\{ \frac{-272}{1089} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{11})& = & 7x+\frac{5}{4} \\\Leftrightarrow & 24x+\frac{24}{11}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1056}{ \color{blue}{44} }x+ \frac{96}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1056x \color{red}{+96} & = & \color{red}{308x} +55 \\\Leftrightarrow & 1056x \color{red}{+96} \color{blue}{-96} \color{blue}{-308x} & = & \color{red}{308x} +55 \color{blue}{-308x} \color{blue}{-96} \\\Leftrightarrow & 1056x-308x& = & 55-96 \\\Leftrightarrow & \color{red}{748} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{748} & & \\ & V = \left\{ \frac{-41}{748} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{5}{9})& = & 5x+\frac{4}{11} \\\Leftrightarrow & -12x-\frac{20}{9}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x- \frac{220}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{36}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{-220} & = & \color{red}{495x} +36 \\\Leftrightarrow & -1188x \color{red}{-220} \color{blue}{+220} \color{blue}{-495x} & = & \color{red}{495x} +36 \color{blue}{-495x} \color{blue}{+220} \\\Leftrightarrow & -1188x-495x& = & 36+220 \\\Leftrightarrow & \color{red}{-1683} x& = & 256 \\\Leftrightarrow & x = \frac{256}{-1683} & & \\\Leftrightarrow & x = \frac{-256}{1683} & & \\ & V = \left\{ \frac{-256}{1683} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{4}{3})& = & -9x+\frac{6}{11} \\\Leftrightarrow & -25x-\frac{20}{3}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-825}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -825x \color{red}{-220} & = & \color{red}{-297x} +18 \\\Leftrightarrow & -825x \color{red}{-220} \color{blue}{+220} \color{blue}{+297x} & = & \color{red}{-297x} +18 \color{blue}{+297x} \color{blue}{+220} \\\Leftrightarrow & -825x+297x& = & 18+220 \\\Leftrightarrow & \color{red}{-528} x& = & 238 \\\Leftrightarrow & x = \frac{238}{-528} & & \\\Leftrightarrow & x = \frac{-119}{264} & & \\ & V = \left\{ \frac{-119}{264} \right\} & \\\end{align}\)
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