Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{3})& = & -3x+\frac{2}{5} \\\Leftrightarrow & 20x+\frac{20}{3}& = & -3x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{300}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 300x \color{red}{+100} & = & \color{red}{-45x} +6 \\\Leftrightarrow & 300x \color{red}{+100} \color{blue}{-100} \color{blue}{+45x} & = & \color{red}{-45x} +6 \color{blue}{+45x} \color{blue}{-100} \\\Leftrightarrow & 300x+45x& = & 6-100 \\\Leftrightarrow & \color{red}{345} x& = & -94 \\\Leftrightarrow & x = \frac{-94}{345} & & \\ & V = \left\{ \frac{-94}{345} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{4}{9})& = & 3x+\frac{5}{11} \\\Leftrightarrow & -25x-\frac{20}{9}& = & 3x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2475}{ \color{blue}{99} }x- \frac{220}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2475x \color{red}{-220} & = & \color{red}{297x} +45 \\\Leftrightarrow & -2475x \color{red}{-220} \color{blue}{+220} \color{blue}{-297x} & = & \color{red}{297x} +45 \color{blue}{-297x} \color{blue}{+220} \\\Leftrightarrow & -2475x-297x& = & 45+220 \\\Leftrightarrow & \color{red}{-2772} x& = & 265 \\\Leftrightarrow & x = \frac{265}{-2772} & & \\\Leftrightarrow & x = \frac{-265}{2772} & & \\ & V = \left\{ \frac{-265}{2772} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{3}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 30x+\frac{18}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{150}{ \color{blue}{5} }x+ \frac{18}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 150x \color{red}{+18} & = & \color{red}{-35x} +6 \\\Leftrightarrow & 150x \color{red}{+18} \color{blue}{-18} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{-18} \\\Leftrightarrow & 150x+35x& = & 6-18 \\\Leftrightarrow & \color{red}{185} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{185} & & \\ & V = \left\{ \frac{-12}{185} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{2}{5})& = & 5x+\frac{7}{12} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-720}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{300}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -720x \color{red}{+144} & = & \color{red}{300x} +35 \\\Leftrightarrow & -720x \color{red}{+144} \color{blue}{-144} \color{blue}{-300x} & = & \color{red}{300x} +35 \color{blue}{-300x} \color{blue}{-144} \\\Leftrightarrow & -720x-300x& = & 35-144 \\\Leftrightarrow & \color{red}{-1020} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{-1020} & & \\\Leftrightarrow & x = \frac{109}{1020} & & \\ & V = \left\{ \frac{109}{1020} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{9})& = & 7x+\frac{5}{11} \\\Leftrightarrow & 15x+\frac{20}{9}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1485}{ \color{blue}{99} }x+ \frac{220}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1485x \color{red}{+220} & = & \color{red}{693x} +45 \\\Leftrightarrow & 1485x \color{red}{+220} \color{blue}{-220} \color{blue}{-693x} & = & \color{red}{693x} +45 \color{blue}{-693x} \color{blue}{-220} \\\Leftrightarrow & 1485x-693x& = & 45-220 \\\Leftrightarrow & \color{red}{792} x& = & -175 \\\Leftrightarrow & x = \frac{-175}{792} & & \\ & V = \left\{ \frac{-175}{792} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{11})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 24x+\frac{24}{11}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{264}{ \color{blue}{11} }x+ \frac{24}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 264x \color{red}{+24} & = & \color{red}{-55x} +5 \\\Leftrightarrow & 264x \color{red}{+24} \color{blue}{-24} \color{blue}{+55x} & = & \color{red}{-55x} +5 \color{blue}{+55x} \color{blue}{-24} \\\Leftrightarrow & 264x+55x& = & 5-24 \\\Leftrightarrow & \color{red}{319} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{319} & & \\ & V = \left\{ \frac{-19}{319} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{3}{7})& = & 7x+\frac{9}{5} \\\Leftrightarrow & -6x-\frac{6}{7}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{-30} & = & \color{red}{245x} +63 \\\Leftrightarrow & -210x \color{red}{-30} \color{blue}{+30} \color{blue}{-245x} & = & \color{red}{245x} +63 \color{blue}{-245x} \color{blue}{+30} \\\Leftrightarrow & -210x-245x& = & 63+30 \\\Leftrightarrow & \color{red}{-455} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-455} & & \\\Leftrightarrow & x = \frac{-93}{455} & & \\ & V = \left\{ \frac{-93}{455} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{3}{7})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 12x+\frac{9}{7}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{504}{ \color{blue}{42} }x+ \frac{54}{ \color{blue}{42} })& = & (\frac{-210}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 504x \color{red}{+54} & = & \color{red}{-210x} +35 \\\Leftrightarrow & 504x \color{red}{+54} \color{blue}{-54} \color{blue}{+210x} & = & \color{red}{-210x} +35 \color{blue}{+210x} \color{blue}{-54} \\\Leftrightarrow & 504x+210x& = & 35-54 \\\Leftrightarrow & \color{red}{714} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{714} & & \\ & V = \left\{ \frac{-19}{714} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{5}{11})& = & 9x+\frac{3}{10} \\\Leftrightarrow & -8x-\frac{20}{11}& = & 9x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-880}{ \color{blue}{110} }x- \frac{200}{ \color{blue}{110} })& = & (\frac{990}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -880x \color{red}{-200} & = & \color{red}{990x} +33 \\\Leftrightarrow & -880x \color{red}{-200} \color{blue}{+200} \color{blue}{-990x} & = & \color{red}{990x} +33 \color{blue}{-990x} \color{blue}{+200} \\\Leftrightarrow & -880x-990x& = & 33+200 \\\Leftrightarrow & \color{red}{-1870} x& = & 233 \\\Leftrightarrow & x = \frac{233}{-1870} & & \\\Leftrightarrow & x = \frac{-233}{1870} & & \\ & V = \left\{ \frac{-233}{1870} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{5}{11})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -18x-\frac{30}{11}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-594}{ \color{blue}{33} }x- \frac{90}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -594x \color{red}{-90} & = & \color{red}{-297x} +22 \\\Leftrightarrow & -594x \color{red}{-90} \color{blue}{+90} \color{blue}{+297x} & = & \color{red}{-297x} +22 \color{blue}{+297x} \color{blue}{+90} \\\Leftrightarrow & -594x+297x& = & 22+90 \\\Leftrightarrow & \color{red}{-297} x& = & 112 \\\Leftrightarrow & x = \frac{112}{-297} & & \\\Leftrightarrow & x = \frac{-112}{297} & & \\ & V = \left\{ \frac{-112}{297} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{2}{9})& = & -7x+\frac{7}{11} \\\Leftrightarrow & 20x+\frac{10}{9}& = & -7x+\frac{7}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1980}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{63}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1980x \color{red}{+110} & = & \color{red}{-693x} +63 \\\Leftrightarrow & 1980x \color{red}{+110} \color{blue}{-110} \color{blue}{+693x} & = & \color{red}{-693x} +63 \color{blue}{+693x} \color{blue}{-110} \\\Leftrightarrow & 1980x+693x& = & 63-110 \\\Leftrightarrow & \color{red}{2673} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{2673} & & \\ & V = \left\{ \frac{-47}{2673} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{2}{9})& = & -9x+\frac{5}{7} \\\Leftrightarrow & 8x+\frac{8}{9}& = & -9x+\frac{5}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{45}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{+56} & = & \color{red}{-567x} +45 \\\Leftrightarrow & 504x \color{red}{+56} \color{blue}{-56} \color{blue}{+567x} & = & \color{red}{-567x} +45 \color{blue}{+567x} \color{blue}{-56} \\\Leftrightarrow & 504x+567x& = & 45-56 \\\Leftrightarrow & \color{red}{1071} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{1071} & & \\ & V = \left\{ \frac{-11}{1071} \right\} & \\\end{align}\)
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