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Alles samen. Gebruik stappenplan en ZRM!

  1. \(-3(-x+\frac{4}{11})=-5x+\frac{4}{15}\)
  2. \(-2(-5x+\frac{2}{5})=9x+\frac{9}{13}\)
  3. \(-(-5x+\frac{5}{12})=-4x+\frac{7}{6}\)
  4. \(7(5x+\frac{4}{7})=-8x+\frac{8}{7}\)
  5. \(2(-5x+\frac{4}{13})=x+\frac{8}{15}\)
  6. \(3(x+\frac{4}{7})=8x+\frac{6}{5}\)
  7. \(-3(3x-\frac{4}{3})=7x+\frac{6}{7}\)
  8. \((-4x-\frac{3}{14})=-7x+\frac{4}{5}\)
  9. \(-3(3x+\frac{4}{15})=2x+\frac{8}{7}\)
  10. \(2(-2x+\frac{3}{10})=3x+\frac{9}{14}\)
  11. \(6(x+\frac{4}{11})=7x+\frac{8}{3}\)
  12. \(6(4x+\frac{5}{7})=x+\frac{3}{8}\)

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-x+\frac{4}{11})& = & -5x+\frac{4}{15} \\\Leftrightarrow & 3x-\frac{12}{11}& = & -5x+\frac{4}{15} \\ & & & \text{kgv van noemers 11 en 15 is 165} \\\Leftrightarrow & \color{blue}{165} .(3x-\frac{12}{11})& = & (-5x+\frac{4}{15}). \color{blue}{165} \\\Leftrightarrow & 495x \color{red}{-180} & = & \color{red}{-825x} +44 \\\Leftrightarrow & 495x \color{red}{-180} \color{blue}{+180} \color{blue}{+825x} & = & \color{red}{-825x} +44 \color{blue}{+825x} \color{blue}{+180} \\\Leftrightarrow & 495x+825x& = & 44+180 \\\Leftrightarrow & \color{red}{1320} x& = & 224 \\\Leftrightarrow & x = \frac{224}{1320} & & \\\Leftrightarrow & x = \frac{28}{165} & & \\ & V = \left\{ \frac{28}{165} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{2}{5})& = & 9x+\frac{9}{13} \\\Leftrightarrow & 10x-\frac{4}{5}& = & 9x+\frac{9}{13} \\ & & & \text{kgv van noemers 5 en 13 is 65} \\\Leftrightarrow & \color{blue}{65} .(10x-\frac{4}{5})& = & (9x+\frac{9}{13}). \color{blue}{65} \\\Leftrightarrow & 650x \color{red}{-52} & = & \color{red}{585x} +45 \\\Leftrightarrow & 650x \color{red}{-52} \color{blue}{+52} \color{blue}{-585x} & = & \color{red}{585x} +45 \color{blue}{-585x} \color{blue}{+52} \\\Leftrightarrow & 650x-585x& = & 45+52 \\\Leftrightarrow & \color{red}{65} x& = & 97 \\\Leftrightarrow & x = \frac{97}{65} & & \\ & V = \left\{ \frac{97}{65} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-} (-5x+\frac{5}{12})& = & -4x+\frac{7}{6} \\\Leftrightarrow & 5x-\frac{5}{12}& = & -4x+\frac{7}{6} \\ & & & \text{kgv van noemers 12 en 6 is 12} \\\Leftrightarrow & \color{blue}{12} .(5x-\frac{5}{12})& = & (-4x+\frac{7}{6}). \color{blue}{12} \\\Leftrightarrow & 60x \color{red}{-5} & = & \color{red}{-48x} +14 \\\Leftrightarrow & 60x \color{red}{-5} \color{blue}{+5} \color{blue}{+48x} & = & \color{red}{-48x} +14 \color{blue}{+48x} \color{blue}{+5} \\\Leftrightarrow & 60x+48x& = & 14+5 \\\Leftrightarrow & \color{red}{108} x& = & 19 \\\Leftrightarrow & x = \frac{19}{108} & & \\ & V = \left\{ \frac{19}{108} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{4}{7})& = & -8x+\frac{8}{7} \\\Leftrightarrow & 35x+4& = & -8x+\frac{8}{7} \\ & & & \text{kgv van noemers 1 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(35x+4)& = & (-8x+\frac{8}{7}). \color{blue}{7} \\\Leftrightarrow & 245x \color{red}{+28} & = & \color{red}{-56x} +8 \\\Leftrightarrow & 245x \color{red}{+28} \color{blue}{-28} \color{blue}{+56x} & = & \color{red}{-56x} +8 \color{blue}{+56x} \color{blue}{-28} \\\Leftrightarrow & 245x+56x& = & 8-28 \\\Leftrightarrow & \color{red}{301} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{301} & & \\ & V = \left\{ \frac{-20}{301} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{4}{13})& = & x+\frac{8}{15} \\\Leftrightarrow & -10x+\frac{8}{13}& = & x+\frac{8}{15} \\ & & & \text{kgv van noemers 13 en 15 is 195} \\\Leftrightarrow & \color{blue}{195} .(-10x+\frac{8}{13})& = & (x+\frac{8}{15}). \color{blue}{195} \\\Leftrightarrow & -1950x \color{red}{+120} & = & \color{red}{195x} +104 \\\Leftrightarrow & -1950x \color{red}{+120} \color{blue}{-120} \color{blue}{-195x} & = & \color{red}{195x} +104 \color{blue}{-195x} \color{blue}{-120} \\\Leftrightarrow & -1950x-195x& = & 104-120 \\\Leftrightarrow & \color{red}{-2145} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-2145} & & \\\Leftrightarrow & x = \frac{16}{2145} & & \\ & V = \left\{ \frac{16}{2145} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (x+\frac{4}{7})& = & 8x+\frac{6}{5} \\\Leftrightarrow & 3x+\frac{12}{7}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(3x+\frac{12}{7})& = & (8x+\frac{6}{5}). \color{blue}{35} \\\Leftrightarrow & 105x \color{red}{+60} & = & \color{red}{280x} +42 \\\Leftrightarrow & 105x \color{red}{+60} \color{blue}{-60} \color{blue}{-280x} & = & \color{red}{280x} +42 \color{blue}{-280x} \color{blue}{-60} \\\Leftrightarrow & 105x-280x& = & 42-60 \\\Leftrightarrow & \color{red}{-175} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-175} & & \\\Leftrightarrow & x = \frac{18}{175} & & \\ & V = \left\{ \frac{18}{175} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{4}{3})& = & 7x+\frac{6}{7} \\\Leftrightarrow & -9x+4& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 1 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(-9x+4)& = & (7x+\frac{6}{7}). \color{blue}{7} \\\Leftrightarrow & -63x \color{red}{+28} & = & \color{red}{49x} +6 \\\Leftrightarrow & -63x \color{red}{+28} \color{blue}{-28} \color{blue}{-49x} & = & \color{red}{49x} +6 \color{blue}{-49x} \color{blue}{-28} \\\Leftrightarrow & -63x-49x& = & 6-28 \\\Leftrightarrow & \color{red}{-112} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-112} & & \\\Leftrightarrow & x = \frac{11}{56} & & \\ & V = \left\{ \frac{11}{56} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (-4x-\frac{3}{14})& = & -7x+\frac{4}{5} \\\Leftrightarrow & -4x-\frac{3}{14}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 14 en 5 is 70} \\\Leftrightarrow & \color{blue}{70} .(-4x-\frac{3}{14})& = & (-7x+\frac{4}{5}). \color{blue}{70} \\\Leftrightarrow & -280x \color{red}{-15} & = & \color{red}{-490x} +56 \\\Leftrightarrow & -280x \color{red}{-15} \color{blue}{+15} \color{blue}{+490x} & = & \color{red}{-490x} +56 \color{blue}{+490x} \color{blue}{+15} \\\Leftrightarrow & -280x+490x& = & 56+15 \\\Leftrightarrow & \color{red}{210} x& = & 71 \\\Leftrightarrow & x = \frac{71}{210} & & \\ & V = \left\{ \frac{71}{210} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{4}{15})& = & 2x+\frac{8}{7} \\\Leftrightarrow & -9x-\frac{4}{5}& = & 2x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(-9x-\frac{4}{5})& = & (2x+\frac{8}{7}). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{-28} & = & \color{red}{70x} +40 \\\Leftrightarrow & -315x \color{red}{-28} \color{blue}{+28} \color{blue}{-70x} & = & \color{red}{70x} +40 \color{blue}{-70x} \color{blue}{+28} \\\Leftrightarrow & -315x-70x& = & 40+28 \\\Leftrightarrow & \color{red}{-385} x& = & 68 \\\Leftrightarrow & x = \frac{68}{-385} & & \\\Leftrightarrow & x = \frac{-68}{385} & & \\ & V = \left\{ \frac{-68}{385} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{10})& = & 3x+\frac{9}{14} \\\Leftrightarrow & -4x+\frac{3}{5}& = & 3x+\frac{9}{14} \\ & & & \text{kgv van noemers 5 en 14 is 70} \\\Leftrightarrow & \color{blue}{70} .(-4x+\frac{3}{5})& = & (3x+\frac{9}{14}). \color{blue}{70} \\\Leftrightarrow & -280x \color{red}{+42} & = & \color{red}{210x} +45 \\\Leftrightarrow & -280x \color{red}{+42} \color{blue}{-42} \color{blue}{-210x} & = & \color{red}{210x} +45 \color{blue}{-210x} \color{blue}{-42} \\\Leftrightarrow & -280x-210x& = & 45-42 \\\Leftrightarrow & \color{red}{-490} x& = & 3 \\\Leftrightarrow & x = \frac{3}{-490} & & \\\Leftrightarrow & x = \frac{-3}{490} & & \\ & V = \left\{ \frac{-3}{490} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (x+\frac{4}{11})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 6x+\frac{24}{11}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(6x+\frac{24}{11})& = & (7x+\frac{8}{3}). \color{blue}{33} \\\Leftrightarrow & 198x \color{red}{+72} & = & \color{red}{231x} +88 \\\Leftrightarrow & 198x \color{red}{+72} \color{blue}{-72} \color{blue}{-231x} & = & \color{red}{231x} +88 \color{blue}{-231x} \color{blue}{-72} \\\Leftrightarrow & 198x-231x& = & 88-72 \\\Leftrightarrow & \color{red}{-33} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-33} & & \\\Leftrightarrow & x = \frac{-16}{33} & & \\ & V = \left\{ \frac{-16}{33} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{5}{7})& = & x+\frac{3}{8} \\\Leftrightarrow & 24x+\frac{30}{7}& = & x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(24x+\frac{30}{7})& = & (x+\frac{3}{8}). \color{blue}{56} \\\Leftrightarrow & 1344x \color{red}{+240} & = & \color{red}{56x} +21 \\\Leftrightarrow & 1344x \color{red}{+240} \color{blue}{-240} \color{blue}{-56x} & = & \color{red}{56x} +21 \color{blue}{-56x} \color{blue}{-240} \\\Leftrightarrow & 1344x-56x& = & 21-240 \\\Leftrightarrow & \color{red}{1288} x& = & -219 \\\Leftrightarrow & x = \frac{-219}{1288} & & \\ & V = \left\{ \frac{-219}{1288} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-04-03 05:05:26