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Alles samen. Gebruik stappenplan en ZRM!

  1. \((5x-\frac{2}{3})=2x+\frac{10}{9}\)
  2. \(7(x+\frac{3}{7})=-6x+\frac{4}{9}\)
  3. \(-5(5x-\frac{3}{11})=9x+\frac{4}{5}\)
  4. \(5(3x+\frac{3}{5})=-7x+\frac{9}{11}\)
  5. \(-5(2x+\frac{3}{16})=3x+\frac{10}{9}\)
  6. \(-2(-4x-\frac{4}{3})=-7x+\frac{6}{11}\)
  7. \(2(-5x-\frac{2}{5})=7x+\frac{3}{4}\)
  8. \(7(5x-\frac{5}{16})=4x+\frac{6}{5}\)
  9. \(-(-4x-\frac{5}{9})=-7x+\frac{6}{13}\)
  10. \(6(x-\frac{3}{11})=7x+\frac{7}{13}\)
  11. \(4(-4x-\frac{3}{2})=7x+\frac{5}{8}\)
  12. \(7(5x+\frac{5}{2})=8x+\frac{3}{8}\)

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (5x-\frac{2}{3})& = & 2x+\frac{10}{9} \\\Leftrightarrow & 5x-\frac{2}{3}& = & 2x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(5x-\frac{2}{3})& = & (2x+\frac{10}{9}). \color{blue}{9} \\\Leftrightarrow & 45x \color{red}{-6} & = & \color{red}{18x} +10 \\\Leftrightarrow & 45x \color{red}{-6} \color{blue}{+6} \color{blue}{-18x} & = & \color{red}{18x} +10 \color{blue}{-18x} \color{blue}{+6} \\\Leftrightarrow & 45x-18x& = & 10+6 \\\Leftrightarrow & \color{red}{27} x& = & 16 \\\Leftrightarrow & x = \frac{16}{27} & & \\ & V = \left\{ \frac{16}{27} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (x+\frac{3}{7})& = & -6x+\frac{4}{9} \\\Leftrightarrow & 7x+3& = & -6x+\frac{4}{9} \\ & & & \text{kgv van noemers 1 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(7x+3)& = & (-6x+\frac{4}{9}). \color{blue}{9} \\\Leftrightarrow & 63x \color{red}{+27} & = & \color{red}{-54x} +4 \\\Leftrightarrow & 63x \color{red}{+27} \color{blue}{-27} \color{blue}{+54x} & = & \color{red}{-54x} +4 \color{blue}{+54x} \color{blue}{-27} \\\Leftrightarrow & 63x+54x& = & 4-27 \\\Leftrightarrow & \color{red}{117} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{117} & & \\ & V = \left\{ \frac{-23}{117} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{3}{11})& = & 9x+\frac{4}{5} \\\Leftrightarrow & -25x+\frac{15}{11}& = & 9x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(-25x+\frac{15}{11})& = & (9x+\frac{4}{5}). \color{blue}{55} \\\Leftrightarrow & -1375x \color{red}{+75} & = & \color{red}{495x} +44 \\\Leftrightarrow & -1375x \color{red}{+75} \color{blue}{-75} \color{blue}{-495x} & = & \color{red}{495x} +44 \color{blue}{-495x} \color{blue}{-75} \\\Leftrightarrow & -1375x-495x& = & 44-75 \\\Leftrightarrow & \color{red}{-1870} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-1870} & & \\\Leftrightarrow & x = \frac{31}{1870} & & \\ & V = \left\{ \frac{31}{1870} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{3}{5})& = & -7x+\frac{9}{11} \\\Leftrightarrow & 15x+3& = & -7x+\frac{9}{11} \\ & & & \text{kgv van noemers 1 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(15x+3)& = & (-7x+\frac{9}{11}). \color{blue}{11} \\\Leftrightarrow & 165x \color{red}{+33} & = & \color{red}{-77x} +9 \\\Leftrightarrow & 165x \color{red}{+33} \color{blue}{-33} \color{blue}{+77x} & = & \color{red}{-77x} +9 \color{blue}{+77x} \color{blue}{-33} \\\Leftrightarrow & 165x+77x& = & 9-33 \\\Leftrightarrow & \color{red}{242} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{242} & & \\\Leftrightarrow & x = \frac{-12}{121} & & \\ & V = \left\{ \frac{-12}{121} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{3}{16})& = & 3x+\frac{10}{9} \\\Leftrightarrow & -10x-\frac{15}{16}& = & 3x+\frac{10}{9} \\ & & & \text{kgv van noemers 16 en 9 is 144} \\\Leftrightarrow & \color{blue}{144} .(-10x-\frac{15}{16})& = & (3x+\frac{10}{9}). \color{blue}{144} \\\Leftrightarrow & -1440x \color{red}{-135} & = & \color{red}{432x} +160 \\\Leftrightarrow & -1440x \color{red}{-135} \color{blue}{+135} \color{blue}{-432x} & = & \color{red}{432x} +160 \color{blue}{-432x} \color{blue}{+135} \\\Leftrightarrow & -1440x-432x& = & 160+135 \\\Leftrightarrow & \color{red}{-1872} x& = & 295 \\\Leftrightarrow & x = \frac{295}{-1872} & & \\\Leftrightarrow & x = \frac{-295}{1872} & & \\ & V = \left\{ \frac{-295}{1872} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{4}{3})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 8x+\frac{8}{3}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(8x+\frac{8}{3})& = & (-7x+\frac{6}{11}). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{+88} & = & \color{red}{-231x} +18 \\\Leftrightarrow & 264x \color{red}{+88} \color{blue}{-88} \color{blue}{+231x} & = & \color{red}{-231x} +18 \color{blue}{+231x} \color{blue}{-88} \\\Leftrightarrow & 264x+231x& = & 18-88 \\\Leftrightarrow & \color{red}{495} x& = & -70 \\\Leftrightarrow & x = \frac{-70}{495} & & \\\Leftrightarrow & x = \frac{-14}{99} & & \\ & V = \left\{ \frac{-14}{99} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{2}{5})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -10x-\frac{4}{5}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(-10x-\frac{4}{5})& = & (7x+\frac{3}{4}). \color{blue}{20} \\\Leftrightarrow & -200x \color{red}{-16} & = & \color{red}{140x} +15 \\\Leftrightarrow & -200x \color{red}{-16} \color{blue}{+16} \color{blue}{-140x} & = & \color{red}{140x} +15 \color{blue}{-140x} \color{blue}{+16} \\\Leftrightarrow & -200x-140x& = & 15+16 \\\Leftrightarrow & \color{red}{-340} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-340} & & \\\Leftrightarrow & x = \frac{-31}{340} & & \\ & V = \left\{ \frac{-31}{340} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{5}{16})& = & 4x+\frac{6}{5} \\\Leftrightarrow & 35x-\frac{35}{16}& = & 4x+\frac{6}{5} \\ & & & \text{kgv van noemers 16 en 5 is 80} \\\Leftrightarrow & \color{blue}{80} .(35x-\frac{35}{16})& = & (4x+\frac{6}{5}). \color{blue}{80} \\\Leftrightarrow & 2800x \color{red}{-175} & = & \color{red}{320x} +96 \\\Leftrightarrow & 2800x \color{red}{-175} \color{blue}{+175} \color{blue}{-320x} & = & \color{red}{320x} +96 \color{blue}{-320x} \color{blue}{+175} \\\Leftrightarrow & 2800x-320x& = & 96+175 \\\Leftrightarrow & \color{red}{2480} x& = & 271 \\\Leftrightarrow & x = \frac{271}{2480} & & \\ & V = \left\{ \frac{271}{2480} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-} (-4x-\frac{5}{9})& = & -7x+\frac{6}{13} \\\Leftrightarrow & 4x+\frac{5}{9}& = & -7x+\frac{6}{13} \\ & & & \text{kgv van noemers 9 en 13 is 117} \\\Leftrightarrow & \color{blue}{117} .(4x+\frac{5}{9})& = & (-7x+\frac{6}{13}). \color{blue}{117} \\\Leftrightarrow & 468x \color{red}{+65} & = & \color{red}{-819x} +54 \\\Leftrightarrow & 468x \color{red}{+65} \color{blue}{-65} \color{blue}{+819x} & = & \color{red}{-819x} +54 \color{blue}{+819x} \color{blue}{-65} \\\Leftrightarrow & 468x+819x& = & 54-65 \\\Leftrightarrow & \color{red}{1287} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{1287} & & \\\Leftrightarrow & x = \frac{-1}{117} & & \\ & V = \left\{ \frac{-1}{117} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (x-\frac{3}{11})& = & 7x+\frac{7}{13} \\\Leftrightarrow & 6x-\frac{18}{11}& = & 7x+\frac{7}{13} \\ & & & \text{kgv van noemers 11 en 13 is 143} \\\Leftrightarrow & \color{blue}{143} .(6x-\frac{18}{11})& = & (7x+\frac{7}{13}). \color{blue}{143} \\\Leftrightarrow & 858x \color{red}{-234} & = & \color{red}{1001x} +77 \\\Leftrightarrow & 858x \color{red}{-234} \color{blue}{+234} \color{blue}{-1001x} & = & \color{red}{1001x} +77 \color{blue}{-1001x} \color{blue}{+234} \\\Leftrightarrow & 858x-1001x& = & 77+234 \\\Leftrightarrow & \color{red}{-143} x& = & 311 \\\Leftrightarrow & x = \frac{311}{-143} & & \\\Leftrightarrow & x = \frac{-311}{143} & & \\ & V = \left\{ \frac{-311}{143} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{3}{2})& = & 7x+\frac{5}{8} \\\Leftrightarrow & -16x-6& = & 7x+\frac{5}{8} \\ & & & \text{kgv van noemers 1 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(-16x-6)& = & (7x+\frac{5}{8}). \color{blue}{8} \\\Leftrightarrow & -128x \color{red}{-48} & = & \color{red}{56x} +5 \\\Leftrightarrow & -128x \color{red}{-48} \color{blue}{+48} \color{blue}{-56x} & = & \color{red}{56x} +5 \color{blue}{-56x} \color{blue}{+48} \\\Leftrightarrow & -128x-56x& = & 5+48 \\\Leftrightarrow & \color{red}{-184} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-184} & & \\\Leftrightarrow & x = \frac{-53}{184} & & \\ & V = \left\{ \frac{-53}{184} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{5}{2})& = & 8x+\frac{3}{8} \\\Leftrightarrow & 35x+\frac{35}{2}& = & 8x+\frac{3}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(35x+\frac{35}{2})& = & (8x+\frac{3}{8}). \color{blue}{8} \\\Leftrightarrow & 280x \color{red}{+140} & = & \color{red}{64x} +3 \\\Leftrightarrow & 280x \color{red}{+140} \color{blue}{-140} \color{blue}{-64x} & = & \color{red}{64x} +3 \color{blue}{-64x} \color{blue}{-140} \\\Leftrightarrow & 280x-64x& = & 3-140 \\\Leftrightarrow & \color{red}{216} x& = & -137 \\\Leftrightarrow & x = \frac{-137}{216} & & \\ & V = \left\{ \frac{-137}{216} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-05-07 10:45:41