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Alles samen. Gebruik stappenplan en ZRM!

  1. \(-5(4x+\frac{2}{11})=19x+\frac{8}{7}\)
  2. \(2(-3x+\frac{4}{13})=5x+\frac{4}{15}\)
  3. \(-4(-x+\frac{4}{13})=7x+\frac{5}{9}\)
  4. \(-2(-4x+\frac{3}{8})=9x+\frac{4}{11}\)
  5. \(-5(4x-\frac{4}{13})=9x+\frac{8}{3}\)
  6. \(-4(5x+\frac{5}{16})=7x+\frac{5}{14}\)
  7. \(7(-2x-\frac{5}{6})=-9x+\frac{8}{15}\)
  8. \(-(-3x+\frac{5}{3})=10x+\frac{8}{15}\)
  9. \(-6(2x+\frac{4}{5})=11x+\frac{3}{5}\)
  10. \(-5(-3x-\frac{3}{7})=x+\frac{9}{13}\)
  11. \(-(-2x-\frac{4}{9})=9x+\frac{6}{13}\)
  12. \(-3(-3x+\frac{5}{14})=7x+\frac{5}{4}\)

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{11})& = & 19x+\frac{8}{7} \\\Leftrightarrow & -20x-\frac{10}{11}& = & 19x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(-20x-\frac{10}{11})& = & (19x+\frac{8}{7}). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{-70} & = & \color{red}{1463x} +88 \\\Leftrightarrow & -1540x \color{red}{-70} \color{blue}{+70} \color{blue}{-1463x} & = & \color{red}{1463x} +88 \color{blue}{-1463x} \color{blue}{+70} \\\Leftrightarrow & -1540x-1463x& = & 88+70 \\\Leftrightarrow & \color{red}{-3003} x& = & 158 \\\Leftrightarrow & x = \frac{158}{-3003} & & \\\Leftrightarrow & x = \frac{-158}{3003} & & \\ & V = \left\{ \frac{-158}{3003} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{13})& = & 5x+\frac{4}{15} \\\Leftrightarrow & -6x+\frac{8}{13}& = & 5x+\frac{4}{15} \\ & & & \text{kgv van noemers 13 en 15 is 195} \\\Leftrightarrow & \color{blue}{195} .(-6x+\frac{8}{13})& = & (5x+\frac{4}{15}). \color{blue}{195} \\\Leftrightarrow & -1170x \color{red}{+120} & = & \color{red}{975x} +52 \\\Leftrightarrow & -1170x \color{red}{+120} \color{blue}{-120} \color{blue}{-975x} & = & \color{red}{975x} +52 \color{blue}{-975x} \color{blue}{-120} \\\Leftrightarrow & -1170x-975x& = & 52-120 \\\Leftrightarrow & \color{red}{-2145} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{-2145} & & \\\Leftrightarrow & x = \frac{68}{2145} & & \\ & V = \left\{ \frac{68}{2145} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-x+\frac{4}{13})& = & 7x+\frac{5}{9} \\\Leftrightarrow & 4x-\frac{16}{13}& = & 7x+\frac{5}{9} \\ & & & \text{kgv van noemers 13 en 9 is 117} \\\Leftrightarrow & \color{blue}{117} .(4x-\frac{16}{13})& = & (7x+\frac{5}{9}). \color{blue}{117} \\\Leftrightarrow & 468x \color{red}{-144} & = & \color{red}{819x} +65 \\\Leftrightarrow & 468x \color{red}{-144} \color{blue}{+144} \color{blue}{-819x} & = & \color{red}{819x} +65 \color{blue}{-819x} \color{blue}{+144} \\\Leftrightarrow & 468x-819x& = & 65+144 \\\Leftrightarrow & \color{red}{-351} x& = & 209 \\\Leftrightarrow & x = \frac{209}{-351} & & \\\Leftrightarrow & x = \frac{-209}{351} & & \\ & V = \left\{ \frac{-209}{351} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{3}{8})& = & 9x+\frac{4}{11} \\\Leftrightarrow & 8x-\frac{3}{4}& = & 9x+\frac{4}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(8x-\frac{3}{4})& = & (9x+\frac{4}{11}). \color{blue}{44} \\\Leftrightarrow & 352x \color{red}{-33} & = & \color{red}{396x} +16 \\\Leftrightarrow & 352x \color{red}{-33} \color{blue}{+33} \color{blue}{-396x} & = & \color{red}{396x} +16 \color{blue}{-396x} \color{blue}{+33} \\\Leftrightarrow & 352x-396x& = & 16+33 \\\Leftrightarrow & \color{red}{-44} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-44} & & \\\Leftrightarrow & x = \frac{-49}{44} & & \\ & V = \left\{ \frac{-49}{44} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{4}{13})& = & 9x+\frac{8}{3} \\\Leftrightarrow & -20x+\frac{20}{13}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 13 en 3 is 39} \\\Leftrightarrow & \color{blue}{39} .(-20x+\frac{20}{13})& = & (9x+\frac{8}{3}). \color{blue}{39} \\\Leftrightarrow & -780x \color{red}{+60} & = & \color{red}{351x} +104 \\\Leftrightarrow & -780x \color{red}{+60} \color{blue}{-60} \color{blue}{-351x} & = & \color{red}{351x} +104 \color{blue}{-351x} \color{blue}{-60} \\\Leftrightarrow & -780x-351x& = & 104-60 \\\Leftrightarrow & \color{red}{-1131} x& = & 44 \\\Leftrightarrow & x = \frac{44}{-1131} & & \\\Leftrightarrow & x = \frac{-44}{1131} & & \\ & V = \left\{ \frac{-44}{1131} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{5}{16})& = & 7x+\frac{5}{14} \\\Leftrightarrow & -20x-\frac{5}{4}& = & 7x+\frac{5}{14} \\ & & & \text{kgv van noemers 4 en 14 is 28} \\\Leftrightarrow & \color{blue}{28} .(-20x-\frac{5}{4})& = & (7x+\frac{5}{14}). \color{blue}{28} \\\Leftrightarrow & -560x \color{red}{-35} & = & \color{red}{196x} +10 \\\Leftrightarrow & -560x \color{red}{-35} \color{blue}{+35} \color{blue}{-196x} & = & \color{red}{196x} +10 \color{blue}{-196x} \color{blue}{+35} \\\Leftrightarrow & -560x-196x& = & 10+35 \\\Leftrightarrow & \color{red}{-756} x& = & 45 \\\Leftrightarrow & x = \frac{45}{-756} & & \\\Leftrightarrow & x = \frac{-5}{84} & & \\ & V = \left\{ \frac{-5}{84} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{5}{6})& = & -9x+\frac{8}{15} \\\Leftrightarrow & -14x-\frac{35}{6}& = & -9x+\frac{8}{15} \\ & & & \text{kgv van noemers 6 en 15 is 30} \\\Leftrightarrow & \color{blue}{30} .(-14x-\frac{35}{6})& = & (-9x+\frac{8}{15}). \color{blue}{30} \\\Leftrightarrow & -420x \color{red}{-175} & = & \color{red}{-270x} +16 \\\Leftrightarrow & -420x \color{red}{-175} \color{blue}{+175} \color{blue}{+270x} & = & \color{red}{-270x} +16 \color{blue}{+270x} \color{blue}{+175} \\\Leftrightarrow & -420x+270x& = & 16+175 \\\Leftrightarrow & \color{red}{-150} x& = & 191 \\\Leftrightarrow & x = \frac{191}{-150} & & \\\Leftrightarrow & x = \frac{-191}{150} & & \\ & V = \left\{ \frac{-191}{150} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-} (-3x+\frac{5}{3})& = & 10x+\frac{8}{15} \\\Leftrightarrow & 3x-\frac{5}{3}& = & 10x+\frac{8}{15} \\ & & & \text{kgv van noemers 3 en 15 is 15} \\\Leftrightarrow & \color{blue}{15} .(3x-\frac{5}{3})& = & (10x+\frac{8}{15}). \color{blue}{15} \\\Leftrightarrow & 45x \color{red}{-25} & = & \color{red}{150x} +8 \\\Leftrightarrow & 45x \color{red}{-25} \color{blue}{+25} \color{blue}{-150x} & = & \color{red}{150x} +8 \color{blue}{-150x} \color{blue}{+25} \\\Leftrightarrow & 45x-150x& = & 8+25 \\\Leftrightarrow & \color{red}{-105} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-105} & & \\\Leftrightarrow & x = \frac{-11}{35} & & \\ & V = \left\{ \frac{-11}{35} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{4}{5})& = & 11x+\frac{3}{5} \\\Leftrightarrow & -12x-\frac{24}{5}& = & 11x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(-12x-\frac{24}{5})& = & (11x+\frac{3}{5}). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{-24} & = & \color{red}{55x} +3 \\\Leftrightarrow & -60x \color{red}{-24} \color{blue}{+24} \color{blue}{-55x} & = & \color{red}{55x} +3 \color{blue}{-55x} \color{blue}{+24} \\\Leftrightarrow & -60x-55x& = & 3+24 \\\Leftrightarrow & \color{red}{-115} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-115} & & \\\Leftrightarrow & x = \frac{-27}{115} & & \\ & V = \left\{ \frac{-27}{115} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{3}{7})& = & x+\frac{9}{13} \\\Leftrightarrow & 15x+\frac{15}{7}& = & x+\frac{9}{13} \\ & & & \text{kgv van noemers 7 en 13 is 91} \\\Leftrightarrow & \color{blue}{91} .(15x+\frac{15}{7})& = & (x+\frac{9}{13}). \color{blue}{91} \\\Leftrightarrow & 1365x \color{red}{+195} & = & \color{red}{91x} +63 \\\Leftrightarrow & 1365x \color{red}{+195} \color{blue}{-195} \color{blue}{-91x} & = & \color{red}{91x} +63 \color{blue}{-91x} \color{blue}{-195} \\\Leftrightarrow & 1365x-91x& = & 63-195 \\\Leftrightarrow & \color{red}{1274} x& = & -132 \\\Leftrightarrow & x = \frac{-132}{1274} & & \\\Leftrightarrow & x = \frac{-66}{637} & & \\ & V = \left\{ \frac{-66}{637} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-} (-2x-\frac{4}{9})& = & 9x+\frac{6}{13} \\\Leftrightarrow & 2x+\frac{4}{9}& = & 9x+\frac{6}{13} \\ & & & \text{kgv van noemers 9 en 13 is 117} \\\Leftrightarrow & \color{blue}{117} .(2x+\frac{4}{9})& = & (9x+\frac{6}{13}). \color{blue}{117} \\\Leftrightarrow & 234x \color{red}{+52} & = & \color{red}{1053x} +54 \\\Leftrightarrow & 234x \color{red}{+52} \color{blue}{-52} \color{blue}{-1053x} & = & \color{red}{1053x} +54 \color{blue}{-1053x} \color{blue}{-52} \\\Leftrightarrow & 234x-1053x& = & 54-52 \\\Leftrightarrow & \color{red}{-819} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-819} & & \\\Leftrightarrow & x = \frac{-2}{819} & & \\ & V = \left\{ \frac{-2}{819} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{14})& = & 7x+\frac{5}{4} \\\Leftrightarrow & 9x-\frac{15}{14}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 14 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(9x-\frac{15}{14})& = & (7x+\frac{5}{4}). \color{blue}{28} \\\Leftrightarrow & 252x \color{red}{-30} & = & \color{red}{196x} +35 \\\Leftrightarrow & 252x \color{red}{-30} \color{blue}{+30} \color{blue}{-196x} & = & \color{red}{196x} +35 \color{blue}{-196x} \color{blue}{+30} \\\Leftrightarrow & 252x-196x& = & 35+30 \\\Leftrightarrow & \color{red}{56} x& = & 65 \\\Leftrightarrow & x = \frac{65}{56} & & \\ & V = \left\{ \frac{65}{56} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-11-21 12:47:13