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Alles samen. Gebruik stappenplan en ZRM!

  1. \(-7(-x+\frac{3}{14})=10x+\frac{4}{11}\)
  2. \(-5(x+\frac{5}{6})=-9x+\frac{8}{7}\)
  3. \(-6(-4x+\frac{5}{3})=23x+\frac{5}{16}\)
  4. \(-3(4x+\frac{3}{13})=5x+\frac{9}{8}\)
  5. \(4(-2x+\frac{2}{15})=9x+\frac{8}{7}\)
  6. \(-7(4x+\frac{4}{9})=-5x+\frac{7}{3}\)
  7. \(-3(-2x+\frac{3}{14})=x+\frac{10}{11}\)
  8. \(-3(-x-\frac{2}{15})=8x+\frac{2}{5}\)
  9. \(6(2x-\frac{2}{9})=7x+\frac{6}{7}\)
  10. \(5(-4x-\frac{2}{15})=x+\frac{6}{7}\)
  11. \(-(-3x-\frac{3}{8})=5x+\frac{7}{4}\)
  12. \(-4(-x+\frac{4}{5})=5x+\frac{4}{7}\)

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-x+\frac{3}{14})& = & 10x+\frac{4}{11} \\\Leftrightarrow & 7x-\frac{3}{2}& = & 10x+\frac{4}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(7x-\frac{3}{2})& = & (10x+\frac{4}{11}). \color{blue}{22} \\\Leftrightarrow & 154x \color{red}{-33} & = & \color{red}{220x} +8 \\\Leftrightarrow & 154x \color{red}{-33} \color{blue}{+33} \color{blue}{-220x} & = & \color{red}{220x} +8 \color{blue}{-220x} \color{blue}{+33} \\\Leftrightarrow & 154x-220x& = & 8+33 \\\Leftrightarrow & \color{red}{-66} x& = & 41 \\\Leftrightarrow & x = \frac{41}{-66} & & \\\Leftrightarrow & x = \frac{-41}{66} & & \\ & V = \left\{ \frac{-41}{66} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (x+\frac{5}{6})& = & -9x+\frac{8}{7} \\\Leftrightarrow & -5x-\frac{25}{6}& = & -9x+\frac{8}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(-5x-\frac{25}{6})& = & (-9x+\frac{8}{7}). \color{blue}{42} \\\Leftrightarrow & -210x \color{red}{-175} & = & \color{red}{-378x} +48 \\\Leftrightarrow & -210x \color{red}{-175} \color{blue}{+175} \color{blue}{+378x} & = & \color{red}{-378x} +48 \color{blue}{+378x} \color{blue}{+175} \\\Leftrightarrow & -210x+378x& = & 48+175 \\\Leftrightarrow & \color{red}{168} x& = & 223 \\\Leftrightarrow & x = \frac{223}{168} & & \\ & V = \left\{ \frac{223}{168} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{5}{3})& = & 23x+\frac{5}{16} \\\Leftrightarrow & 24x-10& = & 23x+\frac{5}{16} \\ & & & \text{kgv van noemers 1 en 16 is 16} \\\Leftrightarrow & \color{blue}{16} .(24x-10)& = & (23x+\frac{5}{16}). \color{blue}{16} \\\Leftrightarrow & 384x \color{red}{-160} & = & \color{red}{368x} +5 \\\Leftrightarrow & 384x \color{red}{-160} \color{blue}{+160} \color{blue}{-368x} & = & \color{red}{368x} +5 \color{blue}{-368x} \color{blue}{+160} \\\Leftrightarrow & 384x-368x& = & 5+160 \\\Leftrightarrow & \color{red}{16} x& = & 165 \\\Leftrightarrow & x = \frac{165}{16} & & \\ & V = \left\{ \frac{165}{16} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{3}{13})& = & 5x+\frac{9}{8} \\\Leftrightarrow & -12x-\frac{9}{13}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 13 en 8 is 104} \\\Leftrightarrow & \color{blue}{104} .(-12x-\frac{9}{13})& = & (5x+\frac{9}{8}). \color{blue}{104} \\\Leftrightarrow & -1248x \color{red}{-72} & = & \color{red}{520x} +117 \\\Leftrightarrow & -1248x \color{red}{-72} \color{blue}{+72} \color{blue}{-520x} & = & \color{red}{520x} +117 \color{blue}{-520x} \color{blue}{+72} \\\Leftrightarrow & -1248x-520x& = & 117+72 \\\Leftrightarrow & \color{red}{-1768} x& = & 189 \\\Leftrightarrow & x = \frac{189}{-1768} & & \\\Leftrightarrow & x = \frac{-189}{1768} & & \\ & V = \left\{ \frac{-189}{1768} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{15})& = & 9x+\frac{8}{7} \\\Leftrightarrow & -8x+\frac{8}{15}& = & 9x+\frac{8}{7} \\ & & & \text{kgv van noemers 15 en 7 is 105} \\\Leftrightarrow & \color{blue}{105} .(-8x+\frac{8}{15})& = & (9x+\frac{8}{7}). \color{blue}{105} \\\Leftrightarrow & -840x \color{red}{+56} & = & \color{red}{945x} +120 \\\Leftrightarrow & -840x \color{red}{+56} \color{blue}{-56} \color{blue}{-945x} & = & \color{red}{945x} +120 \color{blue}{-945x} \color{blue}{-56} \\\Leftrightarrow & -840x-945x& = & 120-56 \\\Leftrightarrow & \color{red}{-1785} x& = & 64 \\\Leftrightarrow & x = \frac{64}{-1785} & & \\\Leftrightarrow & x = \frac{-64}{1785} & & \\ & V = \left\{ \frac{-64}{1785} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{4}{9})& = & -5x+\frac{7}{3} \\\Leftrightarrow & -28x-\frac{28}{9}& = & -5x+\frac{7}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(-28x-\frac{28}{9})& = & (-5x+\frac{7}{3}). \color{blue}{9} \\\Leftrightarrow & -252x \color{red}{-28} & = & \color{red}{-45x} +21 \\\Leftrightarrow & -252x \color{red}{-28} \color{blue}{+28} \color{blue}{+45x} & = & \color{red}{-45x} +21 \color{blue}{+45x} \color{blue}{+28} \\\Leftrightarrow & -252x+45x& = & 21+28 \\\Leftrightarrow & \color{red}{-207} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-207} & & \\\Leftrightarrow & x = \frac{-49}{207} & & \\ & V = \left\{ \frac{-49}{207} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{3}{14})& = & x+\frac{10}{11} \\\Leftrightarrow & 6x-\frac{9}{14}& = & x+\frac{10}{11} \\ & & & \text{kgv van noemers 14 en 11 is 154} \\\Leftrightarrow & \color{blue}{154} .(6x-\frac{9}{14})& = & (x+\frac{10}{11}). \color{blue}{154} \\\Leftrightarrow & 924x \color{red}{-99} & = & \color{red}{154x} +140 \\\Leftrightarrow & 924x \color{red}{-99} \color{blue}{+99} \color{blue}{-154x} & = & \color{red}{154x} +140 \color{blue}{-154x} \color{blue}{+99} \\\Leftrightarrow & 924x-154x& = & 140+99 \\\Leftrightarrow & \color{red}{770} x& = & 239 \\\Leftrightarrow & x = \frac{239}{770} & & \\ & V = \left\{ \frac{239}{770} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-x-\frac{2}{15})& = & 8x+\frac{2}{5} \\\Leftrightarrow & 3x+\frac{2}{5}& = & 8x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(3x+\frac{2}{5})& = & (8x+\frac{2}{5}). \color{blue}{5} \\\Leftrightarrow & 15x \color{red}{+2} & = & \color{red}{40x} +2 \\\Leftrightarrow & 15x \color{red}{+2} \color{blue}{-2} \color{blue}{-40x} & = & \color{red}{40x} +2 \color{blue}{-40x} \color{blue}{-2} \\\Leftrightarrow & 15x-40x& = & 2-2 \\\Leftrightarrow & \color{red}{-25} x& = & 0 \\\Leftrightarrow & x = \frac{0}{-25} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{2}{9})& = & 7x+\frac{6}{7} \\\Leftrightarrow & 12x-\frac{4}{3}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(12x-\frac{4}{3})& = & (7x+\frac{6}{7}). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{-28} & = & \color{red}{147x} +18 \\\Leftrightarrow & 252x \color{red}{-28} \color{blue}{+28} \color{blue}{-147x} & = & \color{red}{147x} +18 \color{blue}{-147x} \color{blue}{+28} \\\Leftrightarrow & 252x-147x& = & 18+28 \\\Leftrightarrow & \color{red}{105} x& = & 46 \\\Leftrightarrow & x = \frac{46}{105} & & \\ & V = \left\{ \frac{46}{105} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{2}{15})& = & x+\frac{6}{7} \\\Leftrightarrow & -20x-\frac{2}{3}& = & x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(-20x-\frac{2}{3})& = & (x+\frac{6}{7}). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{-14} & = & \color{red}{21x} +18 \\\Leftrightarrow & -420x \color{red}{-14} \color{blue}{+14} \color{blue}{-21x} & = & \color{red}{21x} +18 \color{blue}{-21x} \color{blue}{+14} \\\Leftrightarrow & -420x-21x& = & 18+14 \\\Leftrightarrow & \color{red}{-441} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-441} & & \\\Leftrightarrow & x = \frac{-32}{441} & & \\ & V = \left\{ \frac{-32}{441} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-} (-3x-\frac{3}{8})& = & 5x+\frac{7}{4} \\\Leftrightarrow & 3x+\frac{3}{8}& = & 5x+\frac{7}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(3x+\frac{3}{8})& = & (5x+\frac{7}{4}). \color{blue}{8} \\\Leftrightarrow & 24x \color{red}{+3} & = & \color{red}{40x} +14 \\\Leftrightarrow & 24x \color{red}{+3} \color{blue}{-3} \color{blue}{-40x} & = & \color{red}{40x} +14 \color{blue}{-40x} \color{blue}{-3} \\\Leftrightarrow & 24x-40x& = & 14-3 \\\Leftrightarrow & \color{red}{-16} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-16} & & \\\Leftrightarrow & x = \frac{-11}{16} & & \\ & V = \left\{ \frac{-11}{16} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-x+\frac{4}{5})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 4x-\frac{16}{5}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(4x-\frac{16}{5})& = & (5x+\frac{4}{7}). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{-112} & = & \color{red}{175x} +20 \\\Leftrightarrow & 140x \color{red}{-112} \color{blue}{+112} \color{blue}{-175x} & = & \color{red}{175x} +20 \color{blue}{-175x} \color{blue}{+112} \\\Leftrightarrow & 140x-175x& = & 20+112 \\\Leftrightarrow & \color{red}{-35} x& = & 132 \\\Leftrightarrow & x = \frac{132}{-35} & & \\\Leftrightarrow & x = \frac{-132}{35} & & \\ & V = \left\{ \frac{-132}{35} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2026-09-13 19:30:33