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Alles samen. Gebruik stappenplan en ZRM!

  1. \(-5(-2x-\frac{5}{11})=-9x+\frac{10}{7}\)
  2. \(-4(-2x+\frac{3}{8})=9x+\frac{8}{9}\)
  3. \(6(5x-\frac{3}{2})=29x+\frac{10}{11}\)
  4. \(-2(-3x+\frac{2}{3})=-5x+\frac{8}{11}\)
  5. \(-6(5x-\frac{3}{16})=7x+\frac{7}{4}\)
  6. \(4(-3x+\frac{3}{4})=7x+\frac{5}{8}\)
  7. \(-5(5x+\frac{3}{7})=-2x+\frac{6}{7}\)
  8. \(4(5x+\frac{4}{5})=19x+\frac{3}{4}\)
  9. \(3(-x+\frac{3}{8})=7x+\frac{5}{7}\)
  10. \(3(-5x-\frac{2}{13})=4x+\frac{7}{6}\)
  11. \(-3(-2x+\frac{5}{16})=5x+\frac{6}{7}\)
  12. \(5(-2x-\frac{2}{5})=-9x+\frac{8}{9}\)

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{5}{11})& = & -9x+\frac{10}{7} \\\Leftrightarrow & 10x+\frac{25}{11}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(10x+\frac{25}{11})& = & (-9x+\frac{10}{7}). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+175} & = & \color{red}{-693x} +110 \\\Leftrightarrow & 770x \color{red}{+175} \color{blue}{-175} \color{blue}{+693x} & = & \color{red}{-693x} +110 \color{blue}{+693x} \color{blue}{-175} \\\Leftrightarrow & 770x+693x& = & 110-175 \\\Leftrightarrow & \color{red}{1463} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{1463} & & \\ & V = \left\{ \frac{-65}{1463} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{3}{8})& = & 9x+\frac{8}{9} \\\Leftrightarrow & 8x-\frac{3}{2}& = & 9x+\frac{8}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(8x-\frac{3}{2})& = & (9x+\frac{8}{9}). \color{blue}{18} \\\Leftrightarrow & 144x \color{red}{-27} & = & \color{red}{162x} +16 \\\Leftrightarrow & 144x \color{red}{-27} \color{blue}{+27} \color{blue}{-162x} & = & \color{red}{162x} +16 \color{blue}{-162x} \color{blue}{+27} \\\Leftrightarrow & 144x-162x& = & 16+27 \\\Leftrightarrow & \color{red}{-18} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-18} & & \\\Leftrightarrow & x = \frac{-43}{18} & & \\ & V = \left\{ \frac{-43}{18} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{3}{2})& = & 29x+\frac{10}{11} \\\Leftrightarrow & 30x-9& = & 29x+\frac{10}{11} \\ & & & \text{kgv van noemers 1 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(30x-9)& = & (29x+\frac{10}{11}). \color{blue}{11} \\\Leftrightarrow & 330x \color{red}{-99} & = & \color{red}{319x} +10 \\\Leftrightarrow & 330x \color{red}{-99} \color{blue}{+99} \color{blue}{-319x} & = & \color{red}{319x} +10 \color{blue}{-319x} \color{blue}{+99} \\\Leftrightarrow & 330x-319x& = & 10+99 \\\Leftrightarrow & \color{red}{11} x& = & 109 \\\Leftrightarrow & x = \frac{109}{11} & & \\ & V = \left\{ \frac{109}{11} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{2}{3})& = & -5x+\frac{8}{11} \\\Leftrightarrow & 6x-\frac{4}{3}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(6x-\frac{4}{3})& = & (-5x+\frac{8}{11}). \color{blue}{33} \\\Leftrightarrow & 198x \color{red}{-44} & = & \color{red}{-165x} +24 \\\Leftrightarrow & 198x \color{red}{-44} \color{blue}{+44} \color{blue}{+165x} & = & \color{red}{-165x} +24 \color{blue}{+165x} \color{blue}{+44} \\\Leftrightarrow & 198x+165x& = & 24+44 \\\Leftrightarrow & \color{red}{363} x& = & 68 \\\Leftrightarrow & x = \frac{68}{363} & & \\ & V = \left\{ \frac{68}{363} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{3}{16})& = & 7x+\frac{7}{4} \\\Leftrightarrow & -30x+\frac{9}{8}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(-30x+\frac{9}{8})& = & (7x+\frac{7}{4}). \color{blue}{8} \\\Leftrightarrow & -240x \color{red}{+9} & = & \color{red}{56x} +14 \\\Leftrightarrow & -240x \color{red}{+9} \color{blue}{-9} \color{blue}{-56x} & = & \color{red}{56x} +14 \color{blue}{-56x} \color{blue}{-9} \\\Leftrightarrow & -240x-56x& = & 14-9 \\\Leftrightarrow & \color{red}{-296} x& = & 5 \\\Leftrightarrow & x = \frac{5}{-296} & & \\\Leftrightarrow & x = \frac{-5}{296} & & \\ & V = \left\{ \frac{-5}{296} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{3}{4})& = & 7x+\frac{5}{8} \\\Leftrightarrow & -12x+3& = & 7x+\frac{5}{8} \\ & & & \text{kgv van noemers 1 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(-12x+3)& = & (7x+\frac{5}{8}). \color{blue}{8} \\\Leftrightarrow & -96x \color{red}{+24} & = & \color{red}{56x} +5 \\\Leftrightarrow & -96x \color{red}{+24} \color{blue}{-24} \color{blue}{-56x} & = & \color{red}{56x} +5 \color{blue}{-56x} \color{blue}{-24} \\\Leftrightarrow & -96x-56x& = & 5-24 \\\Leftrightarrow & \color{red}{-152} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{-152} & & \\\Leftrightarrow & x = \frac{1}{8} & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{3}{7})& = & -2x+\frac{6}{7} \\\Leftrightarrow & -25x-\frac{15}{7}& = & -2x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(-25x-\frac{15}{7})& = & (-2x+\frac{6}{7}). \color{blue}{7} \\\Leftrightarrow & -175x \color{red}{-15} & = & \color{red}{-14x} +6 \\\Leftrightarrow & -175x \color{red}{-15} \color{blue}{+15} \color{blue}{+14x} & = & \color{red}{-14x} +6 \color{blue}{+14x} \color{blue}{+15} \\\Leftrightarrow & -175x+14x& = & 6+15 \\\Leftrightarrow & \color{red}{-161} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-161} & & \\\Leftrightarrow & x = \frac{-3}{23} & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{4}{5})& = & 19x+\frac{3}{4} \\\Leftrightarrow & 20x+\frac{16}{5}& = & 19x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(20x+\frac{16}{5})& = & (19x+\frac{3}{4}). \color{blue}{20} \\\Leftrightarrow & 400x \color{red}{+64} & = & \color{red}{380x} +15 \\\Leftrightarrow & 400x \color{red}{+64} \color{blue}{-64} \color{blue}{-380x} & = & \color{red}{380x} +15 \color{blue}{-380x} \color{blue}{-64} \\\Leftrightarrow & 400x-380x& = & 15-64 \\\Leftrightarrow & \color{red}{20} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{20} & & \\ & V = \left\{ \frac{-49}{20} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-x+\frac{3}{8})& = & 7x+\frac{5}{7} \\\Leftrightarrow & -3x+\frac{9}{8}& = & 7x+\frac{5}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(-3x+\frac{9}{8})& = & (7x+\frac{5}{7}). \color{blue}{56} \\\Leftrightarrow & -168x \color{red}{+63} & = & \color{red}{392x} +40 \\\Leftrightarrow & -168x \color{red}{+63} \color{blue}{-63} \color{blue}{-392x} & = & \color{red}{392x} +40 \color{blue}{-392x} \color{blue}{-63} \\\Leftrightarrow & -168x-392x& = & 40-63 \\\Leftrightarrow & \color{red}{-560} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-560} & & \\\Leftrightarrow & x = \frac{23}{560} & & \\ & V = \left\{ \frac{23}{560} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{13})& = & 4x+\frac{7}{6} \\\Leftrightarrow & -15x-\frac{6}{13}& = & 4x+\frac{7}{6} \\ & & & \text{kgv van noemers 13 en 6 is 78} \\\Leftrightarrow & \color{blue}{78} .(-15x-\frac{6}{13})& = & (4x+\frac{7}{6}). \color{blue}{78} \\\Leftrightarrow & -1170x \color{red}{-36} & = & \color{red}{312x} +91 \\\Leftrightarrow & -1170x \color{red}{-36} \color{blue}{+36} \color{blue}{-312x} & = & \color{red}{312x} +91 \color{blue}{-312x} \color{blue}{+36} \\\Leftrightarrow & -1170x-312x& = & 91+36 \\\Leftrightarrow & \color{red}{-1482} x& = & 127 \\\Leftrightarrow & x = \frac{127}{-1482} & & \\\Leftrightarrow & x = \frac{-127}{1482} & & \\ & V = \left\{ \frac{-127}{1482} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{5}{16})& = & 5x+\frac{6}{7} \\\Leftrightarrow & 6x-\frac{15}{16}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 16 en 7 is 112} \\\Leftrightarrow & \color{blue}{112} .(6x-\frac{15}{16})& = & (5x+\frac{6}{7}). \color{blue}{112} \\\Leftrightarrow & 672x \color{red}{-105} & = & \color{red}{560x} +96 \\\Leftrightarrow & 672x \color{red}{-105} \color{blue}{+105} \color{blue}{-560x} & = & \color{red}{560x} +96 \color{blue}{-560x} \color{blue}{+105} \\\Leftrightarrow & 672x-560x& = & 96+105 \\\Leftrightarrow & \color{red}{112} x& = & 201 \\\Leftrightarrow & x = \frac{201}{112} & & \\ & V = \left\{ \frac{201}{112} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{2}{5})& = & -9x+\frac{8}{9} \\\Leftrightarrow & -10x-2& = & -9x+\frac{8}{9} \\ & & & \text{kgv van noemers 1 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(-10x-2)& = & (-9x+\frac{8}{9}). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{-18} & = & \color{red}{-81x} +8 \\\Leftrightarrow & -90x \color{red}{-18} \color{blue}{+18} \color{blue}{+81x} & = & \color{red}{-81x} +8 \color{blue}{+81x} \color{blue}{+18} \\\Leftrightarrow & -90x+81x& = & 8+18 \\\Leftrightarrow & \color{red}{-9} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-9} & & \\\Leftrightarrow & x = \frac{-26}{9} & & \\ & V = \left\{ \frac{-26}{9} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-05-08 13:44:39