Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{3}{14})& = & 5x+\frac{4}{11} \\\Leftrightarrow & -16x+\frac{6}{7}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(-16x+\frac{6}{7})& = & (5x+\frac{4}{11}). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{+66} & = & \color{red}{385x} +28 \\\Leftrightarrow & -1232x \color{red}{+66} \color{blue}{-66} \color{blue}{-385x} & = & \color{red}{385x} +28 \color{blue}{-385x} \color{blue}{-66} \\\Leftrightarrow & -1232x-385x& = & 28-66 \\\Leftrightarrow & \color{red}{-1617} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-1617} & & \\\Leftrightarrow & x = \frac{38}{1617} & & \\ & V = \left\{ \frac{38}{1617} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{3}{11})& = & 19x+\frac{3}{13} \\\Leftrightarrow & 20x+\frac{15}{11}& = & 19x+\frac{3}{13} \\ & & & \text{kgv van noemers 11 en 13 is 143} \\\Leftrightarrow & \color{blue}{143} .(20x+\frac{15}{11})& = & (19x+\frac{3}{13}). \color{blue}{143} \\\Leftrightarrow & 2860x \color{red}{+195} & = & \color{red}{2717x} +33 \\\Leftrightarrow & 2860x \color{red}{+195} \color{blue}{-195} \color{blue}{-2717x} & = & \color{red}{2717x} +33 \color{blue}{-2717x} \color{blue}{-195} \\\Leftrightarrow & 2860x-2717x& = & 33-195 \\\Leftrightarrow & \color{red}{143} x& = & -162 \\\Leftrightarrow & x = \frac{-162}{143} & & \\ & V = \left\{ \frac{-162}{143} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{5}{6})& = & 4x+\frac{4}{9} \\\Leftrightarrow & 15x+\frac{5}{2}& = & 4x+\frac{4}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(15x+\frac{5}{2})& = & (4x+\frac{4}{9}). \color{blue}{18} \\\Leftrightarrow & 270x \color{red}{+45} & = & \color{red}{72x} +8 \\\Leftrightarrow & 270x \color{red}{+45} \color{blue}{-45} \color{blue}{-72x} & = & \color{red}{72x} +8 \color{blue}{-72x} \color{blue}{-45} \\\Leftrightarrow & 270x-72x& = & 8-45 \\\Leftrightarrow & \color{red}{198} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{198} & & \\ & V = \left\{ \frac{-37}{198} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (-5x+\frac{2}{9})& = & -2x+\frac{5}{4} \\\Leftrightarrow & -5x+\frac{2}{9}& = & -2x+\frac{5}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(-5x+\frac{2}{9})& = & (-2x+\frac{5}{4}). \color{blue}{36} \\\Leftrightarrow & -180x \color{red}{+8} & = & \color{red}{-72x} +45 \\\Leftrightarrow & -180x \color{red}{+8} \color{blue}{-8} \color{blue}{+72x} & = & \color{red}{-72x} +45 \color{blue}{+72x} \color{blue}{-8} \\\Leftrightarrow & -180x+72x& = & 45-8 \\\Leftrightarrow & \color{red}{-108} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-108} & & \\\Leftrightarrow & x = \frac{-37}{108} & & \\ & V = \left\{ \frac{-37}{108} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{5})& = & -3x+\frac{4}{13} \\\Leftrightarrow & -10x-3& = & -3x+\frac{4}{13} \\ & & & \text{kgv van noemers 1 en 13 is 13} \\\Leftrightarrow & \color{blue}{13} .(-10x-3)& = & (-3x+\frac{4}{13}). \color{blue}{13} \\\Leftrightarrow & -130x \color{red}{-39} & = & \color{red}{-39x} +4 \\\Leftrightarrow & -130x \color{red}{-39} \color{blue}{+39} \color{blue}{+39x} & = & \color{red}{-39x} +4 \color{blue}{+39x} \color{blue}{+39} \\\Leftrightarrow & -130x+39x& = & 4+39 \\\Leftrightarrow & \color{red}{-91} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-91} & & \\\Leftrightarrow & x = \frac{-43}{91} & & \\ & V = \left\{ \frac{-43}{91} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{3}{16})& = & 2x+\frac{4}{13} \\\Leftrightarrow & 15x+\frac{15}{16}& = & 2x+\frac{4}{13} \\ & & & \text{kgv van noemers 16 en 13 is 208} \\\Leftrightarrow & \color{blue}{208} .(15x+\frac{15}{16})& = & (2x+\frac{4}{13}). \color{blue}{208} \\\Leftrightarrow & 3120x \color{red}{+195} & = & \color{red}{416x} +64 \\\Leftrightarrow & 3120x \color{red}{+195} \color{blue}{-195} \color{blue}{-416x} & = & \color{red}{416x} +64 \color{blue}{-416x} \color{blue}{-195} \\\Leftrightarrow & 3120x-416x& = & 64-195 \\\Leftrightarrow & \color{red}{2704} x& = & -131 \\\Leftrightarrow & x = \frac{-131}{2704} & & \\ & V = \left\{ \frac{-131}{2704} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{2}{13})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 9x-\frac{6}{13}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 13 en 3 is 39} \\\Leftrightarrow & \color{blue}{39} .(9x-\frac{6}{13})& = & (5x+\frac{8}{3}). \color{blue}{39} \\\Leftrightarrow & 351x \color{red}{-18} & = & \color{red}{195x} +104 \\\Leftrightarrow & 351x \color{red}{-18} \color{blue}{+18} \color{blue}{-195x} & = & \color{red}{195x} +104 \color{blue}{-195x} \color{blue}{+18} \\\Leftrightarrow & 351x-195x& = & 104+18 \\\Leftrightarrow & \color{red}{156} x& = & 122 \\\Leftrightarrow & x = \frac{122}{156} & & \\\Leftrightarrow & x = \frac{61}{78} & & \\ & V = \left\{ \frac{61}{78} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{11})& = & 9x+\frac{5}{16} \\\Leftrightarrow & -10x+\frac{4}{11}& = & 9x+\frac{5}{16} \\ & & & \text{kgv van noemers 11 en 16 is 176} \\\Leftrightarrow & \color{blue}{176} .(-10x+\frac{4}{11})& = & (9x+\frac{5}{16}). \color{blue}{176} \\\Leftrightarrow & -1760x \color{red}{+64} & = & \color{red}{1584x} +55 \\\Leftrightarrow & -1760x \color{red}{+64} \color{blue}{-64} \color{blue}{-1584x} & = & \color{red}{1584x} +55 \color{blue}{-1584x} \color{blue}{-64} \\\Leftrightarrow & -1760x-1584x& = & 55-64 \\\Leftrightarrow & \color{red}{-3344} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-3344} & & \\\Leftrightarrow & x = \frac{9}{3344} & & \\ & V = \left\{ \frac{9}{3344} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (x+\frac{5}{4})& = & 10x+\frac{6}{5} \\\Leftrightarrow & -3x-\frac{15}{4}& = & 10x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(-3x-\frac{15}{4})& = & (10x+\frac{6}{5}). \color{blue}{20} \\\Leftrightarrow & -60x \color{red}{-75} & = & \color{red}{200x} +24 \\\Leftrightarrow & -60x \color{red}{-75} \color{blue}{+75} \color{blue}{-200x} & = & \color{red}{200x} +24 \color{blue}{-200x} \color{blue}{+75} \\\Leftrightarrow & -60x-200x& = & 24+75 \\\Leftrightarrow & \color{red}{-260} x& = & 99 \\\Leftrightarrow & x = \frac{99}{-260} & & \\\Leftrightarrow & x = \frac{-99}{260} & & \\ & V = \left\{ \frac{-99}{260} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (x-\frac{4}{15})& = & 10x+\frac{9}{2} \\\Leftrightarrow & 3x-\frac{4}{5}& = & 10x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(3x-\frac{4}{5})& = & (10x+\frac{9}{2}). \color{blue}{10} \\\Leftrightarrow & 30x \color{red}{-8} & = & \color{red}{100x} +45 \\\Leftrightarrow & 30x \color{red}{-8} \color{blue}{+8} \color{blue}{-100x} & = & \color{red}{100x} +45 \color{blue}{-100x} \color{blue}{+8} \\\Leftrightarrow & 30x-100x& = & 45+8 \\\Leftrightarrow & \color{red}{-70} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-70} & & \\\Leftrightarrow & x = \frac{-53}{70} & & \\ & V = \left\{ \frac{-53}{70} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{4}{3})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -12x-8& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 1 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(-12x-8)& = & (-7x+\frac{5}{2}). \color{blue}{2} \\\Leftrightarrow & -24x \color{red}{-16} & = & \color{red}{-14x} +5 \\\Leftrightarrow & -24x \color{red}{-16} \color{blue}{+16} \color{blue}{+14x} & = & \color{red}{-14x} +5 \color{blue}{+14x} \color{blue}{+16} \\\Leftrightarrow & -24x+14x& = & 5+16 \\\Leftrightarrow & \color{red}{-10} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-10} & & \\\Leftrightarrow & x = \frac{-21}{10} & & \\ & V = \left\{ \frac{-21}{10} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-} (-3x+\frac{5}{12})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 3x-\frac{5}{12}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 12 en 5 is 60} \\\Leftrightarrow & \color{blue}{60} .(3x-\frac{5}{12})& = & (5x+\frac{6}{5}). \color{blue}{60} \\\Leftrightarrow & 180x \color{red}{-25} & = & \color{red}{300x} +72 \\\Leftrightarrow & 180x \color{red}{-25} \color{blue}{+25} \color{blue}{-300x} & = & \color{red}{300x} +72 \color{blue}{-300x} \color{blue}{+25} \\\Leftrightarrow & 180x-300x& = & 72+25 \\\Leftrightarrow & \color{red}{-120} x& = & 97 \\\Leftrightarrow & x = \frac{97}{-120} & & \\\Leftrightarrow & x = \frac{-97}{120} & & \\ & V = \left\{ \frac{-97}{120} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-05-09 13:09:03