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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{4}{7})& = & x+\frac{10}{9} \\\Leftrightarrow & -8x+\frac{16}{7}& = & x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(-8x+\frac{16}{7})& = & (x+\frac{10}{9}). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{+144} & = & \color{red}{63x} +70 \\\Leftrightarrow & -504x \color{red}{+144} \color{blue}{-144} \color{blue}{-63x} & = & \color{red}{63x} +70 \color{blue}{-63x} \color{blue}{-144} \\\Leftrightarrow & -504x-63x& = & 70-144 \\\Leftrightarrow & \color{red}{-567} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{-567} & & \\\Leftrightarrow & x = \frac{74}{567} & & \\ & V = \left\{ \frac{74}{567} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{3}{14})& = & 4x+\frac{10}{11} \\\Leftrightarrow & 25x+\frac{15}{14}& = & 4x+\frac{10}{11} \\ & & & \text{kgv van noemers 14 en 11 is 154} \\\Leftrightarrow & \color{blue}{154} .(25x+\frac{15}{14})& = & (4x+\frac{10}{11}). \color{blue}{154} \\\Leftrightarrow & 3850x \color{red}{+165} & = & \color{red}{616x} +140 \\\Leftrightarrow & 3850x \color{red}{+165} \color{blue}{-165} \color{blue}{-616x} & = & \color{red}{616x} +140 \color{blue}{-616x} \color{blue}{-165} \\\Leftrightarrow & 3850x-616x& = & 140-165 \\\Leftrightarrow & \color{red}{3234} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{3234} & & \\ & V = \left\{ \frac{-25}{3234} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{10})& = & 9x+\frac{4}{9} \\\Leftrightarrow & -10x-\frac{3}{5}& = & 9x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(-10x-\frac{3}{5})& = & (9x+\frac{4}{9}). \color{blue}{45} \\\Leftrightarrow & -450x \color{red}{-27} & = & \color{red}{405x} +20 \\\Leftrightarrow & -450x \color{red}{-27} \color{blue}{+27} \color{blue}{-405x} & = & \color{red}{405x} +20 \color{blue}{-405x} \color{blue}{+27} \\\Leftrightarrow & -450x-405x& = & 20+27 \\\Leftrightarrow & \color{red}{-855} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-855} & & \\\Leftrightarrow & x = \frac{-47}{855} & & \\ & V = \left\{ \frac{-47}{855} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{3}{10})& = & 5x+\frac{3}{8} \\\Leftrightarrow & -9x+\frac{9}{10}& = & 5x+\frac{3}{8} \\ & & & \text{kgv van noemers 10 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(-9x+\frac{9}{10})& = & (5x+\frac{3}{8}). \color{blue}{40} \\\Leftrightarrow & -360x \color{red}{+36} & = & \color{red}{200x} +15 \\\Leftrightarrow & -360x \color{red}{+36} \color{blue}{-36} \color{blue}{-200x} & = & \color{red}{200x} +15 \color{blue}{-200x} \color{blue}{-36} \\\Leftrightarrow & -360x-200x& = & 15-36 \\\Leftrightarrow & \color{red}{-560} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-560} & & \\\Leftrightarrow & x = \frac{3}{80} & & \\ & V = \left\{ \frac{3}{80} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{5}{3})& = & 7x+\frac{7}{3} \\\Leftrightarrow & 12x+5& = & 7x+\frac{7}{3} \\ & & & \text{kgv van noemers 1 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(12x+5)& = & (7x+\frac{7}{3}). \color{blue}{3} \\\Leftrightarrow & 36x \color{red}{+15} & = & \color{red}{21x} +7 \\\Leftrightarrow & 36x \color{red}{+15} \color{blue}{-15} \color{blue}{-21x} & = & \color{red}{21x} +7 \color{blue}{-21x} \color{blue}{-15} \\\Leftrightarrow & 36x-21x& = & 7-15 \\\Leftrightarrow & \color{red}{15} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{15} & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{5}{7})& = & 5x+\frac{4}{7} \\\Leftrightarrow & -6x+\frac{15}{7}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(-6x+\frac{15}{7})& = & (5x+\frac{4}{7}). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{+15} & = & \color{red}{35x} +4 \\\Leftrightarrow & -42x \color{red}{+15} \color{blue}{-15} \color{blue}{-35x} & = & \color{red}{35x} +4 \color{blue}{-35x} \color{blue}{-15} \\\Leftrightarrow & -42x-35x& = & 4-15 \\\Leftrightarrow & \color{red}{-77} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-77} & & \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{3}{7})& = & 5x+\frac{5}{9} \\\Leftrightarrow & 14x-3& = & 5x+\frac{5}{9} \\ & & & \text{kgv van noemers 1 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(14x-3)& = & (5x+\frac{5}{9}). \color{blue}{9} \\\Leftrightarrow & 126x \color{red}{-27} & = & \color{red}{45x} +5 \\\Leftrightarrow & 126x \color{red}{-27} \color{blue}{+27} \color{blue}{-45x} & = & \color{red}{45x} +5 \color{blue}{-45x} \color{blue}{+27} \\\Leftrightarrow & 126x-45x& = & 5+27 \\\Leftrightarrow & \color{red}{81} x& = & 32 \\\Leftrightarrow & x = \frac{32}{81} & & \\ & V = \left\{ \frac{32}{81} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{3}{8})& = & -7x+\frac{5}{7} \\\Leftrightarrow & -18x-\frac{9}{4}& = & -7x+\frac{5}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(-18x-\frac{9}{4})& = & (-7x+\frac{5}{7}). \color{blue}{28} \\\Leftrightarrow & -504x \color{red}{-63} & = & \color{red}{-196x} +20 \\\Leftrightarrow & -504x \color{red}{-63} \color{blue}{+63} \color{blue}{+196x} & = & \color{red}{-196x} +20 \color{blue}{+196x} \color{blue}{+63} \\\Leftrightarrow & -504x+196x& = & 20+63 \\\Leftrightarrow & \color{red}{-308} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-308} & & \\\Leftrightarrow & x = \frac{-83}{308} & & \\ & V = \left\{ \frac{-83}{308} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (-3x-\frac{3}{7})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -3x-\frac{3}{7}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(-3x-\frac{3}{7})& = & (7x+\frac{9}{7}). \color{blue}{7} \\\Leftrightarrow & -21x \color{red}{-3} & = & \color{red}{49x} +9 \\\Leftrightarrow & -21x \color{red}{-3} \color{blue}{+3} \color{blue}{-49x} & = & \color{red}{49x} +9 \color{blue}{-49x} \color{blue}{+3} \\\Leftrightarrow & -21x-49x& = & 9+3 \\\Leftrightarrow & \color{red}{-70} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-70} & & \\\Leftrightarrow & x = \frac{-6}{35} & & \\ & V = \left\{ \frac{-6}{35} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{10})& = & 5x+\frac{3}{5} \\\Leftrightarrow & 21x+\frac{21}{10}& = & 5x+\frac{3}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(21x+\frac{21}{10})& = & (5x+\frac{3}{5}). \color{blue}{10} \\\Leftrightarrow & 210x \color{red}{+21} & = & \color{red}{50x} +6 \\\Leftrightarrow & 210x \color{red}{+21} \color{blue}{-21} \color{blue}{-50x} & = & \color{red}{50x} +6 \color{blue}{-50x} \color{blue}{-21} \\\Leftrightarrow & 210x-50x& = & 6-21 \\\Leftrightarrow & \color{red}{160} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{160} & & \\\Leftrightarrow & x = \frac{-3}{32} & & \\ & V = \left\{ \frac{-3}{32} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{2}{15})& = & 5x+\frac{10}{11} \\\Leftrightarrow & -12x+\frac{4}{5}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(-12x+\frac{4}{5})& = & (5x+\frac{10}{11}). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+44} & = & \color{red}{275x} +50 \\\Leftrightarrow & -660x \color{red}{+44} \color{blue}{-44} \color{blue}{-275x} & = & \color{red}{275x} +50 \color{blue}{-275x} \color{blue}{-44} \\\Leftrightarrow & -660x-275x& = & 50-44 \\\Leftrightarrow & \color{red}{-935} x& = & 6 \\\Leftrightarrow & x = \frac{6}{-935} & & \\\Leftrightarrow & x = \frac{-6}{935} & & \\ & V = \left\{ \frac{-6}{935} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (x-\frac{4}{5})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -4x+\frac{16}{5}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(-4x+\frac{16}{5})& = & (7x+\frac{2}{3}). \color{blue}{15} \\\Leftrightarrow & -60x \color{red}{+48} & = & \color{red}{105x} +10 \\\Leftrightarrow & -60x \color{red}{+48} \color{blue}{-48} \color{blue}{-105x} & = & \color{red}{105x} +10 \color{blue}{-105x} \color{blue}{-48} \\\Leftrightarrow & -60x-105x& = & 10-48 \\\Leftrightarrow & \color{red}{-165} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-165} & & \\\Leftrightarrow & x = \frac{38}{165} & & \\ & V = \left\{ \frac{38}{165} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-05-03 17:26:50