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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{5}{7})& = & 5x+\frac{7}{9} \\\Leftrightarrow & 24x+\frac{30}{7}& = & 5x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1512}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1512x \color{red}{+270} & = & \color{red}{315x} +49 \\\Leftrightarrow & 1512x \color{red}{+270} \color{blue}{-270} \color{blue}{-315x} & = & \color{red}{315x} +49 \color{blue}{-315x} \color{blue}{-270} \\\Leftrightarrow & 1512x-315x& = & 49-270 \\\Leftrightarrow & \color{red}{1197} x& = & -221 \\\Leftrightarrow & x = \frac{-221}{1197} & & \\ & V = \left\{ \frac{-221}{1197} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{3}{5})& = & -7x+\frac{4}{5} \\\Leftrightarrow & -16x-\frac{12}{5}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-80}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -80x \color{red}{-12} & = & \color{red}{-35x} +4 \\\Leftrightarrow & -80x \color{red}{-12} \color{blue}{+12} \color{blue}{+35x} & = & \color{red}{-35x} +4 \color{blue}{+35x} \color{blue}{+12} \\\Leftrightarrow & -80x+35x& = & 4+12 \\\Leftrightarrow & \color{red}{-45} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-45} & & \\\Leftrightarrow & x = \frac{-16}{45} & & \\ & V = \left\{ \frac{-16}{45} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{5}{3})& = & 5x+\frac{7}{9} \\\Leftrightarrow & 16x-\frac{20}{3}& = & 5x+\frac{7}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{144}{ \color{blue}{9} }x- \frac{60}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 144x \color{red}{-60} & = & \color{red}{45x} +7 \\\Leftrightarrow & 144x \color{red}{-60} \color{blue}{+60} \color{blue}{-45x} & = & \color{red}{45x} +7 \color{blue}{-45x} \color{blue}{+60} \\\Leftrightarrow & 144x-45x& = & 7+60 \\\Leftrightarrow & \color{red}{99} x& = & 67 \\\Leftrightarrow & x = \frac{67}{99} & & \\ & V = \left\{ \frac{67}{99} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -28x-\frac{28}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-140}{ \color{blue}{5} }x- \frac{28}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -140x \color{red}{-28} & = & \color{red}{25x} +6 \\\Leftrightarrow & -140x \color{red}{-28} \color{blue}{+28} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{+28} \\\Leftrightarrow & -140x-25x& = & 6+28 \\\Leftrightarrow & \color{red}{-165} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-165} & & \\\Leftrightarrow & x = \frac{-34}{165} & & \\ & V = \left\{ \frac{-34}{165} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{7})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -20x-\frac{25}{7}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-280}{ \color{blue}{14} }x- \frac{50}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -280x \color{red}{-50} & = & \color{red}{-98x} +35 \\\Leftrightarrow & -280x \color{red}{-50} \color{blue}{+50} \color{blue}{+98x} & = & \color{red}{-98x} +35 \color{blue}{+98x} \color{blue}{+50} \\\Leftrightarrow & -280x+98x& = & 35+50 \\\Leftrightarrow & \color{red}{-182} x& = & 85 \\\Leftrightarrow & x = \frac{85}{-182} & & \\\Leftrightarrow & x = \frac{-85}{182} & & \\ & V = \left\{ \frac{-85}{182} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{5}{11})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 12x+\frac{30}{11}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1188}{ \color{blue}{99} }x+ \frac{270}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1188x \color{red}{+270} & = & \color{red}{-495x} +88 \\\Leftrightarrow & 1188x \color{red}{+270} \color{blue}{-270} \color{blue}{+495x} & = & \color{red}{-495x} +88 \color{blue}{+495x} \color{blue}{-270} \\\Leftrightarrow & 1188x+495x& = & 88-270 \\\Leftrightarrow & \color{red}{1683} x& = & -182 \\\Leftrightarrow & x = \frac{-182}{1683} & & \\ & V = \left\{ \frac{-182}{1683} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{3}{11})& = & 5x+\frac{3}{10} \\\Leftrightarrow & -18x-\frac{18}{11}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1980}{ \color{blue}{110} }x- \frac{180}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1980x \color{red}{-180} & = & \color{red}{550x} +33 \\\Leftrightarrow & -1980x \color{red}{-180} \color{blue}{+180} \color{blue}{-550x} & = & \color{red}{550x} +33 \color{blue}{-550x} \color{blue}{+180} \\\Leftrightarrow & -1980x-550x& = & 33+180 \\\Leftrightarrow & \color{red}{-2530} x& = & 213 \\\Leftrightarrow & x = \frac{213}{-2530} & & \\\Leftrightarrow & x = \frac{-213}{2530} & & \\ & V = \left\{ \frac{-213}{2530} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{9})& = & 8x+\frac{2}{3} \\\Leftrightarrow & -21x-\frac{14}{9}& = & 8x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-189}{ \color{blue}{9} }x- \frac{14}{ \color{blue}{9} })& = & (\frac{72}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -189x \color{red}{-14} & = & \color{red}{72x} +6 \\\Leftrightarrow & -189x \color{red}{-14} \color{blue}{+14} \color{blue}{-72x} & = & \color{red}{72x} +6 \color{blue}{-72x} \color{blue}{+14} \\\Leftrightarrow & -189x-72x& = & 6+14 \\\Leftrightarrow & \color{red}{-261} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-261} & & \\\Leftrightarrow & x = \frac{-20}{261} & & \\ & V = \left\{ \frac{-20}{261} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{5}{3})& = & -3x+\frac{2}{3} \\\Leftrightarrow & -20x-\frac{20}{3}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-60}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -60x \color{red}{-20} & = & \color{red}{-9x} +2 \\\Leftrightarrow & -60x \color{red}{-20} \color{blue}{+20} \color{blue}{+9x} & = & \color{red}{-9x} +2 \color{blue}{+9x} \color{blue}{+20} \\\Leftrightarrow & -60x+9x& = & 2+20 \\\Leftrightarrow & \color{red}{-51} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-51} & & \\\Leftrightarrow & x = \frac{-22}{51} & & \\ & V = \left\{ \frac{-22}{51} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{2}{3})& = & 8x+\frac{9}{8} \\\Leftrightarrow & -21x-\frac{14}{3}& = & 8x+\frac{9}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-504}{ \color{blue}{24} }x- \frac{112}{ \color{blue}{24} })& = & (\frac{192}{ \color{blue}{24} }x+ \frac{27}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -504x \color{red}{-112} & = & \color{red}{192x} +27 \\\Leftrightarrow & -504x \color{red}{-112} \color{blue}{+112} \color{blue}{-192x} & = & \color{red}{192x} +27 \color{blue}{-192x} \color{blue}{+112} \\\Leftrightarrow & -504x-192x& = & 27+112 \\\Leftrightarrow & \color{red}{-696} x& = & 139 \\\Leftrightarrow & x = \frac{139}{-696} & & \\\Leftrightarrow & x = \frac{-139}{696} & & \\ & V = \left\{ \frac{-139}{696} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{5}{7})& = & -9x+\frac{3}{5} \\\Leftrightarrow & -4x-\frac{10}{7}& = & -9x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-140}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -140x \color{red}{-50} & = & \color{red}{-315x} +21 \\\Leftrightarrow & -140x \color{red}{-50} \color{blue}{+50} \color{blue}{+315x} & = & \color{red}{-315x} +21 \color{blue}{+315x} \color{blue}{+50} \\\Leftrightarrow & -140x+315x& = & 21+50 \\\Leftrightarrow & \color{red}{175} x& = & 71 \\\Leftrightarrow & x = \frac{71}{175} & & \\ & V = \left\{ \frac{71}{175} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{4}{3})& = & 3x+\frac{10}{7} \\\Leftrightarrow & 10x+\frac{8}{3}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{+56} & = & \color{red}{63x} +30 \\\Leftrightarrow & 210x \color{red}{+56} \color{blue}{-56} \color{blue}{-63x} & = & \color{red}{63x} +30 \color{blue}{-63x} \color{blue}{-56} \\\Leftrightarrow & 210x-63x& = & 30-56 \\\Leftrightarrow & \color{red}{147} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{147} & & \\ & V = \left\{ \frac{-26}{147} \right\} & \\\end{align}\)
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