Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{2}{5})& = & 7x+\frac{2}{11} \\\Leftrightarrow & -30x-\frac{12}{5}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{-132} & = & \color{red}{385x} +10 \\\Leftrightarrow & -1650x \color{red}{-132} \color{blue}{+132} \color{blue}{-385x} & = & \color{red}{385x} +10 \color{blue}{-385x} \color{blue}{+132} \\\Leftrightarrow & -1650x-385x& = & 10+132 \\\Leftrightarrow & \color{red}{-2035} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-2035} & & \\\Leftrightarrow & x = \frac{-142}{2035} & & \\ & V = \left\{ \frac{-142}{2035} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{5})& = & 3x+\frac{9}{4} \\\Leftrightarrow & -20x+\frac{16}{5}& = & 3x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-400}{ \color{blue}{20} }x+ \frac{64}{ \color{blue}{20} })& = & (\frac{60}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -400x \color{red}{+64} & = & \color{red}{60x} +45 \\\Leftrightarrow & -400x \color{red}{+64} \color{blue}{-64} \color{blue}{-60x} & = & \color{red}{60x} +45 \color{blue}{-60x} \color{blue}{-64} \\\Leftrightarrow & -400x-60x& = & 45-64 \\\Leftrightarrow & \color{red}{-460} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{-460} & & \\\Leftrightarrow & x = \frac{19}{460} & & \\ & V = \left\{ \frac{19}{460} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{3}{5})& = & 9x+\frac{6}{11} \\\Leftrightarrow & 8x-\frac{12}{5}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-132} & = & \color{red}{495x} +30 \\\Leftrightarrow & 440x \color{red}{-132} \color{blue}{+132} \color{blue}{-495x} & = & \color{red}{495x} +30 \color{blue}{-495x} \color{blue}{+132} \\\Leftrightarrow & 440x-495x& = & 30+132 \\\Leftrightarrow & \color{red}{-55} x& = & 162 \\\Leftrightarrow & x = \frac{162}{-55} & & \\\Leftrightarrow & x = \frac{-162}{55} & & \\ & V = \left\{ \frac{-162}{55} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{3}{5})& = & 7x+\frac{3}{10} \\\Leftrightarrow & 18x+\frac{18}{5}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{180}{ \color{blue}{10} }x+ \frac{36}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 180x \color{red}{+36} & = & \color{red}{70x} +3 \\\Leftrightarrow & 180x \color{red}{+36} \color{blue}{-36} \color{blue}{-70x} & = & \color{red}{70x} +3 \color{blue}{-70x} \color{blue}{-36} \\\Leftrightarrow & 180x-70x& = & 3-36 \\\Leftrightarrow & \color{red}{110} x& = & -33 \\\Leftrightarrow & x = \frac{-33}{110} & & \\\Leftrightarrow & x = \frac{-3}{10} & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{5})& = & 7x+\frac{4}{7} \\\Leftrightarrow & 20x+\frac{8}{5}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{+56} & = & \color{red}{245x} +20 \\\Leftrightarrow & 700x \color{red}{+56} \color{blue}{-56} \color{blue}{-245x} & = & \color{red}{245x} +20 \color{blue}{-245x} \color{blue}{-56} \\\Leftrightarrow & 700x-245x& = & 20-56 \\\Leftrightarrow & \color{red}{455} x& = & -36 \\\Leftrightarrow & x = \frac{-36}{455} & & \\ & V = \left\{ \frac{-36}{455} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{5}{4})& = & -4x+\frac{4}{3} \\\Leftrightarrow & 15x+\frac{15}{4}& = & -4x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{-48}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{+45} & = & \color{red}{-48x} +16 \\\Leftrightarrow & 180x \color{red}{+45} \color{blue}{-45} \color{blue}{+48x} & = & \color{red}{-48x} +16 \color{blue}{+48x} \color{blue}{-45} \\\Leftrightarrow & 180x+48x& = & 16-45 \\\Leftrightarrow & \color{red}{228} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{228} & & \\ & V = \left\{ \frac{-29}{228} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{3}{11})& = & -8x+\frac{10}{11} \\\Leftrightarrow & -28x-\frac{21}{11}& = & -8x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-308}{ \color{blue}{11} }x- \frac{21}{ \color{blue}{11} })& = & (\frac{-88}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -308x \color{red}{-21} & = & \color{red}{-88x} +10 \\\Leftrightarrow & -308x \color{red}{-21} \color{blue}{+21} \color{blue}{+88x} & = & \color{red}{-88x} +10 \color{blue}{+88x} \color{blue}{+21} \\\Leftrightarrow & -308x+88x& = & 10+21 \\\Leftrightarrow & \color{red}{-220} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-220} & & \\\Leftrightarrow & x = \frac{-31}{220} & & \\ & V = \left\{ \frac{-31}{220} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{4}{5})& = & 7x+\frac{4}{5} \\\Leftrightarrow & -20x-\frac{16}{5}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-100}{ \color{blue}{5} }x- \frac{16}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -100x \color{red}{-16} & = & \color{red}{35x} +4 \\\Leftrightarrow & -100x \color{red}{-16} \color{blue}{+16} \color{blue}{-35x} & = & \color{red}{35x} +4 \color{blue}{-35x} \color{blue}{+16} \\\Leftrightarrow & -100x-35x& = & 4+16 \\\Leftrightarrow & \color{red}{-135} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-135} & & \\\Leftrightarrow & x = \frac{-4}{27} & & \\ & V = \left\{ \frac{-4}{27} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{4}{9})& = & -9x+\frac{8}{3} \\\Leftrightarrow & -35x+\frac{28}{9}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-315}{ \color{blue}{9} }x+ \frac{28}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -315x \color{red}{+28} & = & \color{red}{-81x} +24 \\\Leftrightarrow & -315x \color{red}{+28} \color{blue}{-28} \color{blue}{+81x} & = & \color{red}{-81x} +24 \color{blue}{+81x} \color{blue}{-28} \\\Leftrightarrow & -315x+81x& = & 24-28 \\\Leftrightarrow & \color{red}{-234} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-234} & & \\\Leftrightarrow & x = \frac{2}{117} & & \\ & V = \left\{ \frac{2}{117} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{3})& = & 5x+\frac{4}{9} \\\Leftrightarrow & 8x+\frac{8}{3}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{+24} & = & \color{red}{45x} +4 \\\Leftrightarrow & 72x \color{red}{+24} \color{blue}{-24} \color{blue}{-45x} & = & \color{red}{45x} +4 \color{blue}{-45x} \color{blue}{-24} \\\Leftrightarrow & 72x-45x& = & 4-24 \\\Leftrightarrow & \color{red}{27} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{27} & & \\ & V = \left\{ \frac{-20}{27} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{5})& = & 5x+\frac{5}{8} \\\Leftrightarrow & 24x+\frac{24}{5}& = & 5x+\frac{5}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{960}{ \color{blue}{40} }x+ \frac{192}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{25}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 960x \color{red}{+192} & = & \color{red}{200x} +25 \\\Leftrightarrow & 960x \color{red}{+192} \color{blue}{-192} \color{blue}{-200x} & = & \color{red}{200x} +25 \color{blue}{-200x} \color{blue}{-192} \\\Leftrightarrow & 960x-200x& = & 25-192 \\\Leftrightarrow & \color{red}{760} x& = & -167 \\\Leftrightarrow & x = \frac{-167}{760} & & \\ & V = \left\{ \frac{-167}{760} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{5}{7})& = & 5x+\frac{5}{2} \\\Leftrightarrow & 24x+\frac{30}{7}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{336}{ \color{blue}{14} }x+ \frac{60}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 336x \color{red}{+60} & = & \color{red}{70x} +35 \\\Leftrightarrow & 336x \color{red}{+60} \color{blue}{-60} \color{blue}{-70x} & = & \color{red}{70x} +35 \color{blue}{-70x} \color{blue}{-60} \\\Leftrightarrow & 336x-70x& = & 35-60 \\\Leftrightarrow & \color{red}{266} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{266} & & \\ & V = \left\{ \frac{-25}{266} \right\} & \\\end{align}\)
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