Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{2}{3})& = & 8x+\frac{9}{8} \\\Leftrightarrow & -25x+\frac{10}{3}& = & 8x+\frac{9}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-600}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} })& = & (\frac{192}{ \color{blue}{24} }x+ \frac{27}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -600x \color{red}{+80} & = & \color{red}{192x} +27 \\\Leftrightarrow & -600x \color{red}{+80} \color{blue}{-80} \color{blue}{-192x} & = & \color{red}{192x} +27 \color{blue}{-192x} \color{blue}{-80} \\\Leftrightarrow & -600x-192x& = & 27-80 \\\Leftrightarrow & \color{red}{-792} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-792} & & \\\Leftrightarrow & x = \frac{53}{792} & & \\ & V = \left\{ \frac{53}{792} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{5}{2})& = & 3x+\frac{6}{5} \\\Leftrightarrow & -14x+\frac{35}{2}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-140}{ \color{blue}{10} }x+ \frac{175}{ \color{blue}{10} })& = & (\frac{30}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -140x \color{red}{+175} & = & \color{red}{30x} +12 \\\Leftrightarrow & -140x \color{red}{+175} \color{blue}{-175} \color{blue}{-30x} & = & \color{red}{30x} +12 \color{blue}{-30x} \color{blue}{-175} \\\Leftrightarrow & -140x-30x& = & 12-175 \\\Leftrightarrow & \color{red}{-170} x& = & -163 \\\Leftrightarrow & x = \frac{-163}{-170} & & \\\Leftrightarrow & x = \frac{163}{170} & & \\ & V = \left\{ \frac{163}{170} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{3}{11})& = & -3x+\frac{4}{7} \\\Leftrightarrow & -20x-\frac{15}{11}& = & -3x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x- \frac{105}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{-105} & = & \color{red}{-231x} +44 \\\Leftrightarrow & -1540x \color{red}{-105} \color{blue}{+105} \color{blue}{+231x} & = & \color{red}{-231x} +44 \color{blue}{+231x} \color{blue}{+105} \\\Leftrightarrow & -1540x+231x& = & 44+105 \\\Leftrightarrow & \color{red}{-1309} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-1309} & & \\\Leftrightarrow & x = \frac{-149}{1309} & & \\ & V = \left\{ \frac{-149}{1309} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{2})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -6x+\frac{15}{2}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-84}{ \color{blue}{14} }x+ \frac{105}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -84x \color{red}{+105} & = & \color{red}{-98x} +20 \\\Leftrightarrow & -84x \color{red}{+105} \color{blue}{-105} \color{blue}{+98x} & = & \color{red}{-98x} +20 \color{blue}{+98x} \color{blue}{-105} \\\Leftrightarrow & -84x+98x& = & 20-105 \\\Leftrightarrow & \color{red}{14} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{14} & & \\ & V = \left\{ \frac{-85}{14} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{11})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 12x+\frac{12}{11}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x+ \frac{36}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{+36} & = & \color{red}{-165x} +22 \\\Leftrightarrow & 396x \color{red}{+36} \color{blue}{-36} \color{blue}{+165x} & = & \color{red}{-165x} +22 \color{blue}{+165x} \color{blue}{-36} \\\Leftrightarrow & 396x+165x& = & 22-36 \\\Leftrightarrow & \color{red}{561} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{561} & & \\ & V = \left\{ \frac{-14}{561} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{5}{7})& = & 5x+\frac{9}{10} \\\Leftrightarrow & 6x+\frac{10}{7}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{420}{ \color{blue}{70} }x+ \frac{100}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 420x \color{red}{+100} & = & \color{red}{350x} +63 \\\Leftrightarrow & 420x \color{red}{+100} \color{blue}{-100} \color{blue}{-350x} & = & \color{red}{350x} +63 \color{blue}{-350x} \color{blue}{-100} \\\Leftrightarrow & 420x-350x& = & 63-100 \\\Leftrightarrow & \color{red}{70} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{70} & & \\ & V = \left\{ \frac{-37}{70} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{3}{5})& = & 5x+\frac{3}{4} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{+48} & = & \color{red}{100x} +15 \\\Leftrightarrow & -240x \color{red}{+48} \color{blue}{-48} \color{blue}{-100x} & = & \color{red}{100x} +15 \color{blue}{-100x} \color{blue}{-48} \\\Leftrightarrow & -240x-100x& = & 15-48 \\\Leftrightarrow & \color{red}{-340} x& = & -33 \\\Leftrightarrow & x = \frac{-33}{-340} & & \\\Leftrightarrow & x = \frac{33}{340} & & \\ & V = \left\{ \frac{33}{340} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{2}{9})& = & -9x+\frac{9}{2} \\\Leftrightarrow & -20x+\frac{8}{9}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-360}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{-162}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -360x \color{red}{+16} & = & \color{red}{-162x} +81 \\\Leftrightarrow & -360x \color{red}{+16} \color{blue}{-16} \color{blue}{+162x} & = & \color{red}{-162x} +81 \color{blue}{+162x} \color{blue}{-16} \\\Leftrightarrow & -360x+162x& = & 81-16 \\\Leftrightarrow & \color{red}{-198} x& = & 65 \\\Leftrightarrow & x = \frac{65}{-198} & & \\\Leftrightarrow & x = \frac{-65}{198} & & \\ & V = \left\{ \frac{-65}{198} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{3}{7})& = & -5x+\frac{9}{10} \\\Leftrightarrow & 8x+\frac{6}{7}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{560}{ \color{blue}{70} }x+ \frac{60}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 560x \color{red}{+60} & = & \color{red}{-350x} +63 \\\Leftrightarrow & 560x \color{red}{+60} \color{blue}{-60} \color{blue}{+350x} & = & \color{red}{-350x} +63 \color{blue}{+350x} \color{blue}{-60} \\\Leftrightarrow & 560x+350x& = & 63-60 \\\Leftrightarrow & \color{red}{910} x& = & 3 \\\Leftrightarrow & x = \frac{3}{910} & & \\ & V = \left\{ \frac{3}{910} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{4}{7})& = & -5x+\frac{2}{9} \\\Leftrightarrow & 6x-\frac{8}{7}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x- \frac{72}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{-72} & = & \color{red}{-315x} +14 \\\Leftrightarrow & 378x \color{red}{-72} \color{blue}{+72} \color{blue}{+315x} & = & \color{red}{-315x} +14 \color{blue}{+315x} \color{blue}{+72} \\\Leftrightarrow & 378x+315x& = & 14+72 \\\Leftrightarrow & \color{red}{693} x& = & 86 \\\Leftrightarrow & x = \frac{86}{693} & & \\ & V = \left\{ \frac{86}{693} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{3}{4})& = & 8x+\frac{2}{11} \\\Leftrightarrow & -15x-\frac{15}{4}& = & 8x+\frac{2}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-660}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{352}{ \color{blue}{44} }x+ \frac{8}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -660x \color{red}{-165} & = & \color{red}{352x} +8 \\\Leftrightarrow & -660x \color{red}{-165} \color{blue}{+165} \color{blue}{-352x} & = & \color{red}{352x} +8 \color{blue}{-352x} \color{blue}{+165} \\\Leftrightarrow & -660x-352x& = & 8+165 \\\Leftrightarrow & \color{red}{-1012} x& = & 173 \\\Leftrightarrow & x = \frac{173}{-1012} & & \\\Leftrightarrow & x = \frac{-173}{1012} & & \\ & V = \left\{ \frac{-173}{1012} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{4}{3})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -10x-\frac{20}{3}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{-220} & = & \color{red}{-231x} +18 \\\Leftrightarrow & -330x \color{red}{-220} \color{blue}{+220} \color{blue}{+231x} & = & \color{red}{-231x} +18 \color{blue}{+231x} \color{blue}{+220} \\\Leftrightarrow & -330x+231x& = & 18+220 \\\Leftrightarrow & \color{red}{-99} x& = & 238 \\\Leftrightarrow & x = \frac{238}{-99} & & \\\Leftrightarrow & x = \frac{-238}{99} & & \\ & V = \left\{ \frac{-238}{99} \right\} & \\\end{align}\)
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