Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{7})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -30x-\frac{18}{7}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-420}{ \color{blue}{14} }x- \frac{36}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -420x \color{red}{-36} & = & \color{red}{-98x} +21 \\\Leftrightarrow & -420x \color{red}{-36} \color{blue}{+36} \color{blue}{+98x} & = & \color{red}{-98x} +21 \color{blue}{+98x} \color{blue}{+36} \\\Leftrightarrow & -420x+98x& = & 21+36 \\\Leftrightarrow & \color{red}{-322} x& = & 57 \\\Leftrightarrow & x = \frac{57}{-322} & & \\\Leftrightarrow & x = \frac{-57}{322} & & \\ & V = \left\{ \frac{-57}{322} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{2}{7})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 15x+\frac{10}{7}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{210}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 210x \color{red}{+20} & = & \color{red}{-98x} +49 \\\Leftrightarrow & 210x \color{red}{+20} \color{blue}{-20} \color{blue}{+98x} & = & \color{red}{-98x} +49 \color{blue}{+98x} \color{blue}{-20} \\\Leftrightarrow & 210x+98x& = & 49-20 \\\Leftrightarrow & \color{red}{308} x& = & 29 \\\Leftrightarrow & x = \frac{29}{308} & & \\ & V = \left\{ \frac{29}{308} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{5}{7})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 12x-\frac{30}{7}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{-30} & = & \color{red}{-35x} +3 \\\Leftrightarrow & 84x \color{red}{-30} \color{blue}{+30} \color{blue}{+35x} & = & \color{red}{-35x} +3 \color{blue}{+35x} \color{blue}{+30} \\\Leftrightarrow & 84x+35x& = & 3+30 \\\Leftrightarrow & \color{red}{119} x& = & 33 \\\Leftrightarrow & x = \frac{33}{119} & & \\ & V = \left\{ \frac{33}{119} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{11})& = & -3x+\frac{4}{5} \\\Leftrightarrow & 4x+\frac{8}{11}& = & -3x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{220}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 220x \color{red}{+40} & = & \color{red}{-165x} +44 \\\Leftrightarrow & 220x \color{red}{+40} \color{blue}{-40} \color{blue}{+165x} & = & \color{red}{-165x} +44 \color{blue}{+165x} \color{blue}{-40} \\\Leftrightarrow & 220x+165x& = & 44-40 \\\Leftrightarrow & \color{red}{385} x& = & 4 \\\Leftrightarrow & x = \frac{4}{385} & & \\ & V = \left\{ \frac{4}{385} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{2})& = & -9x+\frac{6}{5} \\\Leftrightarrow & 10x+\frac{25}{2}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{100}{ \color{blue}{10} }x+ \frac{125}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 100x \color{red}{+125} & = & \color{red}{-90x} +12 \\\Leftrightarrow & 100x \color{red}{+125} \color{blue}{-125} \color{blue}{+90x} & = & \color{red}{-90x} +12 \color{blue}{+90x} \color{blue}{-125} \\\Leftrightarrow & 100x+90x& = & 12-125 \\\Leftrightarrow & \color{red}{190} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{190} & & \\ & V = \left\{ \frac{-113}{190} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{5}{3})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -12x+\frac{20}{3}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-72}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -72x \color{red}{+40} & = & \color{red}{-30x} +9 \\\Leftrightarrow & -72x \color{red}{+40} \color{blue}{-40} \color{blue}{+30x} & = & \color{red}{-30x} +9 \color{blue}{+30x} \color{blue}{-40} \\\Leftrightarrow & -72x+30x& = & 9-40 \\\Leftrightarrow & \color{red}{-42} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-42} & & \\\Leftrightarrow & x = \frac{31}{42} & & \\ & V = \left\{ \frac{31}{42} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{3}{10})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -6x+\frac{9}{10}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{+9} & = & \color{red}{-70x} +12 \\\Leftrightarrow & -60x \color{red}{+9} \color{blue}{-9} \color{blue}{+70x} & = & \color{red}{-70x} +12 \color{blue}{+70x} \color{blue}{-9} \\\Leftrightarrow & -60x+70x& = & 12-9 \\\Leftrightarrow & \color{red}{10} x& = & 3 \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{2}{7})& = & -8x+\frac{5}{6} \\\Leftrightarrow & 15x+\frac{10}{7}& = & -8x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{630}{ \color{blue}{42} }x+ \frac{60}{ \color{blue}{42} })& = & (\frac{-336}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 630x \color{red}{+60} & = & \color{red}{-336x} +35 \\\Leftrightarrow & 630x \color{red}{+60} \color{blue}{-60} \color{blue}{+336x} & = & \color{red}{-336x} +35 \color{blue}{+336x} \color{blue}{-60} \\\Leftrightarrow & 630x+336x& = & 35-60 \\\Leftrightarrow & \color{red}{966} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{966} & & \\ & V = \left\{ \frac{-25}{966} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{7})& = & 3x+\frac{5}{8} \\\Leftrightarrow & 16x+\frac{20}{7}& = & 3x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{896}{ \color{blue}{56} }x+ \frac{160}{ \color{blue}{56} })& = & (\frac{168}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 896x \color{red}{+160} & = & \color{red}{168x} +35 \\\Leftrightarrow & 896x \color{red}{+160} \color{blue}{-160} \color{blue}{-168x} & = & \color{red}{168x} +35 \color{blue}{-168x} \color{blue}{-160} \\\Leftrightarrow & 896x-168x& = & 35-160 \\\Leftrightarrow & \color{red}{728} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{728} & & \\ & V = \left\{ \frac{-125}{728} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{5})& = & 8x+\frac{7}{6} \\\Leftrightarrow & -21x-\frac{14}{5}& = & 8x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-630}{ \color{blue}{30} }x- \frac{84}{ \color{blue}{30} })& = & (\frac{240}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -630x \color{red}{-84} & = & \color{red}{240x} +35 \\\Leftrightarrow & -630x \color{red}{-84} \color{blue}{+84} \color{blue}{-240x} & = & \color{red}{240x} +35 \color{blue}{-240x} \color{blue}{+84} \\\Leftrightarrow & -630x-240x& = & 35+84 \\\Leftrightarrow & \color{red}{-870} x& = & 119 \\\Leftrightarrow & x = \frac{119}{-870} & & \\\Leftrightarrow & x = \frac{-119}{870} & & \\ & V = \left\{ \frac{-119}{870} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{2}{5})& = & 5x+\frac{4}{5} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{+12} & = & \color{red}{25x} +4 \\\Leftrightarrow & 60x \color{red}{+12} \color{blue}{-12} \color{blue}{-25x} & = & \color{red}{25x} +4 \color{blue}{-25x} \color{blue}{-12} \\\Leftrightarrow & 60x-25x& = & 4-12 \\\Leftrightarrow & \color{red}{35} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{35} & & \\ & V = \left\{ \frac{-8}{35} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{4}{9})& = & 9x+\frac{6}{11} \\\Leftrightarrow & 4x-\frac{8}{9}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{396}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 396x \color{red}{-88} & = & \color{red}{891x} +54 \\\Leftrightarrow & 396x \color{red}{-88} \color{blue}{+88} \color{blue}{-891x} & = & \color{red}{891x} +54 \color{blue}{-891x} \color{blue}{+88} \\\Leftrightarrow & 396x-891x& = & 54+88 \\\Leftrightarrow & \color{red}{-495} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-495} & & \\\Leftrightarrow & x = \frac{-142}{495} & & \\ & V = \left\{ \frac{-142}{495} \right\} & \\\end{align}\)
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