Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{2}{7})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 12x-\frac{6}{7}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{-54} & = & \color{red}{441x} +28 \\\Leftrightarrow & 756x \color{red}{-54} \color{blue}{+54} \color{blue}{-441x} & = & \color{red}{441x} +28 \color{blue}{-441x} \color{blue}{+54} \\\Leftrightarrow & 756x-441x& = & 28+54 \\\Leftrightarrow & \color{red}{315} x& = & 82 \\\Leftrightarrow & x = \frac{82}{315} & & \\ & V = \left\{ \frac{82}{315} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{5}{11})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 4x+\frac{10}{11}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{308}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 308x \color{red}{+70} & = & \color{red}{539x} +110 \\\Leftrightarrow & 308x \color{red}{+70} \color{blue}{-70} \color{blue}{-539x} & = & \color{red}{539x} +110 \color{blue}{-539x} \color{blue}{-70} \\\Leftrightarrow & 308x-539x& = & 110-70 \\\Leftrightarrow & \color{red}{-231} x& = & 40 \\\Leftrightarrow & x = \frac{40}{-231} & & \\\Leftrightarrow & x = \frac{-40}{231} & & \\ & V = \left\{ \frac{-40}{231} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{3}{8})& = & 8x+\frac{8}{9} \\\Leftrightarrow & -21x-\frac{21}{8}& = & 8x+\frac{8}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1512}{ \color{blue}{72} }x- \frac{189}{ \color{blue}{72} })& = & (\frac{576}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1512x \color{red}{-189} & = & \color{red}{576x} +64 \\\Leftrightarrow & -1512x \color{red}{-189} \color{blue}{+189} \color{blue}{-576x} & = & \color{red}{576x} +64 \color{blue}{-576x} \color{blue}{+189} \\\Leftrightarrow & -1512x-576x& = & 64+189 \\\Leftrightarrow & \color{red}{-2088} x& = & 253 \\\Leftrightarrow & x = \frac{253}{-2088} & & \\\Leftrightarrow & x = \frac{-253}{2088} & & \\ & V = \left\{ \frac{-253}{2088} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{1}{2})& = & -7x+\frac{10}{9} \\\Leftrightarrow & 20x-\frac{5}{2}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{360}{ \color{blue}{18} }x- \frac{45}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{20}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 360x \color{red}{-45} & = & \color{red}{-126x} +20 \\\Leftrightarrow & 360x \color{red}{-45} \color{blue}{+45} \color{blue}{+126x} & = & \color{red}{-126x} +20 \color{blue}{+126x} \color{blue}{+45} \\\Leftrightarrow & 360x+126x& = & 20+45 \\\Leftrightarrow & \color{red}{486} x& = & 65 \\\Leftrightarrow & x = \frac{65}{486} & & \\ & V = \left\{ \frac{65}{486} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{3}{5})& = & -3x+\frac{10}{3} \\\Leftrightarrow & 8x+\frac{12}{5}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+36} & = & \color{red}{-45x} +50 \\\Leftrightarrow & 120x \color{red}{+36} \color{blue}{-36} \color{blue}{+45x} & = & \color{red}{-45x} +50 \color{blue}{+45x} \color{blue}{-36} \\\Leftrightarrow & 120x+45x& = & 50-36 \\\Leftrightarrow & \color{red}{165} x& = & 14 \\\Leftrightarrow & x = \frac{14}{165} & & \\ & V = \left\{ \frac{14}{165} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{3}{7})& = & -5x+\frac{7}{9} \\\Leftrightarrow & 6x-\frac{6}{7}& = & -5x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{-54} & = & \color{red}{-315x} +49 \\\Leftrightarrow & 378x \color{red}{-54} \color{blue}{+54} \color{blue}{+315x} & = & \color{red}{-315x} +49 \color{blue}{+315x} \color{blue}{+54} \\\Leftrightarrow & 378x+315x& = & 49+54 \\\Leftrightarrow & \color{red}{693} x& = & 103 \\\Leftrightarrow & x = \frac{103}{693} & & \\ & V = \left\{ \frac{103}{693} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{3}{10})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -6x+\frac{9}{10}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-660}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} })& = & (\frac{770}{ \color{blue}{110} }x+ \frac{80}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -660x \color{red}{+99} & = & \color{red}{770x} +80 \\\Leftrightarrow & -660x \color{red}{+99} \color{blue}{-99} \color{blue}{-770x} & = & \color{red}{770x} +80 \color{blue}{-770x} \color{blue}{-99} \\\Leftrightarrow & -660x-770x& = & 80-99 \\\Leftrightarrow & \color{red}{-1430} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{-1430} & & \\\Leftrightarrow & x = \frac{19}{1430} & & \\ & V = \left\{ \frac{19}{1430} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{9})& = & 9x+\frac{9}{4} \\\Leftrightarrow & 14x+\frac{28}{9}& = & 9x+\frac{9}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{504}{ \color{blue}{36} }x+ \frac{112}{ \color{blue}{36} })& = & (\frac{324}{ \color{blue}{36} }x+ \frac{81}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 504x \color{red}{+112} & = & \color{red}{324x} +81 \\\Leftrightarrow & 504x \color{red}{+112} \color{blue}{-112} \color{blue}{-324x} & = & \color{red}{324x} +81 \color{blue}{-324x} \color{blue}{-112} \\\Leftrightarrow & 504x-324x& = & 81-112 \\\Leftrightarrow & \color{red}{180} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{180} & & \\ & V = \left\{ \frac{-31}{180} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{2}{3})& = & 8x+\frac{9}{5} \\\Leftrightarrow & -28x+\frac{14}{3}& = & 8x+\frac{9}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-420}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -420x \color{red}{+70} & = & \color{red}{120x} +27 \\\Leftrightarrow & -420x \color{red}{+70} \color{blue}{-70} \color{blue}{-120x} & = & \color{red}{120x} +27 \color{blue}{-120x} \color{blue}{-70} \\\Leftrightarrow & -420x-120x& = & 27-70 \\\Leftrightarrow & \color{red}{-540} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-540} & & \\\Leftrightarrow & x = \frac{43}{540} & & \\ & V = \left\{ \frac{43}{540} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 15x+\frac{12}{5}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{150}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 150x \color{red}{+24} & = & \color{red}{-70x} +15 \\\Leftrightarrow & 150x \color{red}{+24} \color{blue}{-24} \color{blue}{+70x} & = & \color{red}{-70x} +15 \color{blue}{+70x} \color{blue}{-24} \\\Leftrightarrow & 150x+70x& = & 15-24 \\\Leftrightarrow & \color{red}{220} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{220} & & \\ & V = \left\{ \frac{-9}{220} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{2}{3})& = & 8x+\frac{2}{5} \\\Leftrightarrow & -15x-\frac{10}{3}& = & 8x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x- \frac{50}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{-50} & = & \color{red}{120x} +6 \\\Leftrightarrow & -225x \color{red}{-50} \color{blue}{+50} \color{blue}{-120x} & = & \color{red}{120x} +6 \color{blue}{-120x} \color{blue}{+50} \\\Leftrightarrow & -225x-120x& = & 6+50 \\\Leftrightarrow & \color{red}{-345} x& = & 56 \\\Leftrightarrow & x = \frac{56}{-345} & & \\\Leftrightarrow & x = \frac{-56}{345} & & \\ & V = \left\{ \frac{-56}{345} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{4}{5})& = & 5x+\frac{2}{11} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+132} & = & \color{red}{275x} +10 \\\Leftrightarrow & 660x \color{red}{+132} \color{blue}{-132} \color{blue}{-275x} & = & \color{red}{275x} +10 \color{blue}{-275x} \color{blue}{-132} \\\Leftrightarrow & 660x-275x& = & 10-132 \\\Leftrightarrow & \color{red}{385} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{385} & & \\ & V = \left\{ \frac{-122}{385} \right\} & \\\end{align}\)
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