Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{5}{7})& = & 5x+\frac{5}{2} \\\Leftrightarrow & -24x-\frac{30}{7}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-336}{ \color{blue}{14} }x- \frac{60}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -336x \color{red}{-60} & = & \color{red}{70x} +35 \\\Leftrightarrow & -336x \color{red}{-60} \color{blue}{+60} \color{blue}{-70x} & = & \color{red}{70x} +35 \color{blue}{-70x} \color{blue}{+60} \\\Leftrightarrow & -336x-70x& = & 35+60 \\\Leftrightarrow & \color{red}{-406} x& = & 95 \\\Leftrightarrow & x = \frac{95}{-406} & & \\\Leftrightarrow & x = \frac{-95}{406} & & \\ & V = \left\{ \frac{-95}{406} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{5}{8})& = & -5x+\frac{2}{5} \\\Leftrightarrow & 12x-\frac{15}{8}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x- \frac{75}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{16}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{-75} & = & \color{red}{-200x} +16 \\\Leftrightarrow & 480x \color{red}{-75} \color{blue}{+75} \color{blue}{+200x} & = & \color{red}{-200x} +16 \color{blue}{+200x} \color{blue}{+75} \\\Leftrightarrow & 480x+200x& = & 16+75 \\\Leftrightarrow & \color{red}{680} x& = & 91 \\\Leftrightarrow & x = \frac{91}{680} & & \\ & V = \left\{ \frac{91}{680} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{3}{5})& = & 7x+\frac{5}{12} \\\Leftrightarrow & 8x+\frac{6}{5}& = & 7x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{480}{ \color{blue}{60} }x+ \frac{72}{ \color{blue}{60} })& = & (\frac{420}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 480x \color{red}{+72} & = & \color{red}{420x} +25 \\\Leftrightarrow & 480x \color{red}{+72} \color{blue}{-72} \color{blue}{-420x} & = & \color{red}{420x} +25 \color{blue}{-420x} \color{blue}{-72} \\\Leftrightarrow & 480x-420x& = & 25-72 \\\Leftrightarrow & \color{red}{60} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{60} & & \\ & V = \left\{ \frac{-47}{60} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{4}{11})& = & 5x+\frac{5}{6} \\\Leftrightarrow & -12x-\frac{24}{11}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-792}{ \color{blue}{66} }x- \frac{144}{ \color{blue}{66} })& = & (\frac{330}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -792x \color{red}{-144} & = & \color{red}{330x} +55 \\\Leftrightarrow & -792x \color{red}{-144} \color{blue}{+144} \color{blue}{-330x} & = & \color{red}{330x} +55 \color{blue}{-330x} \color{blue}{+144} \\\Leftrightarrow & -792x-330x& = & 55+144 \\\Leftrightarrow & \color{red}{-1122} x& = & 199 \\\Leftrightarrow & x = \frac{199}{-1122} & & \\\Leftrightarrow & x = \frac{-199}{1122} & & \\ & V = \left\{ \frac{-199}{1122} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{9})& = & -5x+\frac{9}{8} \\\Leftrightarrow & 4x-\frac{4}{9}& = & -5x+\frac{9}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{288}{ \color{blue}{72} }x- \frac{32}{ \color{blue}{72} })& = & (\frac{-360}{ \color{blue}{72} }x+ \frac{81}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 288x \color{red}{-32} & = & \color{red}{-360x} +81 \\\Leftrightarrow & 288x \color{red}{-32} \color{blue}{+32} \color{blue}{+360x} & = & \color{red}{-360x} +81 \color{blue}{+360x} \color{blue}{+32} \\\Leftrightarrow & 288x+360x& = & 81+32 \\\Leftrightarrow & \color{red}{648} x& = & 113 \\\Leftrightarrow & x = \frac{113}{648} & & \\ & V = \left\{ \frac{113}{648} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{5}{9})& = & 3x+\frac{6}{11} \\\Leftrightarrow & -14x+\frac{35}{9}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1386}{ \color{blue}{99} }x+ \frac{385}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1386x \color{red}{+385} & = & \color{red}{297x} +54 \\\Leftrightarrow & -1386x \color{red}{+385} \color{blue}{-385} \color{blue}{-297x} & = & \color{red}{297x} +54 \color{blue}{-297x} \color{blue}{-385} \\\Leftrightarrow & -1386x-297x& = & 54-385 \\\Leftrightarrow & \color{red}{-1683} x& = & -331 \\\Leftrightarrow & x = \frac{-331}{-1683} & & \\\Leftrightarrow & x = \frac{331}{1683} & & \\ & V = \left\{ \frac{331}{1683} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{3}{8})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -35x+\frac{21}{8}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-840}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -840x \color{red}{+63} & = & \color{red}{-72x} +64 \\\Leftrightarrow & -840x \color{red}{+63} \color{blue}{-63} \color{blue}{+72x} & = & \color{red}{-72x} +64 \color{blue}{+72x} \color{blue}{-63} \\\Leftrightarrow & -840x+72x& = & 64-63 \\\Leftrightarrow & \color{red}{-768} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-768} & & \\\Leftrightarrow & x = \frac{-1}{768} & & \\ & V = \left\{ \frac{-1}{768} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{8})& = & 8x+\frac{7}{2} \\\Leftrightarrow & -15x-\frac{15}{8}& = & 8x+\frac{7}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-120}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{64}{ \color{blue}{8} }x+ \frac{28}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -120x \color{red}{-15} & = & \color{red}{64x} +28 \\\Leftrightarrow & -120x \color{red}{-15} \color{blue}{+15} \color{blue}{-64x} & = & \color{red}{64x} +28 \color{blue}{-64x} \color{blue}{+15} \\\Leftrightarrow & -120x-64x& = & 28+15 \\\Leftrightarrow & \color{red}{-184} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-184} & & \\\Leftrightarrow & x = \frac{-43}{184} & & \\ & V = \left\{ \frac{-43}{184} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{5}{11})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -12x+\frac{20}{11}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x+ \frac{20}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{+20} & = & \color{red}{55x} +2 \\\Leftrightarrow & -132x \color{red}{+20} \color{blue}{-20} \color{blue}{-55x} & = & \color{red}{55x} +2 \color{blue}{-55x} \color{blue}{-20} \\\Leftrightarrow & -132x-55x& = & 2-20 \\\Leftrightarrow & \color{red}{-187} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-187} & & \\\Leftrightarrow & x = \frac{18}{187} & & \\ & V = \left\{ \frac{18}{187} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{3}{5})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 15x-\frac{9}{5}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{150}{ \color{blue}{10} }x- \frac{18}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 150x \color{red}{-18} & = & \color{red}{-70x} +15 \\\Leftrightarrow & 150x \color{red}{-18} \color{blue}{+18} \color{blue}{+70x} & = & \color{red}{-70x} +15 \color{blue}{+70x} \color{blue}{+18} \\\Leftrightarrow & 150x+70x& = & 15+18 \\\Leftrightarrow & \color{red}{220} x& = & 33 \\\Leftrightarrow & x = \frac{33}{220} & & \\\Leftrightarrow & x = \frac{3}{20} & & \\ & V = \left\{ \frac{3}{20} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{4}{3})& = & -9x+\frac{4}{3} \\\Leftrightarrow & -20x+\frac{20}{3}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-60}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -60x \color{red}{+20} & = & \color{red}{-27x} +4 \\\Leftrightarrow & -60x \color{red}{+20} \color{blue}{-20} \color{blue}{+27x} & = & \color{red}{-27x} +4 \color{blue}{+27x} \color{blue}{-20} \\\Leftrightarrow & -60x+27x& = & 4-20 \\\Leftrightarrow & \color{red}{-33} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-33} & & \\\Leftrightarrow & x = \frac{16}{33} & & \\ & V = \left\{ \frac{16}{33} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{2}{7})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 9x-\frac{6}{7}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{189}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 189x \color{red}{-18} & = & \color{red}{105x} +56 \\\Leftrightarrow & 189x \color{red}{-18} \color{blue}{+18} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{+18} \\\Leftrightarrow & 189x-105x& = & 56+18 \\\Leftrightarrow & \color{red}{84} x& = & 74 \\\Leftrightarrow & x = \frac{74}{84} & & \\\Leftrightarrow & x = \frac{37}{42} & & \\ & V = \left\{ \frac{37}{42} \right\} & \\\end{align}\)
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