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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{8})& = & 3x+\frac{2}{11} \\\Leftrightarrow & 10x-\frac{25}{8}& = & 3x+\frac{2}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{880}{ \color{blue}{88} }x- \frac{275}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{16}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 880x \color{red}{-275} & = & \color{red}{264x} +16 \\\Leftrightarrow & 880x \color{red}{-275} \color{blue}{+275} \color{blue}{-264x} & = & \color{red}{264x} +16 \color{blue}{-264x} \color{blue}{+275} \\\Leftrightarrow & 880x-264x& = & 16+275 \\\Leftrightarrow & \color{red}{616} x& = & 291 \\\Leftrightarrow & x = \frac{291}{616} & & \\ & V = \left\{ \frac{291}{616} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{5}{3})& = & -5x+\frac{3}{11} \\\Leftrightarrow & 12x+\frac{20}{3}& = & -5x+\frac{3}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{9}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{+220} & = & \color{red}{-165x} +9 \\\Leftrightarrow & 396x \color{red}{+220} \color{blue}{-220} \color{blue}{+165x} & = & \color{red}{-165x} +9 \color{blue}{+165x} \color{blue}{-220} \\\Leftrightarrow & 396x+165x& = & 9-220 \\\Leftrightarrow & \color{red}{561} x& = & -211 \\\Leftrightarrow & x = \frac{-211}{561} & & \\ & V = \left\{ \frac{-211}{561} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{12})& = & -3x+\frac{5}{2} \\\Leftrightarrow & 20x+\frac{25}{12}& = & -3x+\frac{5}{2} \\ & & & \text{kgv van noemers 12 en 2 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{240}{ \color{blue}{12} }x+ \frac{25}{ \color{blue}{12} })& = & (\frac{-36}{ \color{blue}{12} }x+ \frac{30}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 240x \color{red}{+25} & = & \color{red}{-36x} +30 \\\Leftrightarrow & 240x \color{red}{+25} \color{blue}{-25} \color{blue}{+36x} & = & \color{red}{-36x} +30 \color{blue}{+36x} \color{blue}{-25} \\\Leftrightarrow & 240x+36x& = & 30-25 \\\Leftrightarrow & \color{red}{276} x& = & 5 \\\Leftrightarrow & x = \frac{5}{276} & & \\ & V = \left\{ \frac{5}{276} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{2}{3})& = & -3x+\frac{3}{10} \\\Leftrightarrow & -20x+\frac{8}{3}& = & -3x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-600}{ \color{blue}{30} }x+ \frac{80}{ \color{blue}{30} })& = & (\frac{-90}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -600x \color{red}{+80} & = & \color{red}{-90x} +9 \\\Leftrightarrow & -600x \color{red}{+80} \color{blue}{-80} \color{blue}{+90x} & = & \color{red}{-90x} +9 \color{blue}{+90x} \color{blue}{-80} \\\Leftrightarrow & -600x+90x& = & 9-80 \\\Leftrightarrow & \color{red}{-510} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{-510} & & \\\Leftrightarrow & x = \frac{71}{510} & & \\ & V = \left\{ \frac{71}{510} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{8})& = & -4x+\frac{2}{3} \\\Leftrightarrow & -15x-\frac{15}{8}& = & -4x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-360}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{-96}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -360x \color{red}{-45} & = & \color{red}{-96x} +16 \\\Leftrightarrow & -360x \color{red}{-45} \color{blue}{+45} \color{blue}{+96x} & = & \color{red}{-96x} +16 \color{blue}{+96x} \color{blue}{+45} \\\Leftrightarrow & -360x+96x& = & 16+45 \\\Leftrightarrow & \color{red}{-264} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-264} & & \\\Leftrightarrow & x = \frac{-61}{264} & & \\ & V = \left\{ \frac{-61}{264} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{3}{8})& = & -3x+\frac{5}{12} \\\Leftrightarrow & -14x+\frac{21}{8}& = & -3x+\frac{5}{12} \\ & & & \text{kgv van noemers 8 en 12 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-336}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{10}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -336x \color{red}{+63} & = & \color{red}{-72x} +10 \\\Leftrightarrow & -336x \color{red}{+63} \color{blue}{-63} \color{blue}{+72x} & = & \color{red}{-72x} +10 \color{blue}{+72x} \color{blue}{-63} \\\Leftrightarrow & -336x+72x& = & 10-63 \\\Leftrightarrow & \color{red}{-264} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-264} & & \\\Leftrightarrow & x = \frac{53}{264} & & \\ & V = \left\{ \frac{53}{264} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{2}{7})& = & -3x+\frac{6}{5} \\\Leftrightarrow & -20x+\frac{10}{7}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{+50} & = & \color{red}{-105x} +42 \\\Leftrightarrow & -700x \color{red}{+50} \color{blue}{-50} \color{blue}{+105x} & = & \color{red}{-105x} +42 \color{blue}{+105x} \color{blue}{-50} \\\Leftrightarrow & -700x+105x& = & 42-50 \\\Leftrightarrow & \color{red}{-595} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-595} & & \\\Leftrightarrow & x = \frac{8}{595} & & \\ & V = \left\{ \frac{8}{595} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{5}{12})& = & -7x+\frac{8}{5} \\\Leftrightarrow & -25x-\frac{25}{12}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 12 en 5 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1500}{ \color{blue}{60} }x- \frac{125}{ \color{blue}{60} })& = & (\frac{-420}{ \color{blue}{60} }x+ \frac{96}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1500x \color{red}{-125} & = & \color{red}{-420x} +96 \\\Leftrightarrow & -1500x \color{red}{-125} \color{blue}{+125} \color{blue}{+420x} & = & \color{red}{-420x} +96 \color{blue}{+420x} \color{blue}{+125} \\\Leftrightarrow & -1500x+420x& = & 96+125 \\\Leftrightarrow & \color{red}{-1080} x& = & 221 \\\Leftrightarrow & x = \frac{221}{-1080} & & \\\Leftrightarrow & x = \frac{-221}{1080} & & \\ & V = \left\{ \frac{-221}{1080} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{5})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -10x-\frac{6}{5}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-42} & = & \color{red}{245x} +45 \\\Leftrightarrow & -350x \color{red}{-42} \color{blue}{+42} \color{blue}{-245x} & = & \color{red}{245x} +45 \color{blue}{-245x} \color{blue}{+42} \\\Leftrightarrow & -350x-245x& = & 45+42 \\\Leftrightarrow & \color{red}{-595} x& = & 87 \\\Leftrightarrow & x = \frac{87}{-595} & & \\\Leftrightarrow & x = \frac{-87}{595} & & \\ & V = \left\{ \frac{-87}{595} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{1}{2})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -10x-\frac{5}{2}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-60}{ \color{blue}{6} }x- \frac{15}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -60x \color{red}{-15} & = & \color{red}{42x} +20 \\\Leftrightarrow & -60x \color{red}{-15} \color{blue}{+15} \color{blue}{-42x} & = & \color{red}{42x} +20 \color{blue}{-42x} \color{blue}{+15} \\\Leftrightarrow & -60x-42x& = & 20+15 \\\Leftrightarrow & \color{red}{-102} x& = & 35 \\\Leftrightarrow & x = \frac{35}{-102} & & \\\Leftrightarrow & x = \frac{-35}{102} & & \\ & V = \left\{ \frac{-35}{102} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{4}{9})& = & -7x+\frac{9}{10} \\\Leftrightarrow & 6x+\frac{8}{9}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{540}{ \color{blue}{90} }x+ \frac{80}{ \color{blue}{90} })& = & (\frac{-630}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 540x \color{red}{+80} & = & \color{red}{-630x} +81 \\\Leftrightarrow & 540x \color{red}{+80} \color{blue}{-80} \color{blue}{+630x} & = & \color{red}{-630x} +81 \color{blue}{+630x} \color{blue}{-80} \\\Leftrightarrow & 540x+630x& = & 81-80 \\\Leftrightarrow & \color{red}{1170} x& = & 1 \\\Leftrightarrow & x = \frac{1}{1170} & & \\ & V = \left\{ \frac{1}{1170} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{7})& = & -5x+\frac{9}{11} \\\Leftrightarrow & 12x+\frac{8}{7}& = & -5x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+88} & = & \color{red}{-385x} +63 \\\Leftrightarrow & 924x \color{red}{+88} \color{blue}{-88} \color{blue}{+385x} & = & \color{red}{-385x} +63 \color{blue}{+385x} \color{blue}{-88} \\\Leftrightarrow & 924x+385x& = & 63-88 \\\Leftrightarrow & \color{red}{1309} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{1309} & & \\ & V = \left\{ \frac{-25}{1309} \right\} & \\\end{align}\)
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