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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{5}{3})& = & -5x+\frac{5}{4} \\\Leftrightarrow & 8x-\frac{20}{3}& = & -5x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{96}{ \color{blue}{12} }x- \frac{80}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 96x \color{red}{-80} & = & \color{red}{-60x} +15 \\\Leftrightarrow & 96x \color{red}{-80} \color{blue}{+80} \color{blue}{+60x} & = & \color{red}{-60x} +15 \color{blue}{+60x} \color{blue}{+80} \\\Leftrightarrow & 96x+60x& = & 15+80 \\\Leftrightarrow & \color{red}{156} x& = & 95 \\\Leftrightarrow & x = \frac{95}{156} & & \\ & V = \left\{ \frac{95}{156} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -10x+\frac{25}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x+ \frac{125}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{+125} & = & \color{red}{-385x} +66 \\\Leftrightarrow & -550x \color{red}{+125} \color{blue}{-125} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{-125} \\\Leftrightarrow & -550x+385x& = & 66-125 \\\Leftrightarrow & \color{red}{-165} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{-165} & & \\\Leftrightarrow & x = \frac{59}{165} & & \\ & V = \left\{ \frac{59}{165} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{5}{12})& = & -8x+\frac{2}{11} \\\Leftrightarrow & -21x+\frac{35}{12}& = & -8x+\frac{2}{11} \\ & & & \text{kgv van noemers 12 en 11 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-2772}{ \color{blue}{132} }x+ \frac{385}{ \color{blue}{132} })& = & (\frac{-1056}{ \color{blue}{132} }x+ \frac{24}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -2772x \color{red}{+385} & = & \color{red}{-1056x} +24 \\\Leftrightarrow & -2772x \color{red}{+385} \color{blue}{-385} \color{blue}{+1056x} & = & \color{red}{-1056x} +24 \color{blue}{+1056x} \color{blue}{-385} \\\Leftrightarrow & -2772x+1056x& = & 24-385 \\\Leftrightarrow & \color{red}{-1716} x& = & -361 \\\Leftrightarrow & x = \frac{-361}{-1716} & & \\\Leftrightarrow & x = \frac{361}{1716} & & \\ & V = \left\{ \frac{361}{1716} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{4}{5})& = & 5x+\frac{5}{6} \\\Leftrightarrow & -14x+\frac{28}{5}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-420}{ \color{blue}{30} }x+ \frac{168}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -420x \color{red}{+168} & = & \color{red}{150x} +25 \\\Leftrightarrow & -420x \color{red}{+168} \color{blue}{-168} \color{blue}{-150x} & = & \color{red}{150x} +25 \color{blue}{-150x} \color{blue}{-168} \\\Leftrightarrow & -420x-150x& = & 25-168 \\\Leftrightarrow & \color{red}{-570} x& = & -143 \\\Leftrightarrow & x = \frac{-143}{-570} & & \\\Leftrightarrow & x = \frac{143}{570} & & \\ & V = \left\{ \frac{143}{570} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{2}{9})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 16x+\frac{8}{9}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{144}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 144x \color{red}{+8} & = & \color{red}{45x} +12 \\\Leftrightarrow & 144x \color{red}{+8} \color{blue}{-8} \color{blue}{-45x} & = & \color{red}{45x} +12 \color{blue}{-45x} \color{blue}{-8} \\\Leftrightarrow & 144x-45x& = & 12-8 \\\Leftrightarrow & \color{red}{99} x& = & 4 \\\Leftrightarrow & x = \frac{4}{99} & & \\ & V = \left\{ \frac{4}{99} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{11})& = & -7x+\frac{5}{6} \\\Leftrightarrow & -30x-\frac{30}{11}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1980}{ \color{blue}{66} }x- \frac{180}{ \color{blue}{66} })& = & (\frac{-462}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1980x \color{red}{-180} & = & \color{red}{-462x} +55 \\\Leftrightarrow & -1980x \color{red}{-180} \color{blue}{+180} \color{blue}{+462x} & = & \color{red}{-462x} +55 \color{blue}{+462x} \color{blue}{+180} \\\Leftrightarrow & -1980x+462x& = & 55+180 \\\Leftrightarrow & \color{red}{-1518} x& = & 235 \\\Leftrightarrow & x = \frac{235}{-1518} & & \\\Leftrightarrow & x = \frac{-235}{1518} & & \\ & V = \left\{ \frac{-235}{1518} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{3})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 20x+\frac{20}{3}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{+40} & = & \color{red}{42x} +9 \\\Leftrightarrow & 120x \color{red}{+40} \color{blue}{-40} \color{blue}{-42x} & = & \color{red}{42x} +9 \color{blue}{-42x} \color{blue}{-40} \\\Leftrightarrow & 120x-42x& = & 9-40 \\\Leftrightarrow & \color{red}{78} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{78} & & \\ & V = \left\{ \frac{-31}{78} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{3})& = & -2x+\frac{5}{12} \\\Leftrightarrow & 15x-\frac{20}{3}& = & -2x+\frac{5}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x- \frac{80}{ \color{blue}{12} })& = & (\frac{-24}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{-80} & = & \color{red}{-24x} +5 \\\Leftrightarrow & 180x \color{red}{-80} \color{blue}{+80} \color{blue}{+24x} & = & \color{red}{-24x} +5 \color{blue}{+24x} \color{blue}{+80} \\\Leftrightarrow & 180x+24x& = & 5+80 \\\Leftrightarrow & \color{red}{204} x& = & 85 \\\Leftrightarrow & x = \frac{85}{204} & & \\\Leftrightarrow & x = \frac{5}{12} & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{4}{9})& = & 8x+\frac{5}{3} \\\Leftrightarrow & -25x-\frac{20}{9}& = & 8x+\frac{5}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-225}{ \color{blue}{9} }x- \frac{20}{ \color{blue}{9} })& = & (\frac{72}{ \color{blue}{9} }x+ \frac{15}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -225x \color{red}{-20} & = & \color{red}{72x} +15 \\\Leftrightarrow & -225x \color{red}{-20} \color{blue}{+20} \color{blue}{-72x} & = & \color{red}{72x} +15 \color{blue}{-72x} \color{blue}{+20} \\\Leftrightarrow & -225x-72x& = & 15+20 \\\Leftrightarrow & \color{red}{-297} x& = & 35 \\\Leftrightarrow & x = \frac{35}{-297} & & \\\Leftrightarrow & x = \frac{-35}{297} & & \\ & V = \left\{ \frac{-35}{297} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{3}{4})& = & -7x+\frac{9}{10} \\\Leftrightarrow & 20x+\frac{15}{4}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{400}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{18}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 400x \color{red}{+75} & = & \color{red}{-140x} +18 \\\Leftrightarrow & 400x \color{red}{+75} \color{blue}{-75} \color{blue}{+140x} & = & \color{red}{-140x} +18 \color{blue}{+140x} \color{blue}{-75} \\\Leftrightarrow & 400x+140x& = & 18-75 \\\Leftrightarrow & \color{red}{540} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{540} & & \\\Leftrightarrow & x = \frac{-19}{180} & & \\ & V = \left\{ \frac{-19}{180} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{6})& = & 2x+\frac{2}{5} \\\Leftrightarrow & 21x-\frac{35}{6}& = & 2x+\frac{2}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{630}{ \color{blue}{30} }x- \frac{175}{ \color{blue}{30} })& = & (\frac{60}{ \color{blue}{30} }x+ \frac{12}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 630x \color{red}{-175} & = & \color{red}{60x} +12 \\\Leftrightarrow & 630x \color{red}{-175} \color{blue}{+175} \color{blue}{-60x} & = & \color{red}{60x} +12 \color{blue}{-60x} \color{blue}{+175} \\\Leftrightarrow & 630x-60x& = & 12+175 \\\Leftrightarrow & \color{red}{570} x& = & 187 \\\Leftrightarrow & x = \frac{187}{570} & & \\ & V = \left\{ \frac{187}{570} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{8})& = & 3x+\frac{2}{11} \\\Leftrightarrow & -14x-\frac{21}{8}& = & 3x+\frac{2}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1232}{ \color{blue}{88} }x- \frac{231}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{16}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1232x \color{red}{-231} & = & \color{red}{264x} +16 \\\Leftrightarrow & -1232x \color{red}{-231} \color{blue}{+231} \color{blue}{-264x} & = & \color{red}{264x} +16 \color{blue}{-264x} \color{blue}{+231} \\\Leftrightarrow & -1232x-264x& = & 16+231 \\\Leftrightarrow & \color{red}{-1496} x& = & 247 \\\Leftrightarrow & x = \frac{247}{-1496} & & \\\Leftrightarrow & x = \frac{-247}{1496} & & \\ & V = \left\{ \frac{-247}{1496} \right\} & \\\end{align}\)
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