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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & -5x+\frac{8}{9} \\\Leftrightarrow & -12x-\frac{18}{11}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x- \frac{162}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{-162} & = & \color{red}{-495x} +88 \\\Leftrightarrow & -1188x \color{red}{-162} \color{blue}{+162} \color{blue}{+495x} & = & \color{red}{-495x} +88 \color{blue}{+495x} \color{blue}{+162} \\\Leftrightarrow & -1188x+495x& = & 88+162 \\\Leftrightarrow & \color{red}{-693} x& = & 250 \\\Leftrightarrow & x = \frac{250}{-693} & & \\\Leftrightarrow & x = \frac{-250}{693} & & \\ & V = \left\{ \frac{-250}{693} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{4}{5})& = & -7x+\frac{9}{10} \\\Leftrightarrow & 12x+\frac{24}{5}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{48}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+48} & = & \color{red}{-70x} +9 \\\Leftrightarrow & 120x \color{red}{+48} \color{blue}{-48} \color{blue}{+70x} & = & \color{red}{-70x} +9 \color{blue}{+70x} \color{blue}{-48} \\\Leftrightarrow & 120x+70x& = & 9-48 \\\Leftrightarrow & \color{red}{190} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{190} & & \\ & V = \left\{ \frac{-39}{190} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{5}{4})& = & 5x+\frac{8}{9} \\\Leftrightarrow & 12x+\frac{15}{4}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{432}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{180}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 432x \color{red}{+135} & = & \color{red}{180x} +32 \\\Leftrightarrow & 432x \color{red}{+135} \color{blue}{-135} \color{blue}{-180x} & = & \color{red}{180x} +32 \color{blue}{-180x} \color{blue}{-135} \\\Leftrightarrow & 432x-180x& = & 32-135 \\\Leftrightarrow & \color{red}{252} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{252} & & \\ & V = \left\{ \frac{-103}{252} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{4}{5})& = & -5x+\frac{6}{7} \\\Leftrightarrow & -24x-\frac{24}{5}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x- \frac{168}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{-168} & = & \color{red}{-175x} +30 \\\Leftrightarrow & -840x \color{red}{-168} \color{blue}{+168} \color{blue}{+175x} & = & \color{red}{-175x} +30 \color{blue}{+175x} \color{blue}{+168} \\\Leftrightarrow & -840x+175x& = & 30+168 \\\Leftrightarrow & \color{red}{-665} x& = & 198 \\\Leftrightarrow & x = \frac{198}{-665} & & \\\Leftrightarrow & x = \frac{-198}{665} & & \\ & V = \left\{ \frac{-198}{665} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{4}{11})& = & -4x+\frac{6}{5} \\\Leftrightarrow & -25x-\frac{20}{11}& = & -4x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1375}{ \color{blue}{55} }x- \frac{100}{ \color{blue}{55} })& = & (\frac{-220}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1375x \color{red}{-100} & = & \color{red}{-220x} +66 \\\Leftrightarrow & -1375x \color{red}{-100} \color{blue}{+100} \color{blue}{+220x} & = & \color{red}{-220x} +66 \color{blue}{+220x} \color{blue}{+100} \\\Leftrightarrow & -1375x+220x& = & 66+100 \\\Leftrightarrow & \color{red}{-1155} x& = & 166 \\\Leftrightarrow & x = \frac{166}{-1155} & & \\\Leftrightarrow & x = \frac{-166}{1155} & & \\ & V = \left\{ \frac{-166}{1155} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{2}{5})& = & -9x+\frac{5}{11} \\\Leftrightarrow & 14x-\frac{14}{5}& = & -9x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{770}{ \color{blue}{55} }x- \frac{154}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 770x \color{red}{-154} & = & \color{red}{-495x} +25 \\\Leftrightarrow & 770x \color{red}{-154} \color{blue}{+154} \color{blue}{+495x} & = & \color{red}{-495x} +25 \color{blue}{+495x} \color{blue}{+154} \\\Leftrightarrow & 770x+495x& = & 25+154 \\\Leftrightarrow & \color{red}{1265} x& = & 179 \\\Leftrightarrow & x = \frac{179}{1265} & & \\ & V = \left\{ \frac{179}{1265} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{3})& = & 9x+\frac{6}{5} \\\Leftrightarrow & 10x+\frac{25}{3}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{150}{ \color{blue}{15} }x+ \frac{125}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 150x \color{red}{+125} & = & \color{red}{135x} +18 \\\Leftrightarrow & 150x \color{red}{+125} \color{blue}{-125} \color{blue}{-135x} & = & \color{red}{135x} +18 \color{blue}{-135x} \color{blue}{-125} \\\Leftrightarrow & 150x-135x& = & 18-125 \\\Leftrightarrow & \color{red}{15} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{15} & & \\ & V = \left\{ \frac{-107}{15} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{2}{5})& = & 9x+\frac{9}{4} \\\Leftrightarrow & -4x-\frac{4}{5}& = & 9x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-80}{ \color{blue}{20} }x- \frac{16}{ \color{blue}{20} })& = & (\frac{180}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -80x \color{red}{-16} & = & \color{red}{180x} +45 \\\Leftrightarrow & -80x \color{red}{-16} \color{blue}{+16} \color{blue}{-180x} & = & \color{red}{180x} +45 \color{blue}{-180x} \color{blue}{+16} \\\Leftrightarrow & -80x-180x& = & 45+16 \\\Leftrightarrow & \color{red}{-260} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-260} & & \\\Leftrightarrow & x = \frac{-61}{260} & & \\ & V = \left\{ \frac{-61}{260} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{4}{5})& = & -7x+\frac{3}{8} \\\Leftrightarrow & -18x+\frac{24}{5}& = & -7x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-720}{ \color{blue}{40} }x+ \frac{192}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -720x \color{red}{+192} & = & \color{red}{-280x} +15 \\\Leftrightarrow & -720x \color{red}{+192} \color{blue}{-192} \color{blue}{+280x} & = & \color{red}{-280x} +15 \color{blue}{+280x} \color{blue}{-192} \\\Leftrightarrow & -720x+280x& = & 15-192 \\\Leftrightarrow & \color{red}{-440} x& = & -177 \\\Leftrightarrow & x = \frac{-177}{-440} & & \\\Leftrightarrow & x = \frac{177}{440} & & \\ & V = \left\{ \frac{177}{440} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{3}{5})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 12x-\frac{18}{5}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{36}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-36} & = & \color{red}{50x} +15 \\\Leftrightarrow & 120x \color{red}{-36} \color{blue}{+36} \color{blue}{-50x} & = & \color{red}{50x} +15 \color{blue}{-50x} \color{blue}{+36} \\\Leftrightarrow & 120x-50x& = & 15+36 \\\Leftrightarrow & \color{red}{70} x& = & 51 \\\Leftrightarrow & x = \frac{51}{70} & & \\ & V = \left\{ \frac{51}{70} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{4}{3})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -10x+\frac{20}{3}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-30}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -30x \color{red}{+20} & = & \color{red}{21x} +4 \\\Leftrightarrow & -30x \color{red}{+20} \color{blue}{-20} \color{blue}{-21x} & = & \color{red}{21x} +4 \color{blue}{-21x} \color{blue}{-20} \\\Leftrightarrow & -30x-21x& = & 4-20 \\\Leftrightarrow & \color{red}{-51} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-51} & & \\\Leftrightarrow & x = \frac{16}{51} & & \\ & V = \left\{ \frac{16}{51} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{5}{11})& = & -7x+\frac{7}{6} \\\Leftrightarrow & -20x-\frac{20}{11}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1320}{ \color{blue}{66} }x- \frac{120}{ \color{blue}{66} })& = & (\frac{-462}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1320x \color{red}{-120} & = & \color{red}{-462x} +77 \\\Leftrightarrow & -1320x \color{red}{-120} \color{blue}{+120} \color{blue}{+462x} & = & \color{red}{-462x} +77 \color{blue}{+462x} \color{blue}{+120} \\\Leftrightarrow & -1320x+462x& = & 77+120 \\\Leftrightarrow & \color{red}{-858} x& = & 197 \\\Leftrightarrow & x = \frac{197}{-858} & & \\\Leftrightarrow & x = \frac{-197}{858} & & \\ & V = \left\{ \frac{-197}{858} \right\} & \\\end{align}\)
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