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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{4}{11})& = & -7x+\frac{8}{7} \\\Leftrightarrow & -20x-\frac{16}{11}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x- \frac{112}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{-112} & = & \color{red}{-539x} +88 \\\Leftrightarrow & -1540x \color{red}{-112} \color{blue}{+112} \color{blue}{+539x} & = & \color{red}{-539x} +88 \color{blue}{+539x} \color{blue}{+112} \\\Leftrightarrow & -1540x+539x& = & 88+112 \\\Leftrightarrow & \color{red}{-1001} x& = & 200 \\\Leftrightarrow & x = \frac{200}{-1001} & & \\\Leftrightarrow & x = \frac{-200}{1001} & & \\ & V = \left\{ \frac{-200}{1001} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{2}{5})& = & 3x+\frac{5}{7} \\\Leftrightarrow & -14x-\frac{14}{5}& = & 3x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-490}{ \color{blue}{35} }x- \frac{98}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -490x \color{red}{-98} & = & \color{red}{105x} +25 \\\Leftrightarrow & -490x \color{red}{-98} \color{blue}{+98} \color{blue}{-105x} & = & \color{red}{105x} +25 \color{blue}{-105x} \color{blue}{+98} \\\Leftrightarrow & -490x-105x& = & 25+98 \\\Leftrightarrow & \color{red}{-595} x& = & 123 \\\Leftrightarrow & x = \frac{123}{-595} & & \\\Leftrightarrow & x = \frac{-123}{595} & & \\ & V = \left\{ \frac{-123}{595} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{5}{11})& = & 3x+\frac{10}{7} \\\Leftrightarrow & -25x+\frac{25}{11}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1925}{ \color{blue}{77} }x+ \frac{175}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1925x \color{red}{+175} & = & \color{red}{231x} +110 \\\Leftrightarrow & -1925x \color{red}{+175} \color{blue}{-175} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{-175} \\\Leftrightarrow & -1925x-231x& = & 110-175 \\\Leftrightarrow & \color{red}{-2156} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{-2156} & & \\\Leftrightarrow & x = \frac{65}{2156} & & \\ & V = \left\{ \frac{65}{2156} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{9})& = & 3x+\frac{8}{9} \\\Leftrightarrow & -20x-\frac{8}{9}& = & 3x+\frac{8}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{-8} & = & \color{red}{27x} +8 \\\Leftrightarrow & -180x \color{red}{-8} \color{blue}{+8} \color{blue}{-27x} & = & \color{red}{27x} +8 \color{blue}{-27x} \color{blue}{+8} \\\Leftrightarrow & -180x-27x& = & 8+8 \\\Leftrightarrow & \color{red}{-207} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-207} & & \\\Leftrightarrow & x = \frac{-16}{207} & & \\ & V = \left\{ \frac{-16}{207} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{7})& = & 5x+\frac{3}{10} \\\Leftrightarrow & -12x-\frac{15}{7}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-840}{ \color{blue}{70} }x- \frac{150}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -840x \color{red}{-150} & = & \color{red}{350x} +21 \\\Leftrightarrow & -840x \color{red}{-150} \color{blue}{+150} \color{blue}{-350x} & = & \color{red}{350x} +21 \color{blue}{-350x} \color{blue}{+150} \\\Leftrightarrow & -840x-350x& = & 21+150 \\\Leftrightarrow & \color{red}{-1190} x& = & 171 \\\Leftrightarrow & x = \frac{171}{-1190} & & \\\Leftrightarrow & x = \frac{-171}{1190} & & \\ & V = \left\{ \frac{-171}{1190} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{2})& = & 3x+\frac{10}{11} \\\Leftrightarrow & 10x-\frac{25}{2}& = & 3x+\frac{10}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{220}{ \color{blue}{22} }x- \frac{275}{ \color{blue}{22} })& = & (\frac{66}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 220x \color{red}{-275} & = & \color{red}{66x} +20 \\\Leftrightarrow & 220x \color{red}{-275} \color{blue}{+275} \color{blue}{-66x} & = & \color{red}{66x} +20 \color{blue}{-66x} \color{blue}{+275} \\\Leftrightarrow & 220x-66x& = & 20+275 \\\Leftrightarrow & \color{red}{154} x& = & 295 \\\Leftrightarrow & x = \frac{295}{154} & & \\ & V = \left\{ \frac{295}{154} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{7})& = & -5x+\frac{7}{5} \\\Leftrightarrow & 12x+\frac{8}{7}& = & -5x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+40} & = & \color{red}{-175x} +49 \\\Leftrightarrow & 420x \color{red}{+40} \color{blue}{-40} \color{blue}{+175x} & = & \color{red}{-175x} +49 \color{blue}{+175x} \color{blue}{-40} \\\Leftrightarrow & 420x+175x& = & 49-40 \\\Leftrightarrow & \color{red}{595} x& = & 9 \\\Leftrightarrow & x = \frac{9}{595} & & \\ & V = \left\{ \frac{9}{595} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{2}{5})& = & 2x+\frac{8}{3} \\\Leftrightarrow & -18x-\frac{12}{5}& = & 2x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-270}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{30}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -270x \color{red}{-36} & = & \color{red}{30x} +40 \\\Leftrightarrow & -270x \color{red}{-36} \color{blue}{+36} \color{blue}{-30x} & = & \color{red}{30x} +40 \color{blue}{-30x} \color{blue}{+36} \\\Leftrightarrow & -270x-30x& = & 40+36 \\\Leftrightarrow & \color{red}{-300} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-300} & & \\\Leftrightarrow & x = \frac{-19}{75} & & \\ & V = \left\{ \frac{-19}{75} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{5}{11})& = & -5x+\frac{8}{7} \\\Leftrightarrow & 18x-\frac{30}{11}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x- \frac{210}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{-210} & = & \color{red}{-385x} +88 \\\Leftrightarrow & 1386x \color{red}{-210} \color{blue}{+210} \color{blue}{+385x} & = & \color{red}{-385x} +88 \color{blue}{+385x} \color{blue}{+210} \\\Leftrightarrow & 1386x+385x& = & 88+210 \\\Leftrightarrow & \color{red}{1771} x& = & 298 \\\Leftrightarrow & x = \frac{298}{1771} & & \\ & V = \left\{ \frac{298}{1771} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{4}{11})& = & 8x+\frac{10}{7} \\\Leftrightarrow & 15x-\frac{12}{11}& = & 8x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{616}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{-84} & = & \color{red}{616x} +110 \\\Leftrightarrow & 1155x \color{red}{-84} \color{blue}{+84} \color{blue}{-616x} & = & \color{red}{616x} +110 \color{blue}{-616x} \color{blue}{+84} \\\Leftrightarrow & 1155x-616x& = & 110+84 \\\Leftrightarrow & \color{red}{539} x& = & 194 \\\Leftrightarrow & x = \frac{194}{539} & & \\ & V = \left\{ \frac{194}{539} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{5})& = & 5x+\frac{5}{6} \\\Leftrightarrow & 6x-\frac{6}{5}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{180}{ \color{blue}{30} }x- \frac{36}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 180x \color{red}{-36} & = & \color{red}{150x} +25 \\\Leftrightarrow & 180x \color{red}{-36} \color{blue}{+36} \color{blue}{-150x} & = & \color{red}{150x} +25 \color{blue}{-150x} \color{blue}{+36} \\\Leftrightarrow & 180x-150x& = & 25+36 \\\Leftrightarrow & \color{red}{30} x& = & 61 \\\Leftrightarrow & x = \frac{61}{30} & & \\ & V = \left\{ \frac{61}{30} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{4}{3})& = & 3x+\frac{5}{6} \\\Leftrightarrow & 20x+\frac{16}{3}& = & 3x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x+ \frac{32}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{+32} & = & \color{red}{18x} +5 \\\Leftrightarrow & 120x \color{red}{+32} \color{blue}{-32} \color{blue}{-18x} & = & \color{red}{18x} +5 \color{blue}{-18x} \color{blue}{-32} \\\Leftrightarrow & 120x-18x& = & 5-32 \\\Leftrightarrow & \color{red}{102} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{102} & & \\\Leftrightarrow & x = \frac{-9}{34} & & \\ & V = \left\{ \frac{-9}{34} \right\} & \\\end{align}\)
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