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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{2}{9})& = & -3x+\frac{9}{2} \\\Leftrightarrow & 8x+\frac{8}{9}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{144}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{-54}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 144x \color{red}{+16} & = & \color{red}{-54x} +81 \\\Leftrightarrow & 144x \color{red}{+16} \color{blue}{-16} \color{blue}{+54x} & = & \color{red}{-54x} +81 \color{blue}{+54x} \color{blue}{-16} \\\Leftrightarrow & 144x+54x& = & 81-16 \\\Leftrightarrow & \color{red}{198} x& = & 65 \\\Leftrightarrow & x = \frac{65}{198} & & \\ & V = \left\{ \frac{65}{198} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{11})& = & 7x+\frac{5}{8} \\\Leftrightarrow & -10x-\frac{6}{11}& = & 7x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-880}{ \color{blue}{88} }x- \frac{48}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -880x \color{red}{-48} & = & \color{red}{616x} +55 \\\Leftrightarrow & -880x \color{red}{-48} \color{blue}{+48} \color{blue}{-616x} & = & \color{red}{616x} +55 \color{blue}{-616x} \color{blue}{+48} \\\Leftrightarrow & -880x-616x& = & 55+48 \\\Leftrightarrow & \color{red}{-1496} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-1496} & & \\\Leftrightarrow & x = \frac{-103}{1496} & & \\ & V = \left\{ \frac{-103}{1496} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{3}{7})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -10x-\frac{6}{7}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-30} & = & \color{red}{245x} +42 \\\Leftrightarrow & -350x \color{red}{-30} \color{blue}{+30} \color{blue}{-245x} & = & \color{red}{245x} +42 \color{blue}{-245x} \color{blue}{+30} \\\Leftrightarrow & -350x-245x& = & 42+30 \\\Leftrightarrow & \color{red}{-595} x& = & 72 \\\Leftrightarrow & x = \frac{72}{-595} & & \\\Leftrightarrow & x = \frac{-72}{595} & & \\ & V = \left\{ \frac{-72}{595} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{4}{5})& = & 7x+\frac{10}{9} \\\Leftrightarrow & -6x-\frac{12}{5}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{-108} & = & \color{red}{315x} +50 \\\Leftrightarrow & -270x \color{red}{-108} \color{blue}{+108} \color{blue}{-315x} & = & \color{red}{315x} +50 \color{blue}{-315x} \color{blue}{+108} \\\Leftrightarrow & -270x-315x& = & 50+108 \\\Leftrightarrow & \color{red}{-585} x& = & 158 \\\Leftrightarrow & x = \frac{158}{-585} & & \\\Leftrightarrow & x = \frac{-158}{585} & & \\ & V = \left\{ \frac{-158}{585} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{3}{7})& = & -9x+\frac{3}{10} \\\Leftrightarrow & -8x+\frac{6}{7}& = & -9x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-560}{ \color{blue}{70} }x+ \frac{60}{ \color{blue}{70} })& = & (\frac{-630}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -560x \color{red}{+60} & = & \color{red}{-630x} +21 \\\Leftrightarrow & -560x \color{red}{+60} \color{blue}{-60} \color{blue}{+630x} & = & \color{red}{-630x} +21 \color{blue}{+630x} \color{blue}{-60} \\\Leftrightarrow & -560x+630x& = & 21-60 \\\Leftrightarrow & \color{red}{70} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{70} & & \\ & V = \left\{ \frac{-39}{70} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{3}{5})& = & 7x+\frac{3}{10} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+24} & = & \color{red}{70x} +3 \\\Leftrightarrow & 120x \color{red}{+24} \color{blue}{-24} \color{blue}{-70x} & = & \color{red}{70x} +3 \color{blue}{-70x} \color{blue}{-24} \\\Leftrightarrow & 120x-70x& = & 3-24 \\\Leftrightarrow & \color{red}{50} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{50} & & \\ & V = \left\{ \frac{-21}{50} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{4}{3})& = & 9x+\frac{9}{5} \\\Leftrightarrow & -8x-\frac{8}{3}& = & 9x+\frac{9}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{-40} & = & \color{red}{135x} +27 \\\Leftrightarrow & -120x \color{red}{-40} \color{blue}{+40} \color{blue}{-135x} & = & \color{red}{135x} +27 \color{blue}{-135x} \color{blue}{+40} \\\Leftrightarrow & -120x-135x& = & 27+40 \\\Leftrightarrow & \color{red}{-255} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-255} & & \\\Leftrightarrow & x = \frac{-67}{255} & & \\ & V = \left\{ \frac{-67}{255} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{2}{5})& = & -3x+\frac{9}{2} \\\Leftrightarrow & -14x+\frac{14}{5}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-140}{ \color{blue}{10} }x+ \frac{28}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -140x \color{red}{+28} & = & \color{red}{-30x} +45 \\\Leftrightarrow & -140x \color{red}{+28} \color{blue}{-28} \color{blue}{+30x} & = & \color{red}{-30x} +45 \color{blue}{+30x} \color{blue}{-28} \\\Leftrightarrow & -140x+30x& = & 45-28 \\\Leftrightarrow & \color{red}{-110} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-110} & & \\\Leftrightarrow & x = \frac{-17}{110} & & \\ & V = \left\{ \frac{-17}{110} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{3}{5})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{18}{5}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{54}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+54} & = & \color{red}{75x} +40 \\\Leftrightarrow & 180x \color{red}{+54} \color{blue}{-54} \color{blue}{-75x} & = & \color{red}{75x} +40 \color{blue}{-75x} \color{blue}{-54} \\\Leftrightarrow & 180x-75x& = & 40-54 \\\Leftrightarrow & \color{red}{105} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{105} & & \\\Leftrightarrow & x = \frac{-2}{15} & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{2}{7})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -16x-\frac{8}{7}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-336}{ \color{blue}{21} }x- \frac{24}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -336x \color{red}{-24} & = & \color{red}{-147x} +56 \\\Leftrightarrow & -336x \color{red}{-24} \color{blue}{+24} \color{blue}{+147x} & = & \color{red}{-147x} +56 \color{blue}{+147x} \color{blue}{+24} \\\Leftrightarrow & -336x+147x& = & 56+24 \\\Leftrightarrow & \color{red}{-189} x& = & 80 \\\Leftrightarrow & x = \frac{80}{-189} & & \\\Leftrightarrow & x = \frac{-80}{189} & & \\ & V = \left\{ \frac{-80}{189} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{7})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -12x-\frac{30}{7}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-330} & = & \color{red}{-385x} +42 \\\Leftrightarrow & -924x \color{red}{-330} \color{blue}{+330} \color{blue}{+385x} & = & \color{red}{-385x} +42 \color{blue}{+385x} \color{blue}{+330} \\\Leftrightarrow & -924x+385x& = & 42+330 \\\Leftrightarrow & \color{red}{-539} x& = & 372 \\\Leftrightarrow & x = \frac{372}{-539} & & \\\Leftrightarrow & x = \frac{-372}{539} & & \\ & V = \left\{ \frac{-372}{539} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{5}{11})& = & 7x+\frac{3}{8} \\\Leftrightarrow & 12x+\frac{30}{11}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1056}{ \color{blue}{88} }x+ \frac{240}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1056x \color{red}{+240} & = & \color{red}{616x} +33 \\\Leftrightarrow & 1056x \color{red}{+240} \color{blue}{-240} \color{blue}{-616x} & = & \color{red}{616x} +33 \color{blue}{-616x} \color{blue}{-240} \\\Leftrightarrow & 1056x-616x& = & 33-240 \\\Leftrightarrow & \color{red}{440} x& = & -207 \\\Leftrightarrow & x = \frac{-207}{440} & & \\ & V = \left\{ \frac{-207}{440} \right\} & \\\end{align}\)
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