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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{7})& = & -5x+\frac{7}{6} \\\Leftrightarrow & -24x-\frac{18}{7}& = & -5x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-1008}{ \color{blue}{42} }x- \frac{108}{ \color{blue}{42} })& = & (\frac{-210}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -1008x \color{red}{-108} & = & \color{red}{-210x} +49 \\\Leftrightarrow & -1008x \color{red}{-108} \color{blue}{+108} \color{blue}{+210x} & = & \color{red}{-210x} +49 \color{blue}{+210x} \color{blue}{+108} \\\Leftrightarrow & -1008x+210x& = & 49+108 \\\Leftrightarrow & \color{red}{-798} x& = & 157 \\\Leftrightarrow & x = \frac{157}{-798} & & \\\Leftrightarrow & x = \frac{-157}{798} & & \\ & V = \left\{ \frac{-157}{798} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{3}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 4x-\frac{6}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{-18} & = & \color{red}{-147x} +70 \\\Leftrightarrow & 84x \color{red}{-18} \color{blue}{+18} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{+18} \\\Leftrightarrow & 84x+147x& = & 70+18 \\\Leftrightarrow & \color{red}{231} x& = & 88 \\\Leftrightarrow & x = \frac{88}{231} & & \\\Leftrightarrow & x = \frac{8}{21} & & \\ & V = \left\{ \frac{8}{21} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{3}{2})& = & -8x+\frac{8}{9} \\\Leftrightarrow & 35x+\frac{21}{2}& = & -8x+\frac{8}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{630}{ \color{blue}{18} }x+ \frac{189}{ \color{blue}{18} })& = & (\frac{-144}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 630x \color{red}{+189} & = & \color{red}{-144x} +16 \\\Leftrightarrow & 630x \color{red}{+189} \color{blue}{-189} \color{blue}{+144x} & = & \color{red}{-144x} +16 \color{blue}{+144x} \color{blue}{-189} \\\Leftrightarrow & 630x+144x& = & 16-189 \\\Leftrightarrow & \color{red}{774} x& = & -173 \\\Leftrightarrow & x = \frac{-173}{774} & & \\ & V = \left\{ \frac{-173}{774} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{3}{11})& = & -3x+\frac{10}{11} \\\Leftrightarrow & -35x+\frac{21}{11}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-385}{ \color{blue}{11} }x+ \frac{21}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -385x \color{red}{+21} & = & \color{red}{-33x} +10 \\\Leftrightarrow & -385x \color{red}{+21} \color{blue}{-21} \color{blue}{+33x} & = & \color{red}{-33x} +10 \color{blue}{+33x} \color{blue}{-21} \\\Leftrightarrow & -385x+33x& = & 10-21 \\\Leftrightarrow & \color{red}{-352} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-352} & & \\\Leftrightarrow & x = \frac{1}{32} & & \\ & V = \left\{ \frac{1}{32} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{5}{11})& = & 5x+\frac{2}{5} \\\Leftrightarrow & -12x+\frac{20}{11}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{100}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+100} & = & \color{red}{275x} +22 \\\Leftrightarrow & -660x \color{red}{+100} \color{blue}{-100} \color{blue}{-275x} & = & \color{red}{275x} +22 \color{blue}{-275x} \color{blue}{-100} \\\Leftrightarrow & -660x-275x& = & 22-100 \\\Leftrightarrow & \color{red}{-935} x& = & -78 \\\Leftrightarrow & x = \frac{-78}{-935} & & \\\Leftrightarrow & x = \frac{78}{935} & & \\ & V = \left\{ \frac{78}{935} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{2}{5})& = & 8x+\frac{2}{3} \\\Leftrightarrow & 35x+\frac{14}{5}& = & 8x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{525}{ \color{blue}{15} }x+ \frac{42}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 525x \color{red}{+42} & = & \color{red}{120x} +10 \\\Leftrightarrow & 525x \color{red}{+42} \color{blue}{-42} \color{blue}{-120x} & = & \color{red}{120x} +10 \color{blue}{-120x} \color{blue}{-42} \\\Leftrightarrow & 525x-120x& = & 10-42 \\\Leftrightarrow & \color{red}{405} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{405} & & \\ & V = \left\{ \frac{-32}{405} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{2}{7})& = & 7x+\frac{5}{11} \\\Leftrightarrow & -20x+\frac{10}{7}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{+110} & = & \color{red}{539x} +35 \\\Leftrightarrow & -1540x \color{red}{+110} \color{blue}{-110} \color{blue}{-539x} & = & \color{red}{539x} +35 \color{blue}{-539x} \color{blue}{-110} \\\Leftrightarrow & -1540x-539x& = & 35-110 \\\Leftrightarrow & \color{red}{-2079} x& = & -75 \\\Leftrightarrow & x = \frac{-75}{-2079} & & \\\Leftrightarrow & x = \frac{25}{693} & & \\ & V = \left\{ \frac{25}{693} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{4}{5})& = & -7x+\frac{2}{5} \\\Leftrightarrow & 30x-\frac{24}{5}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{150}{ \color{blue}{5} }x- \frac{24}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 150x \color{red}{-24} & = & \color{red}{-35x} +2 \\\Leftrightarrow & 150x \color{red}{-24} \color{blue}{+24} \color{blue}{+35x} & = & \color{red}{-35x} +2 \color{blue}{+35x} \color{blue}{+24} \\\Leftrightarrow & 150x+35x& = & 2+24 \\\Leftrightarrow & \color{red}{185} x& = & 26 \\\Leftrightarrow & x = \frac{26}{185} & & \\ & V = \left\{ \frac{26}{185} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{5}{7})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -16x+\frac{20}{7}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-112}{ \color{blue}{7} }x+ \frac{20}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -112x \color{red}{+20} & = & \color{red}{49x} +9 \\\Leftrightarrow & -112x \color{red}{+20} \color{blue}{-20} \color{blue}{-49x} & = & \color{red}{49x} +9 \color{blue}{-49x} \color{blue}{-20} \\\Leftrightarrow & -112x-49x& = & 9-20 \\\Leftrightarrow & \color{red}{-161} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-161} & & \\\Leftrightarrow & x = \frac{11}{161} & & \\ & V = \left\{ \frac{11}{161} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{3}{8})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 15x+\frac{15}{8}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{360}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 360x \color{red}{+45} & = & \color{red}{-168x} +32 \\\Leftrightarrow & 360x \color{red}{+45} \color{blue}{-45} \color{blue}{+168x} & = & \color{red}{-168x} +32 \color{blue}{+168x} \color{blue}{-45} \\\Leftrightarrow & 360x+168x& = & 32-45 \\\Leftrightarrow & \color{red}{528} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{528} & & \\ & V = \left\{ \frac{-13}{528} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{5}{7})& = & 5x+\frac{2}{9} \\\Leftrightarrow & -18x-\frac{30}{7}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1134}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1134x \color{red}{-270} & = & \color{red}{315x} +14 \\\Leftrightarrow & -1134x \color{red}{-270} \color{blue}{+270} \color{blue}{-315x} & = & \color{red}{315x} +14 \color{blue}{-315x} \color{blue}{+270} \\\Leftrightarrow & -1134x-315x& = & 14+270 \\\Leftrightarrow & \color{red}{-1449} x& = & 284 \\\Leftrightarrow & x = \frac{284}{-1449} & & \\\Leftrightarrow & x = \frac{-284}{1449} & & \\ & V = \left\{ \frac{-284}{1449} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{4}{7})& = & 2x+\frac{2}{3} \\\Leftrightarrow & 15x-\frac{20}{7}& = & 2x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{42}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{-60} & = & \color{red}{42x} +14 \\\Leftrightarrow & 315x \color{red}{-60} \color{blue}{+60} \color{blue}{-42x} & = & \color{red}{42x} +14 \color{blue}{-42x} \color{blue}{+60} \\\Leftrightarrow & 315x-42x& = & 14+60 \\\Leftrightarrow & \color{red}{273} x& = & 74 \\\Leftrightarrow & x = \frac{74}{273} & & \\ & V = \left\{ \frac{74}{273} \right\} & \\\end{align}\)
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