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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{3}{11})& = & -9x+\frac{4}{3} \\\Leftrightarrow & 35x+\frac{21}{11}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x+ \frac{63}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{+63} & = & \color{red}{-297x} +44 \\\Leftrightarrow & 1155x \color{red}{+63} \color{blue}{-63} \color{blue}{+297x} & = & \color{red}{-297x} +44 \color{blue}{+297x} \color{blue}{-63} \\\Leftrightarrow & 1155x+297x& = & 44-63 \\\Leftrightarrow & \color{red}{1452} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{1452} & & \\ & V = \left\{ \frac{-19}{1452} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{5}{7})& = & -9x+\frac{9}{2} \\\Leftrightarrow & -8x-\frac{10}{7}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-112}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{-126}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -112x \color{red}{-20} & = & \color{red}{-126x} +63 \\\Leftrightarrow & -112x \color{red}{-20} \color{blue}{+20} \color{blue}{+126x} & = & \color{red}{-126x} +63 \color{blue}{+126x} \color{blue}{+20} \\\Leftrightarrow & -112x+126x& = & 63+20 \\\Leftrightarrow & \color{red}{14} x& = & 83 \\\Leftrightarrow & x = \frac{83}{14} & & \\ & V = \left\{ \frac{83}{14} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{3}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 12x+\frac{18}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x+ \frac{18}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{+18} & = & \color{red}{-25x} +6 \\\Leftrightarrow & 60x \color{red}{+18} \color{blue}{-18} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{-18} \\\Leftrightarrow & 60x+25x& = & 6-18 \\\Leftrightarrow & \color{red}{85} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{85} & & \\ & V = \left\{ \frac{-12}{85} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{9})& = & -6x+\frac{3}{10} \\\Leftrightarrow & -28x-\frac{28}{9}& = & -6x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-2520}{ \color{blue}{90} }x- \frac{280}{ \color{blue}{90} })& = & (\frac{-540}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -2520x \color{red}{-280} & = & \color{red}{-540x} +27 \\\Leftrightarrow & -2520x \color{red}{-280} \color{blue}{+280} \color{blue}{+540x} & = & \color{red}{-540x} +27 \color{blue}{+540x} \color{blue}{+280} \\\Leftrightarrow & -2520x+540x& = & 27+280 \\\Leftrightarrow & \color{red}{-1980} x& = & 307 \\\Leftrightarrow & x = \frac{307}{-1980} & & \\\Leftrightarrow & x = \frac{-307}{1980} & & \\ & V = \left\{ \frac{-307}{1980} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{5})& = & -9x+\frac{4}{3} \\\Leftrightarrow & -8x+\frac{8}{5}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{+24} & = & \color{red}{-135x} +20 \\\Leftrightarrow & -120x \color{red}{+24} \color{blue}{-24} \color{blue}{+135x} & = & \color{red}{-135x} +20 \color{blue}{+135x} \color{blue}{-24} \\\Leftrightarrow & -120x+135x& = & 20-24 \\\Leftrightarrow & \color{red}{15} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{15} & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{4}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -16x+\frac{16}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-336}{ \color{blue}{21} }x+ \frac{48}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -336x \color{red}{+48} & = & \color{red}{147x} +14 \\\Leftrightarrow & -336x \color{red}{+48} \color{blue}{-48} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{-48} \\\Leftrightarrow & -336x-147x& = & 14-48 \\\Leftrightarrow & \color{red}{-483} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-483} & & \\\Leftrightarrow & x = \frac{34}{483} & & \\ & V = \left\{ \frac{34}{483} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{2}{3})& = & -9x+\frac{2}{3} \\\Leftrightarrow & 35x-\frac{14}{3}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{105}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 105x \color{red}{-14} & = & \color{red}{-27x} +2 \\\Leftrightarrow & 105x \color{red}{-14} \color{blue}{+14} \color{blue}{+27x} & = & \color{red}{-27x} +2 \color{blue}{+27x} \color{blue}{+14} \\\Leftrightarrow & 105x+27x& = & 2+14 \\\Leftrightarrow & \color{red}{132} x& = & 16 \\\Leftrightarrow & x = \frac{16}{132} & & \\\Leftrightarrow & x = \frac{4}{33} & & \\ & V = \left\{ \frac{4}{33} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{5}{11})& = & -3x+\frac{6}{7} \\\Leftrightarrow & 10x+\frac{25}{11}& = & -3x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{175}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+175} & = & \color{red}{-231x} +66 \\\Leftrightarrow & 770x \color{red}{+175} \color{blue}{-175} \color{blue}{+231x} & = & \color{red}{-231x} +66 \color{blue}{+231x} \color{blue}{-175} \\\Leftrightarrow & 770x+231x& = & 66-175 \\\Leftrightarrow & \color{red}{1001} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{1001} & & \\ & V = \left\{ \frac{-109}{1001} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{2}{3})& = & 7x+\frac{8}{7} \\\Leftrightarrow & -16x-\frac{8}{3}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-336}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -336x \color{red}{-56} & = & \color{red}{147x} +24 \\\Leftrightarrow & -336x \color{red}{-56} \color{blue}{+56} \color{blue}{-147x} & = & \color{red}{147x} +24 \color{blue}{-147x} \color{blue}{+56} \\\Leftrightarrow & -336x-147x& = & 24+56 \\\Leftrightarrow & \color{red}{-483} x& = & 80 \\\Leftrightarrow & x = \frac{80}{-483} & & \\\Leftrightarrow & x = \frac{-80}{483} & & \\ & V = \left\{ \frac{-80}{483} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{4}{11})& = & -5x+\frac{8}{9} \\\Leftrightarrow & -12x+\frac{16}{11}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x+ \frac{144}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{+144} & = & \color{red}{-495x} +88 \\\Leftrightarrow & -1188x \color{red}{+144} \color{blue}{-144} \color{blue}{+495x} & = & \color{red}{-495x} +88 \color{blue}{+495x} \color{blue}{-144} \\\Leftrightarrow & -1188x+495x& = & 88-144 \\\Leftrightarrow & \color{red}{-693} x& = & -56 \\\Leftrightarrow & x = \frac{-56}{-693} & & \\\Leftrightarrow & x = \frac{8}{99} & & \\ & V = \left\{ \frac{8}{99} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{3}{11})& = & 8x+\frac{3}{2} \\\Leftrightarrow & 21x-\frac{21}{11}& = & 8x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{462}{ \color{blue}{22} }x- \frac{42}{ \color{blue}{22} })& = & (\frac{176}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 462x \color{red}{-42} & = & \color{red}{176x} +33 \\\Leftrightarrow & 462x \color{red}{-42} \color{blue}{+42} \color{blue}{-176x} & = & \color{red}{176x} +33 \color{blue}{-176x} \color{blue}{+42} \\\Leftrightarrow & 462x-176x& = & 33+42 \\\Leftrightarrow & \color{red}{286} x& = & 75 \\\Leftrightarrow & x = \frac{75}{286} & & \\ & V = \left\{ \frac{75}{286} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{3}{2})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -20x+\frac{15}{2}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x+ \frac{45}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{+45} & = & \color{red}{-42x} +8 \\\Leftrightarrow & -120x \color{red}{+45} \color{blue}{-45} \color{blue}{+42x} & = & \color{red}{-42x} +8 \color{blue}{+42x} \color{blue}{-45} \\\Leftrightarrow & -120x+42x& = & 8-45 \\\Leftrightarrow & \color{red}{-78} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-78} & & \\\Leftrightarrow & x = \frac{37}{78} & & \\ & V = \left\{ \frac{37}{78} \right\} & \\\end{align}\)
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