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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{3}{10})& = & -3x+\frac{2}{11} \\\Leftrightarrow & 14x+\frac{21}{10}& = & -3x+\frac{2}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1540}{ \color{blue}{110} }x+ \frac{231}{ \color{blue}{110} })& = & (\frac{-330}{ \color{blue}{110} }x+ \frac{20}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1540x \color{red}{+231} & = & \color{red}{-330x} +20 \\\Leftrightarrow & 1540x \color{red}{+231} \color{blue}{-231} \color{blue}{+330x} & = & \color{red}{-330x} +20 \color{blue}{+330x} \color{blue}{-231} \\\Leftrightarrow & 1540x+330x& = & 20-231 \\\Leftrightarrow & \color{red}{1870} x& = & -211 \\\Leftrightarrow & x = \frac{-211}{1870} & & \\ & V = \left\{ \frac{-211}{1870} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+1)& = & -8x+\frac{9}{4} \\\Leftrightarrow & -21x-7& = & -8x+\frac{9}{4} \\ & & & \text{kgv van noemers 1 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-84}{ \color{blue}{4} }x- \frac{28}{ \color{blue}{4} })& = & (\frac{-32}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -84x \color{red}{-28} & = & \color{red}{-32x} +9 \\\Leftrightarrow & -84x \color{red}{-28} \color{blue}{+28} \color{blue}{+32x} & = & \color{red}{-32x} +9 \color{blue}{+32x} \color{blue}{+28} \\\Leftrightarrow & -84x+32x& = & 9+28 \\\Leftrightarrow & \color{red}{-52} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-52} & & \\\Leftrightarrow & x = \frac{-37}{52} & & \\ & V = \left\{ \frac{-37}{52} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{4}{9})& = & -4x+\frac{4}{3} \\\Leftrightarrow & 35x-\frac{28}{9}& = & -4x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{315}{ \color{blue}{9} }x- \frac{28}{ \color{blue}{9} })& = & (\frac{-36}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 315x \color{red}{-28} & = & \color{red}{-36x} +12 \\\Leftrightarrow & 315x \color{red}{-28} \color{blue}{+28} \color{blue}{+36x} & = & \color{red}{-36x} +12 \color{blue}{+36x} \color{blue}{+28} \\\Leftrightarrow & 315x+36x& = & 12+28 \\\Leftrightarrow & \color{red}{351} x& = & 40 \\\Leftrightarrow & x = \frac{40}{351} & & \\ & V = \left\{ \frac{40}{351} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{4}{11})& = & 8x+\frac{9}{10} \\\Leftrightarrow & -15x-\frac{20}{11}& = & 8x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1650}{ \color{blue}{110} }x- \frac{200}{ \color{blue}{110} })& = & (\frac{880}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1650x \color{red}{-200} & = & \color{red}{880x} +99 \\\Leftrightarrow & -1650x \color{red}{-200} \color{blue}{+200} \color{blue}{-880x} & = & \color{red}{880x} +99 \color{blue}{-880x} \color{blue}{+200} \\\Leftrightarrow & -1650x-880x& = & 99+200 \\\Leftrightarrow & \color{red}{-2530} x& = & 299 \\\Leftrightarrow & x = \frac{299}{-2530} & & \\\Leftrightarrow & x = \frac{-13}{110} & & \\ & V = \left\{ \frac{-13}{110} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{2}{5})& = & -5x+\frac{3}{4} \\\Leftrightarrow & -4x-\frac{4}{5}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-80}{ \color{blue}{20} }x- \frac{16}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -80x \color{red}{-16} & = & \color{red}{-100x} +15 \\\Leftrightarrow & -80x \color{red}{-16} \color{blue}{+16} \color{blue}{+100x} & = & \color{red}{-100x} +15 \color{blue}{+100x} \color{blue}{+16} \\\Leftrightarrow & -80x+100x& = & 15+16 \\\Leftrightarrow & \color{red}{20} x& = & 31 \\\Leftrightarrow & x = \frac{31}{20} & & \\ & V = \left\{ \frac{31}{20} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{2}{5})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -24x-\frac{12}{5}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-360}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -360x \color{red}{-36} & = & \color{red}{-105x} +20 \\\Leftrightarrow & -360x \color{red}{-36} \color{blue}{+36} \color{blue}{+105x} & = & \color{red}{-105x} +20 \color{blue}{+105x} \color{blue}{+36} \\\Leftrightarrow & -360x+105x& = & 20+36 \\\Leftrightarrow & \color{red}{-255} x& = & 56 \\\Leftrightarrow & x = \frac{56}{-255} & & \\\Leftrightarrow & x = \frac{-56}{255} & & \\ & V = \left\{ \frac{-56}{255} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{3}{11})& = & 5x+\frac{10}{9} \\\Leftrightarrow & 18x-\frac{18}{11}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1782}{ \color{blue}{99} }x- \frac{162}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1782x \color{red}{-162} & = & \color{red}{495x} +110 \\\Leftrightarrow & 1782x \color{red}{-162} \color{blue}{+162} \color{blue}{-495x} & = & \color{red}{495x} +110 \color{blue}{-495x} \color{blue}{+162} \\\Leftrightarrow & 1782x-495x& = & 110+162 \\\Leftrightarrow & \color{red}{1287} x& = & 272 \\\Leftrightarrow & x = \frac{272}{1287} & & \\ & V = \left\{ \frac{272}{1287} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{3}{7})& = & 7x+\frac{3}{11} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+66} & = & \color{red}{539x} +21 \\\Leftrightarrow & -462x \color{red}{+66} \color{blue}{-66} \color{blue}{-539x} & = & \color{red}{539x} +21 \color{blue}{-539x} \color{blue}{-66} \\\Leftrightarrow & -462x-539x& = & 21-66 \\\Leftrightarrow & \color{red}{-1001} x& = & -45 \\\Leftrightarrow & x = \frac{-45}{-1001} & & \\\Leftrightarrow & x = \frac{45}{1001} & & \\ & V = \left\{ \frac{45}{1001} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{5}{7})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 6x-\frac{10}{7}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{84}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 84x \color{red}{-20} & = & \color{red}{70x} +21 \\\Leftrightarrow & 84x \color{red}{-20} \color{blue}{+20} \color{blue}{-70x} & = & \color{red}{70x} +21 \color{blue}{-70x} \color{blue}{+20} \\\Leftrightarrow & 84x-70x& = & 21+20 \\\Leftrightarrow & \color{red}{14} x& = & 41 \\\Leftrightarrow & x = \frac{41}{14} & & \\ & V = \left\{ \frac{41}{14} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{2}{9})& = & -3x+\frac{7}{8} \\\Leftrightarrow & 14x-\frac{14}{9}& = & -3x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1008}{ \color{blue}{72} }x- \frac{112}{ \color{blue}{72} })& = & (\frac{-216}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1008x \color{red}{-112} & = & \color{red}{-216x} +63 \\\Leftrightarrow & 1008x \color{red}{-112} \color{blue}{+112} \color{blue}{+216x} & = & \color{red}{-216x} +63 \color{blue}{+216x} \color{blue}{+112} \\\Leftrightarrow & 1008x+216x& = & 63+112 \\\Leftrightarrow & \color{red}{1224} x& = & 175 \\\Leftrightarrow & x = \frac{175}{1224} & & \\ & V = \left\{ \frac{175}{1224} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{4}{7})& = & 9x+\frac{10}{9} \\\Leftrightarrow & 20x+\frac{16}{7}& = & 9x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x+ \frac{144}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{+144} & = & \color{red}{567x} +70 \\\Leftrightarrow & 1260x \color{red}{+144} \color{blue}{-144} \color{blue}{-567x} & = & \color{red}{567x} +70 \color{blue}{-567x} \color{blue}{-144} \\\Leftrightarrow & 1260x-567x& = & 70-144 \\\Leftrightarrow & \color{red}{693} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{693} & & \\ & V = \left\{ \frac{-74}{693} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{3}{4})& = & 8x+\frac{6}{11} \\\Leftrightarrow & -15x+\frac{15}{4}& = & 8x+\frac{6}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-660}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{352}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -660x \color{red}{+165} & = & \color{red}{352x} +24 \\\Leftrightarrow & -660x \color{red}{+165} \color{blue}{-165} \color{blue}{-352x} & = & \color{red}{352x} +24 \color{blue}{-352x} \color{blue}{-165} \\\Leftrightarrow & -660x-352x& = & 24-165 \\\Leftrightarrow & \color{red}{-1012} x& = & -141 \\\Leftrightarrow & x = \frac{-141}{-1012} & & \\\Leftrightarrow & x = \frac{141}{1012} & & \\ & V = \left\{ \frac{141}{1012} \right\} & \\\end{align}\)
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