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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{5}{7})& = & -7x+\frac{7}{10} \\\Leftrightarrow & -6x-\frac{10}{7}& = & -7x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-420}{ \color{blue}{70} }x- \frac{100}{ \color{blue}{70} })& = & (\frac{-490}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -420x \color{red}{-100} & = & \color{red}{-490x} +49 \\\Leftrightarrow & -420x \color{red}{-100} \color{blue}{+100} \color{blue}{+490x} & = & \color{red}{-490x} +49 \color{blue}{+490x} \color{blue}{+100} \\\Leftrightarrow & -420x+490x& = & 49+100 \\\Leftrightarrow & \color{red}{70} x& = & 149 \\\Leftrightarrow & x = \frac{149}{70} & & \\ & V = \left\{ \frac{149}{70} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{3}{8})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -14x+\frac{21}{8}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-560}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -560x \color{red}{+105} & = & \color{red}{-200x} +48 \\\Leftrightarrow & -560x \color{red}{+105} \color{blue}{-105} \color{blue}{+200x} & = & \color{red}{-200x} +48 \color{blue}{+200x} \color{blue}{-105} \\\Leftrightarrow & -560x+200x& = & 48-105 \\\Leftrightarrow & \color{red}{-360} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{-360} & & \\\Leftrightarrow & x = \frac{19}{120} & & \\ & V = \left\{ \frac{19}{120} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{4}{3})& = & -8x+\frac{8}{3} \\\Leftrightarrow & 35x+\frac{28}{3}& = & -8x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{105}{ \color{blue}{3} }x+ \frac{28}{ \color{blue}{3} })& = & (\frac{-24}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 105x \color{red}{+28} & = & \color{red}{-24x} +8 \\\Leftrightarrow & 105x \color{red}{+28} \color{blue}{-28} \color{blue}{+24x} & = & \color{red}{-24x} +8 \color{blue}{+24x} \color{blue}{-28} \\\Leftrightarrow & 105x+24x& = & 8-28 \\\Leftrightarrow & \color{red}{129} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{129} & & \\ & V = \left\{ \frac{-20}{129} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{5}{11})& = & 3x+\frac{9}{11} \\\Leftrightarrow & -14x+\frac{35}{11}& = & 3x+\frac{9}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-154}{ \color{blue}{11} }x+ \frac{35}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -154x \color{red}{+35} & = & \color{red}{33x} +9 \\\Leftrightarrow & -154x \color{red}{+35} \color{blue}{-35} \color{blue}{-33x} & = & \color{red}{33x} +9 \color{blue}{-33x} \color{blue}{-35} \\\Leftrightarrow & -154x-33x& = & 9-35 \\\Leftrightarrow & \color{red}{-187} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-187} & & \\\Leftrightarrow & x = \frac{26}{187} & & \\ & V = \left\{ \frac{26}{187} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{3}{11})& = & -5x+\frac{5}{2} \\\Leftrightarrow & -12x+\frac{18}{11}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-264}{ \color{blue}{22} }x+ \frac{36}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -264x \color{red}{+36} & = & \color{red}{-110x} +55 \\\Leftrightarrow & -264x \color{red}{+36} \color{blue}{-36} \color{blue}{+110x} & = & \color{red}{-110x} +55 \color{blue}{+110x} \color{blue}{-36} \\\Leftrightarrow & -264x+110x& = & 55-36 \\\Leftrightarrow & \color{red}{-154} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-154} & & \\\Leftrightarrow & x = \frac{-19}{154} & & \\ & V = \left\{ \frac{-19}{154} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{5}{3})& = & -8x+\frac{6}{7} \\\Leftrightarrow & 15x-\frac{25}{3}& = & -8x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x- \frac{175}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{-175} & = & \color{red}{-168x} +18 \\\Leftrightarrow & 315x \color{red}{-175} \color{blue}{+175} \color{blue}{+168x} & = & \color{red}{-168x} +18 \color{blue}{+168x} \color{blue}{+175} \\\Leftrightarrow & 315x+168x& = & 18+175 \\\Leftrightarrow & \color{red}{483} x& = & 193 \\\Leftrightarrow & x = \frac{193}{483} & & \\ & V = \left\{ \frac{193}{483} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{4}{11})& = & -7x+\frac{7}{2} \\\Leftrightarrow & -6x-\frac{8}{11}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-132}{ \color{blue}{22} }x- \frac{16}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -132x \color{red}{-16} & = & \color{red}{-154x} +77 \\\Leftrightarrow & -132x \color{red}{-16} \color{blue}{+16} \color{blue}{+154x} & = & \color{red}{-154x} +77 \color{blue}{+154x} \color{blue}{+16} \\\Leftrightarrow & -132x+154x& = & 77+16 \\\Leftrightarrow & \color{red}{22} x& = & 93 \\\Leftrightarrow & x = \frac{93}{22} & & \\ & V = \left\{ \frac{93}{22} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{5}{3})& = & 9x+\frac{9}{11} \\\Leftrightarrow & -35x+\frac{35}{3}& = & 9x+\frac{9}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x+ \frac{385}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{27}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{+385} & = & \color{red}{297x} +27 \\\Leftrightarrow & -1155x \color{red}{+385} \color{blue}{-385} \color{blue}{-297x} & = & \color{red}{297x} +27 \color{blue}{-297x} \color{blue}{-385} \\\Leftrightarrow & -1155x-297x& = & 27-385 \\\Leftrightarrow & \color{red}{-1452} x& = & -358 \\\Leftrightarrow & x = \frac{-358}{-1452} & & \\\Leftrightarrow & x = \frac{179}{726} & & \\ & V = \left\{ \frac{179}{726} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{3}{11})& = & 6x+\frac{8}{5} \\\Leftrightarrow & -18x+\frac{18}{11}& = & 6x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x+ \frac{90}{ \color{blue}{55} })& = & (\frac{330}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{+90} & = & \color{red}{330x} +88 \\\Leftrightarrow & -990x \color{red}{+90} \color{blue}{-90} \color{blue}{-330x} & = & \color{red}{330x} +88 \color{blue}{-330x} \color{blue}{-90} \\\Leftrightarrow & -990x-330x& = & 88-90 \\\Leftrightarrow & \color{red}{-1320} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-1320} & & \\\Leftrightarrow & x = \frac{1}{660} & & \\ & V = \left\{ \frac{1}{660} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{9})& = & -9x+\frac{6}{5} \\\Leftrightarrow & 4x-\frac{4}{9}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{180}{ \color{blue}{45} }x- \frac{20}{ \color{blue}{45} })& = & (\frac{-405}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 180x \color{red}{-20} & = & \color{red}{-405x} +54 \\\Leftrightarrow & 180x \color{red}{-20} \color{blue}{+20} \color{blue}{+405x} & = & \color{red}{-405x} +54 \color{blue}{+405x} \color{blue}{+20} \\\Leftrightarrow & 180x+405x& = & 54+20 \\\Leftrightarrow & \color{red}{585} x& = & 74 \\\Leftrightarrow & x = \frac{74}{585} & & \\ & V = \left\{ \frac{74}{585} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{1}{2})& = & 4x+\frac{7}{3} \\\Leftrightarrow & 15x-\frac{5}{2}& = & 4x+\frac{7}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{90}{ \color{blue}{6} }x- \frac{15}{ \color{blue}{6} })& = & (\frac{24}{ \color{blue}{6} }x+ \frac{14}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 90x \color{red}{-15} & = & \color{red}{24x} +14 \\\Leftrightarrow & 90x \color{red}{-15} \color{blue}{+15} \color{blue}{-24x} & = & \color{red}{24x} +14 \color{blue}{-24x} \color{blue}{+15} \\\Leftrightarrow & 90x-24x& = & 14+15 \\\Leftrightarrow & \color{red}{66} x& = & 29 \\\Leftrightarrow & x = \frac{29}{66} & & \\ & V = \left\{ \frac{29}{66} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 18x+\frac{24}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{90}{ \color{blue}{5} }x+ \frac{24}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 90x \color{red}{+24} & = & \color{red}{25x} +6 \\\Leftrightarrow & 90x \color{red}{+24} \color{blue}{-24} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{-24} \\\Leftrightarrow & 90x-25x& = & 6-24 \\\Leftrightarrow & \color{red}{65} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{65} & & \\ & V = \left\{ \frac{-18}{65} \right\} & \\\end{align}\)
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