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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{5}{7})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -18x+\frac{30}{7}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-252}{ \color{blue}{14} }x+ \frac{60}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -252x \color{red}{+60} & = & \color{red}{-98x} +21 \\\Leftrightarrow & -252x \color{red}{+60} \color{blue}{-60} \color{blue}{+98x} & = & \color{red}{-98x} +21 \color{blue}{+98x} \color{blue}{-60} \\\Leftrightarrow & -252x+98x& = & 21-60 \\\Leftrightarrow & \color{red}{-154} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{-154} & & \\\Leftrightarrow & x = \frac{39}{154} & & \\ & V = \left\{ \frac{39}{154} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{2}{3})& = & -5x+\frac{3}{11} \\\Leftrightarrow & 12x+\frac{8}{3}& = & -5x+\frac{3}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{9}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{+88} & = & \color{red}{-165x} +9 \\\Leftrightarrow & 396x \color{red}{+88} \color{blue}{-88} \color{blue}{+165x} & = & \color{red}{-165x} +9 \color{blue}{+165x} \color{blue}{-88} \\\Leftrightarrow & 396x+165x& = & 9-88 \\\Leftrightarrow & \color{red}{561} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{561} & & \\ & V = \left\{ \frac{-79}{561} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{11})& = & 7x+\frac{9}{5} \\\Leftrightarrow & -30x-\frac{30}{11}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x- \frac{150}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{-150} & = & \color{red}{385x} +99 \\\Leftrightarrow & -1650x \color{red}{-150} \color{blue}{+150} \color{blue}{-385x} & = & \color{red}{385x} +99 \color{blue}{-385x} \color{blue}{+150} \\\Leftrightarrow & -1650x-385x& = & 99+150 \\\Leftrightarrow & \color{red}{-2035} x& = & 249 \\\Leftrightarrow & x = \frac{249}{-2035} & & \\\Leftrightarrow & x = \frac{-249}{2035} & & \\ & V = \left\{ \frac{-249}{2035} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{2}{7})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 10x-\frac{4}{7}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{140}{ \color{blue}{14} }x- \frac{8}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 140x \color{red}{-8} & = & \color{red}{98x} +63 \\\Leftrightarrow & 140x \color{red}{-8} \color{blue}{+8} \color{blue}{-98x} & = & \color{red}{98x} +63 \color{blue}{-98x} \color{blue}{+8} \\\Leftrightarrow & 140x-98x& = & 63+8 \\\Leftrightarrow & \color{red}{42} x& = & 71 \\\Leftrightarrow & x = \frac{71}{42} & & \\ & V = \left\{ \frac{71}{42} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{3}{11})& = & 7x+\frac{3}{8} \\\Leftrightarrow & 30x-\frac{18}{11}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2640}{ \color{blue}{88} }x- \frac{144}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2640x \color{red}{-144} & = & \color{red}{616x} +33 \\\Leftrightarrow & 2640x \color{red}{-144} \color{blue}{+144} \color{blue}{-616x} & = & \color{red}{616x} +33 \color{blue}{-616x} \color{blue}{+144} \\\Leftrightarrow & 2640x-616x& = & 33+144 \\\Leftrightarrow & \color{red}{2024} x& = & 177 \\\Leftrightarrow & x = \frac{177}{2024} & & \\ & V = \left\{ \frac{177}{2024} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{2}{9})& = & -7x+\frac{7}{2} \\\Leftrightarrow & -6x-\frac{4}{9}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-108}{ \color{blue}{18} }x- \frac{8}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{63}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -108x \color{red}{-8} & = & \color{red}{-126x} +63 \\\Leftrightarrow & -108x \color{red}{-8} \color{blue}{+8} \color{blue}{+126x} & = & \color{red}{-126x} +63 \color{blue}{+126x} \color{blue}{+8} \\\Leftrightarrow & -108x+126x& = & 63+8 \\\Leftrightarrow & \color{red}{18} x& = & 71 \\\Leftrightarrow & x = \frac{71}{18} & & \\ & V = \left\{ \frac{71}{18} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{3}{5})& = & -9x+\frac{8}{11} \\\Leftrightarrow & -8x-\frac{12}{5}& = & -9x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{-132} & = & \color{red}{-495x} +40 \\\Leftrightarrow & -440x \color{red}{-132} \color{blue}{+132} \color{blue}{+495x} & = & \color{red}{-495x} +40 \color{blue}{+495x} \color{blue}{+132} \\\Leftrightarrow & -440x+495x& = & 40+132 \\\Leftrightarrow & \color{red}{55} x& = & 172 \\\Leftrightarrow & x = \frac{172}{55} & & \\ & V = \left\{ \frac{172}{55} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{2}{3})& = & -7x+\frac{5}{12} \\\Leftrightarrow & -10x-\frac{4}{3}& = & -7x+\frac{5}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-120}{ \color{blue}{12} }x- \frac{16}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -120x \color{red}{-16} & = & \color{red}{-84x} +5 \\\Leftrightarrow & -120x \color{red}{-16} \color{blue}{+16} \color{blue}{+84x} & = & \color{red}{-84x} +5 \color{blue}{+84x} \color{blue}{+16} \\\Leftrightarrow & -120x+84x& = & 5+16 \\\Leftrightarrow & \color{red}{-36} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-36} & & \\\Leftrightarrow & x = \frac{-7}{12} & & \\ & V = \left\{ \frac{-7}{12} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{3}{7})& = & 9x+\frac{8}{9} \\\Leftrightarrow & 20x-\frac{12}{7}& = & 9x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x- \frac{108}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{-108} & = & \color{red}{567x} +56 \\\Leftrightarrow & 1260x \color{red}{-108} \color{blue}{+108} \color{blue}{-567x} & = & \color{red}{567x} +56 \color{blue}{-567x} \color{blue}{+108} \\\Leftrightarrow & 1260x-567x& = & 56+108 \\\Leftrightarrow & \color{red}{693} x& = & 164 \\\Leftrightarrow & x = \frac{164}{693} & & \\ & V = \left\{ \frac{164}{693} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{4}{3})& = & 8x+\frac{9}{11} \\\Leftrightarrow & -15x+\frac{20}{3}& = & 8x+\frac{9}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-495}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{264}{ \color{blue}{33} }x+ \frac{27}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -495x \color{red}{+220} & = & \color{red}{264x} +27 \\\Leftrightarrow & -495x \color{red}{+220} \color{blue}{-220} \color{blue}{-264x} & = & \color{red}{264x} +27 \color{blue}{-264x} \color{blue}{-220} \\\Leftrightarrow & -495x-264x& = & 27-220 \\\Leftrightarrow & \color{red}{-759} x& = & -193 \\\Leftrightarrow & x = \frac{-193}{-759} & & \\\Leftrightarrow & x = \frac{193}{759} & & \\ & V = \left\{ \frac{193}{759} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{4}{5})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -6x-\frac{12}{5}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{-36} & = & \color{red}{-105x} +50 \\\Leftrightarrow & -90x \color{red}{-36} \color{blue}{+36} \color{blue}{+105x} & = & \color{red}{-105x} +50 \color{blue}{+105x} \color{blue}{+36} \\\Leftrightarrow & -90x+105x& = & 50+36 \\\Leftrightarrow & \color{red}{15} x& = & 86 \\\Leftrightarrow & x = \frac{86}{15} & & \\ & V = \left\{ \frac{86}{15} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{4}{11})& = & 6x+\frac{4}{3} \\\Leftrightarrow & -35x-\frac{28}{11}& = & 6x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x- \frac{84}{ \color{blue}{33} })& = & (\frac{198}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{-84} & = & \color{red}{198x} +44 \\\Leftrightarrow & -1155x \color{red}{-84} \color{blue}{+84} \color{blue}{-198x} & = & \color{red}{198x} +44 \color{blue}{-198x} \color{blue}{+84} \\\Leftrightarrow & -1155x-198x& = & 44+84 \\\Leftrightarrow & \color{red}{-1353} x& = & 128 \\\Leftrightarrow & x = \frac{128}{-1353} & & \\\Leftrightarrow & x = \frac{-128}{1353} & & \\ & V = \left\{ \frac{-128}{1353} \right\} & \\\end{align}\)
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