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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{1}{2})& = & 7x+\frac{7}{3} \\\Leftrightarrow & 20x-\frac{5}{2}& = & 7x+\frac{7}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x- \frac{15}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{14}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{-15} & = & \color{red}{42x} +14 \\\Leftrightarrow & 120x \color{red}{-15} \color{blue}{+15} \color{blue}{-42x} & = & \color{red}{42x} +14 \color{blue}{-42x} \color{blue}{+15} \\\Leftrightarrow & 120x-42x& = & 14+15 \\\Leftrightarrow & \color{red}{78} x& = & 29 \\\Leftrightarrow & x = \frac{29}{78} & & \\ & V = \left\{ \frac{29}{78} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{4}{7})& = & 9x+\frac{5}{2} \\\Leftrightarrow & -8x-\frac{8}{7}& = & 9x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-112}{ \color{blue}{14} }x- \frac{16}{ \color{blue}{14} })& = & (\frac{126}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -112x \color{red}{-16} & = & \color{red}{126x} +35 \\\Leftrightarrow & -112x \color{red}{-16} \color{blue}{+16} \color{blue}{-126x} & = & \color{red}{126x} +35 \color{blue}{-126x} \color{blue}{+16} \\\Leftrightarrow & -112x-126x& = & 35+16 \\\Leftrightarrow & \color{red}{-238} x& = & 51 \\\Leftrightarrow & x = \frac{51}{-238} & & \\\Leftrightarrow & x = \frac{-3}{14} & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{3}{8})& = & -8x+\frac{2}{7} \\\Leftrightarrow & -15x-\frac{15}{8}& = & -8x+\frac{2}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-840}{ \color{blue}{56} }x- \frac{105}{ \color{blue}{56} })& = & (\frac{-448}{ \color{blue}{56} }x+ \frac{16}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -840x \color{red}{-105} & = & \color{red}{-448x} +16 \\\Leftrightarrow & -840x \color{red}{-105} \color{blue}{+105} \color{blue}{+448x} & = & \color{red}{-448x} +16 \color{blue}{+448x} \color{blue}{+105} \\\Leftrightarrow & -840x+448x& = & 16+105 \\\Leftrightarrow & \color{red}{-392} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-392} & & \\\Leftrightarrow & x = \frac{-121}{392} & & \\ & V = \left\{ \frac{-121}{392} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{3}{4})& = & -9x+\frac{8}{5} \\\Leftrightarrow & 10x+\frac{15}{4}& = & -9x+\frac{8}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{200}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{-180}{ \color{blue}{20} }x+ \frac{32}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 200x \color{red}{+75} & = & \color{red}{-180x} +32 \\\Leftrightarrow & 200x \color{red}{+75} \color{blue}{-75} \color{blue}{+180x} & = & \color{red}{-180x} +32 \color{blue}{+180x} \color{blue}{-75} \\\Leftrightarrow & 200x+180x& = & 32-75 \\\Leftrightarrow & \color{red}{380} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{380} & & \\ & V = \left\{ \frac{-43}{380} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{4}{9})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 10x+\frac{8}{9}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{450}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} })& = & (\frac{-135}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 450x \color{red}{+40} & = & \color{red}{-135x} +54 \\\Leftrightarrow & 450x \color{red}{+40} \color{blue}{-40} \color{blue}{+135x} & = & \color{red}{-135x} +54 \color{blue}{+135x} \color{blue}{-40} \\\Leftrightarrow & 450x+135x& = & 54-40 \\\Leftrightarrow & \color{red}{585} x& = & 14 \\\Leftrightarrow & x = \frac{14}{585} & & \\ & V = \left\{ \frac{14}{585} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{3}{11})& = & 3x+\frac{4}{11} \\\Leftrightarrow & -20x-\frac{15}{11}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-220}{ \color{blue}{11} }x- \frac{15}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -220x \color{red}{-15} & = & \color{red}{33x} +4 \\\Leftrightarrow & -220x \color{red}{-15} \color{blue}{+15} \color{blue}{-33x} & = & \color{red}{33x} +4 \color{blue}{-33x} \color{blue}{+15} \\\Leftrightarrow & -220x-33x& = & 4+15 \\\Leftrightarrow & \color{red}{-253} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-253} & & \\\Leftrightarrow & x = \frac{-19}{253} & & \\ & V = \left\{ \frac{-19}{253} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{4}{9})& = & 3x+\frac{2}{11} \\\Leftrightarrow & -28x-\frac{28}{9}& = & 3x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2772}{ \color{blue}{99} }x- \frac{308}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2772x \color{red}{-308} & = & \color{red}{297x} +18 \\\Leftrightarrow & -2772x \color{red}{-308} \color{blue}{+308} \color{blue}{-297x} & = & \color{red}{297x} +18 \color{blue}{-297x} \color{blue}{+308} \\\Leftrightarrow & -2772x-297x& = & 18+308 \\\Leftrightarrow & \color{red}{-3069} x& = & 326 \\\Leftrightarrow & x = \frac{326}{-3069} & & \\\Leftrightarrow & x = \frac{-326}{3069} & & \\ & V = \left\{ \frac{-326}{3069} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{2}{7})& = & 5x+\frac{5}{6} \\\Leftrightarrow & -9x-\frac{6}{7}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-378}{ \color{blue}{42} }x- \frac{36}{ \color{blue}{42} })& = & (\frac{210}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -378x \color{red}{-36} & = & \color{red}{210x} +35 \\\Leftrightarrow & -378x \color{red}{-36} \color{blue}{+36} \color{blue}{-210x} & = & \color{red}{210x} +35 \color{blue}{-210x} \color{blue}{+36} \\\Leftrightarrow & -378x-210x& = & 35+36 \\\Leftrightarrow & \color{red}{-588} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-588} & & \\\Leftrightarrow & x = \frac{-71}{588} & & \\ & V = \left\{ \frac{-71}{588} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{2}{9})& = & -5x+\frac{7}{5} \\\Leftrightarrow & -4x-\frac{4}{9}& = & -5x+\frac{7}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-180}{ \color{blue}{45} }x- \frac{20}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{63}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -180x \color{red}{-20} & = & \color{red}{-225x} +63 \\\Leftrightarrow & -180x \color{red}{-20} \color{blue}{+20} \color{blue}{+225x} & = & \color{red}{-225x} +63 \color{blue}{+225x} \color{blue}{+20} \\\Leftrightarrow & -180x+225x& = & 63+20 \\\Leftrightarrow & \color{red}{45} x& = & 83 \\\Leftrightarrow & x = \frac{83}{45} & & \\ & V = \left\{ \frac{83}{45} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{5}{4})& = & -5x+\frac{10}{11} \\\Leftrightarrow & -12x+\frac{15}{4}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-528}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{40}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -528x \color{red}{+165} & = & \color{red}{-220x} +40 \\\Leftrightarrow & -528x \color{red}{+165} \color{blue}{-165} \color{blue}{+220x} & = & \color{red}{-220x} +40 \color{blue}{+220x} \color{blue}{-165} \\\Leftrightarrow & -528x+220x& = & 40-165 \\\Leftrightarrow & \color{red}{-308} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{-308} & & \\\Leftrightarrow & x = \frac{125}{308} & & \\ & V = \left\{ \frac{125}{308} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{3}{4})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -10x-\frac{15}{4}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-280}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{36}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -280x \color{red}{-105} & = & \color{red}{-196x} +36 \\\Leftrightarrow & -280x \color{red}{-105} \color{blue}{+105} \color{blue}{+196x} & = & \color{red}{-196x} +36 \color{blue}{+196x} \color{blue}{+105} \\\Leftrightarrow & -280x+196x& = & 36+105 \\\Leftrightarrow & \color{red}{-84} x& = & 141 \\\Leftrightarrow & x = \frac{141}{-84} & & \\\Leftrightarrow & x = \frac{-47}{28} & & \\ & V = \left\{ \frac{-47}{28} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{4}{11})& = & 3x+\frac{7}{8} \\\Leftrightarrow & 10x-\frac{8}{11}& = & 3x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{880}{ \color{blue}{88} }x- \frac{64}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 880x \color{red}{-64} & = & \color{red}{264x} +77 \\\Leftrightarrow & 880x \color{red}{-64} \color{blue}{+64} \color{blue}{-264x} & = & \color{red}{264x} +77 \color{blue}{-264x} \color{blue}{+64} \\\Leftrightarrow & 880x-264x& = & 77+64 \\\Leftrightarrow & \color{red}{616} x& = & 141 \\\Leftrightarrow & x = \frac{141}{616} & & \\ & V = \left\{ \frac{141}{616} \right\} & \\\end{align}\)
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