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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{5}{7})& = & -9x+\frac{9}{11} \\\Leftrightarrow & -4x-\frac{10}{7}& = & -9x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-308}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -308x \color{red}{-110} & = & \color{red}{-693x} +63 \\\Leftrightarrow & -308x \color{red}{-110} \color{blue}{+110} \color{blue}{+693x} & = & \color{red}{-693x} +63 \color{blue}{+693x} \color{blue}{+110} \\\Leftrightarrow & -308x+693x& = & 63+110 \\\Leftrightarrow & \color{red}{385} x& = & 173 \\\Leftrightarrow & x = \frac{173}{385} & & \\ & V = \left\{ \frac{173}{385} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{3}{11})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -30x+\frac{18}{11}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2970}{ \color{blue}{99} }x+ \frac{162}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2970x \color{red}{+162} & = & \color{red}{-693x} +44 \\\Leftrightarrow & -2970x \color{red}{+162} \color{blue}{-162} \color{blue}{+693x} & = & \color{red}{-693x} +44 \color{blue}{+693x} \color{blue}{-162} \\\Leftrightarrow & -2970x+693x& = & 44-162 \\\Leftrightarrow & \color{red}{-2277} x& = & -118 \\\Leftrightarrow & x = \frac{-118}{-2277} & & \\\Leftrightarrow & x = \frac{118}{2277} & & \\ & V = \left\{ \frac{118}{2277} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{3}{5})& = & -9x+\frac{3}{10} \\\Leftrightarrow & 20x-\frac{12}{5}& = & -9x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{200}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 200x \color{red}{-24} & = & \color{red}{-90x} +3 \\\Leftrightarrow & 200x \color{red}{-24} \color{blue}{+24} \color{blue}{+90x} & = & \color{red}{-90x} +3 \color{blue}{+90x} \color{blue}{+24} \\\Leftrightarrow & 200x+90x& = & 3+24 \\\Leftrightarrow & \color{red}{290} x& = & 27 \\\Leftrightarrow & x = \frac{27}{290} & & \\ & V = \left\{ \frac{27}{290} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{7})& = & -7x+\frac{5}{8} \\\Leftrightarrow & -16x-\frac{20}{7}& = & -7x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-896}{ \color{blue}{56} }x- \frac{160}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -896x \color{red}{-160} & = & \color{red}{-392x} +35 \\\Leftrightarrow & -896x \color{red}{-160} \color{blue}{+160} \color{blue}{+392x} & = & \color{red}{-392x} +35 \color{blue}{+392x} \color{blue}{+160} \\\Leftrightarrow & -896x+392x& = & 35+160 \\\Leftrightarrow & \color{red}{-504} x& = & 195 \\\Leftrightarrow & x = \frac{195}{-504} & & \\\Leftrightarrow & x = \frac{-65}{168} & & \\ & V = \left\{ \frac{-65}{168} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{4}{3})& = & 2x+\frac{8}{3} \\\Leftrightarrow & 15x-\frac{20}{3}& = & 2x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{45}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{6}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 45x \color{red}{-20} & = & \color{red}{6x} +8 \\\Leftrightarrow & 45x \color{red}{-20} \color{blue}{+20} \color{blue}{-6x} & = & \color{red}{6x} +8 \color{blue}{-6x} \color{blue}{+20} \\\Leftrightarrow & 45x-6x& = & 8+20 \\\Leftrightarrow & \color{red}{39} x& = & 28 \\\Leftrightarrow & x = \frac{28}{39} & & \\ & V = \left\{ \frac{28}{39} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{3}{7})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -10x+\frac{6}{7}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{+66} & = & \color{red}{539x} +70 \\\Leftrightarrow & -770x \color{red}{+66} \color{blue}{-66} \color{blue}{-539x} & = & \color{red}{539x} +70 \color{blue}{-539x} \color{blue}{-66} \\\Leftrightarrow & -770x-539x& = & 70-66 \\\Leftrightarrow & \color{red}{-1309} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-1309} & & \\\Leftrightarrow & x = \frac{-4}{1309} & & \\ & V = \left\{ \frac{-4}{1309} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{4}{11})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -6x-\frac{12}{11}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{-60} & = & \color{red}{-385x} +22 \\\Leftrightarrow & -330x \color{red}{-60} \color{blue}{+60} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{+60} \\\Leftrightarrow & -330x+385x& = & 22+60 \\\Leftrightarrow & \color{red}{55} x& = & 82 \\\Leftrightarrow & x = \frac{82}{55} & & \\ & V = \left\{ \frac{82}{55} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{2}{3})& = & -3x+\frac{10}{7} \\\Leftrightarrow & 28x-\frac{14}{3}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{588}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 588x \color{red}{-98} & = & \color{red}{-63x} +30 \\\Leftrightarrow & 588x \color{red}{-98} \color{blue}{+98} \color{blue}{+63x} & = & \color{red}{-63x} +30 \color{blue}{+63x} \color{blue}{+98} \\\Leftrightarrow & 588x+63x& = & 30+98 \\\Leftrightarrow & \color{red}{651} x& = & 128 \\\Leftrightarrow & x = \frac{128}{651} & & \\ & V = \left\{ \frac{128}{651} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{3}{7})& = & 9x+\frac{9}{5} \\\Leftrightarrow & -8x-\frac{6}{7}& = & 9x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{-30} & = & \color{red}{315x} +63 \\\Leftrightarrow & -280x \color{red}{-30} \color{blue}{+30} \color{blue}{-315x} & = & \color{red}{315x} +63 \color{blue}{-315x} \color{blue}{+30} \\\Leftrightarrow & -280x-315x& = & 63+30 \\\Leftrightarrow & \color{red}{-595} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-595} & & \\\Leftrightarrow & x = \frac{-93}{595} & & \\ & V = \left\{ \frac{-93}{595} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{4}{3})& = & 7x+\frac{7}{6} \\\Leftrightarrow & 8x-\frac{8}{3}& = & 7x+\frac{7}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{48}{ \color{blue}{6} }x- \frac{16}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 48x \color{red}{-16} & = & \color{red}{42x} +7 \\\Leftrightarrow & 48x \color{red}{-16} \color{blue}{+16} \color{blue}{-42x} & = & \color{red}{42x} +7 \color{blue}{-42x} \color{blue}{+16} \\\Leftrightarrow & 48x-42x& = & 7+16 \\\Leftrightarrow & \color{red}{6} x& = & 23 \\\Leftrightarrow & x = \frac{23}{6} & & \\ & V = \left\{ \frac{23}{6} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-24} & = & \color{red}{50x} +45 \\\Leftrightarrow & 120x \color{red}{-24} \color{blue}{+24} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{+24} \\\Leftrightarrow & 120x-50x& = & 45+24 \\\Leftrightarrow & \color{red}{70} x& = & 69 \\\Leftrightarrow & x = \frac{69}{70} & & \\ & V = \left\{ \frac{69}{70} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{4}{11})& = & 3x+\frac{4}{7} \\\Leftrightarrow & 35x-\frac{28}{11}& = & 3x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2695}{ \color{blue}{77} }x- \frac{196}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2695x \color{red}{-196} & = & \color{red}{231x} +44 \\\Leftrightarrow & 2695x \color{red}{-196} \color{blue}{+196} \color{blue}{-231x} & = & \color{red}{231x} +44 \color{blue}{-231x} \color{blue}{+196} \\\Leftrightarrow & 2695x-231x& = & 44+196 \\\Leftrightarrow & \color{red}{2464} x& = & 240 \\\Leftrightarrow & x = \frac{240}{2464} & & \\\Leftrightarrow & x = \frac{15}{154} & & \\ & V = \left\{ \frac{15}{154} \right\} & \\\end{align}\)
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