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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{5})& = & 7x+\frac{5}{9} \\\Leftrightarrow & -20x-\frac{12}{5}& = & 7x+\frac{5}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-900}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{25}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -900x \color{red}{-108} & = & \color{red}{315x} +25 \\\Leftrightarrow & -900x \color{red}{-108} \color{blue}{+108} \color{blue}{-315x} & = & \color{red}{315x} +25 \color{blue}{-315x} \color{blue}{+108} \\\Leftrightarrow & -900x-315x& = & 25+108 \\\Leftrightarrow & \color{red}{-1215} x& = & 133 \\\Leftrightarrow & x = \frac{133}{-1215} & & \\\Leftrightarrow & x = \frac{-133}{1215} & & \\ & V = \left\{ \frac{-133}{1215} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{5}{7})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 6x-\frac{10}{7}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-50} & = & \color{red}{-175x} +42 \\\Leftrightarrow & 210x \color{red}{-50} \color{blue}{+50} \color{blue}{+175x} & = & \color{red}{-175x} +42 \color{blue}{+175x} \color{blue}{+50} \\\Leftrightarrow & 210x+175x& = & 42+50 \\\Leftrightarrow & \color{red}{385} x& = & 92 \\\Leftrightarrow & x = \frac{92}{385} & & \\ & V = \left\{ \frac{92}{385} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{4}{11})& = & 5x+\frac{8}{9} \\\Leftrightarrow & 8x-\frac{8}{11}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{792}{ \color{blue}{99} }x- \frac{72}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 792x \color{red}{-72} & = & \color{red}{495x} +88 \\\Leftrightarrow & 792x \color{red}{-72} \color{blue}{+72} \color{blue}{-495x} & = & \color{red}{495x} +88 \color{blue}{-495x} \color{blue}{+72} \\\Leftrightarrow & 792x-495x& = & 88+72 \\\Leftrightarrow & \color{red}{297} x& = & 160 \\\Leftrightarrow & x = \frac{160}{297} & & \\ & V = \left\{ \frac{160}{297} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{11})& = & -4x+\frac{3}{4} \\\Leftrightarrow & -15x+\frac{6}{11}& = & -4x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-660}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} })& = & (\frac{-176}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -660x \color{red}{+24} & = & \color{red}{-176x} +33 \\\Leftrightarrow & -660x \color{red}{+24} \color{blue}{-24} \color{blue}{+176x} & = & \color{red}{-176x} +33 \color{blue}{+176x} \color{blue}{-24} \\\Leftrightarrow & -660x+176x& = & 33-24 \\\Leftrightarrow & \color{red}{-484} x& = & 9 \\\Leftrightarrow & x = \frac{9}{-484} & & \\\Leftrightarrow & x = \frac{-9}{484} & & \\ & V = \left\{ \frac{-9}{484} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{3}{10})& = & -7x+\frac{8}{11} \\\Leftrightarrow & -6x+\frac{9}{10}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-660}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} })& = & (\frac{-770}{ \color{blue}{110} }x+ \frac{80}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -660x \color{red}{+99} & = & \color{red}{-770x} +80 \\\Leftrightarrow & -660x \color{red}{+99} \color{blue}{-99} \color{blue}{+770x} & = & \color{red}{-770x} +80 \color{blue}{+770x} \color{blue}{-99} \\\Leftrightarrow & -660x+770x& = & 80-99 \\\Leftrightarrow & \color{red}{110} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{110} & & \\ & V = \left\{ \frac{-19}{110} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{3}{5})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{-108} & = & \color{red}{-225x} +40 \\\Leftrightarrow & 540x \color{red}{-108} \color{blue}{+108} \color{blue}{+225x} & = & \color{red}{-225x} +40 \color{blue}{+225x} \color{blue}{+108} \\\Leftrightarrow & 540x+225x& = & 40+108 \\\Leftrightarrow & \color{red}{765} x& = & 148 \\\Leftrightarrow & x = \frac{148}{765} & & \\ & V = \left\{ \frac{148}{765} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{2}{7})& = & -2x+\frac{7}{10} \\\Leftrightarrow & 15x+\frac{10}{7}& = & -2x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1050}{ \color{blue}{70} }x+ \frac{100}{ \color{blue}{70} })& = & (\frac{-140}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1050x \color{red}{+100} & = & \color{red}{-140x} +49 \\\Leftrightarrow & 1050x \color{red}{+100} \color{blue}{-100} \color{blue}{+140x} & = & \color{red}{-140x} +49 \color{blue}{+140x} \color{blue}{-100} \\\Leftrightarrow & 1050x+140x& = & 49-100 \\\Leftrightarrow & \color{red}{1190} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{1190} & & \\\Leftrightarrow & x = \frac{-3}{70} & & \\ & V = \left\{ \frac{-3}{70} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{3}{8})& = & 7x+\frac{4}{7} \\\Leftrightarrow & 20x-\frac{15}{8}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1120}{ \color{blue}{56} }x- \frac{105}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{32}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1120x \color{red}{-105} & = & \color{red}{392x} +32 \\\Leftrightarrow & 1120x \color{red}{-105} \color{blue}{+105} \color{blue}{-392x} & = & \color{red}{392x} +32 \color{blue}{-392x} \color{blue}{+105} \\\Leftrightarrow & 1120x-392x& = & 32+105 \\\Leftrightarrow & \color{red}{728} x& = & 137 \\\Leftrightarrow & x = \frac{137}{728} & & \\ & V = \left\{ \frac{137}{728} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{5}{3})& = & 6x+\frac{3}{8} \\\Leftrightarrow & -25x-\frac{25}{3}& = & 6x+\frac{3}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-600}{ \color{blue}{24} }x- \frac{200}{ \color{blue}{24} })& = & (\frac{144}{ \color{blue}{24} }x+ \frac{9}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -600x \color{red}{-200} & = & \color{red}{144x} +9 \\\Leftrightarrow & -600x \color{red}{-200} \color{blue}{+200} \color{blue}{-144x} & = & \color{red}{144x} +9 \color{blue}{-144x} \color{blue}{+200} \\\Leftrightarrow & -600x-144x& = & 9+200 \\\Leftrightarrow & \color{red}{-744} x& = & 209 \\\Leftrightarrow & x = \frac{209}{-744} & & \\\Leftrightarrow & x = \frac{-209}{744} & & \\ & V = \left\{ \frac{-209}{744} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{3}{4})& = & 2x+\frac{7}{4} \\\Leftrightarrow & -25x-\frac{15}{4}& = & 2x+\frac{7}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-100}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{8}{ \color{blue}{4} }x+ \frac{7}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -100x \color{red}{-15} & = & \color{red}{8x} +7 \\\Leftrightarrow & -100x \color{red}{-15} \color{blue}{+15} \color{blue}{-8x} & = & \color{red}{8x} +7 \color{blue}{-8x} \color{blue}{+15} \\\Leftrightarrow & -100x-8x& = & 7+15 \\\Leftrightarrow & \color{red}{-108} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-108} & & \\\Leftrightarrow & x = \frac{-11}{54} & & \\ & V = \left\{ \frac{-11}{54} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{11})& = & -7x+\frac{3}{7} \\\Leftrightarrow & 20x-\frac{20}{11}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x- \frac{140}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{-140} & = & \color{red}{-539x} +33 \\\Leftrightarrow & 1540x \color{red}{-140} \color{blue}{+140} \color{blue}{+539x} & = & \color{red}{-539x} +33 \color{blue}{+539x} \color{blue}{+140} \\\Leftrightarrow & 1540x+539x& = & 33+140 \\\Leftrightarrow & \color{red}{2079} x& = & 173 \\\Leftrightarrow & x = \frac{173}{2079} & & \\ & V = \left\{ \frac{173}{2079} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{2}{7})& = & -7x+\frac{10}{9} \\\Leftrightarrow & 15x+\frac{6}{7}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{+54} & = & \color{red}{-441x} +70 \\\Leftrightarrow & 945x \color{red}{+54} \color{blue}{-54} \color{blue}{+441x} & = & \color{red}{-441x} +70 \color{blue}{+441x} \color{blue}{-54} \\\Leftrightarrow & 945x+441x& = & 70-54 \\\Leftrightarrow & \color{red}{1386} x& = & 16 \\\Leftrightarrow & x = \frac{16}{1386} & & \\\Leftrightarrow & x = \frac{8}{693} & & \\ & V = \left\{ \frac{8}{693} \right\} & \\\end{align}\)
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