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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{5}{9})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 8x-\frac{10}{9}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{70}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-70} & = & \color{red}{441x} +90 \\\Leftrightarrow & 504x \color{red}{-70} \color{blue}{+70} \color{blue}{-441x} & = & \color{red}{441x} +90 \color{blue}{-441x} \color{blue}{+70} \\\Leftrightarrow & 504x-441x& = & 90+70 \\\Leftrightarrow & \color{red}{63} x& = & 160 \\\Leftrightarrow & x = \frac{160}{63} & & \\ & V = \left\{ \frac{160}{63} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{5}{7})& = & -3x+\frac{6}{5} \\\Leftrightarrow & -18x-\frac{30}{7}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{-150} & = & \color{red}{-105x} +42 \\\Leftrightarrow & -630x \color{red}{-150} \color{blue}{+150} \color{blue}{+105x} & = & \color{red}{-105x} +42 \color{blue}{+105x} \color{blue}{+150} \\\Leftrightarrow & -630x+105x& = & 42+150 \\\Leftrightarrow & \color{red}{-525} x& = & 192 \\\Leftrightarrow & x = \frac{192}{-525} & & \\\Leftrightarrow & x = \frac{-64}{175} & & \\ & V = \left\{ \frac{-64}{175} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{2}{3})& = & -3x+\frac{2}{7} \\\Leftrightarrow & -14x-\frac{14}{3}& = & -3x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-294}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -294x \color{red}{-98} & = & \color{red}{-63x} +6 \\\Leftrightarrow & -294x \color{red}{-98} \color{blue}{+98} \color{blue}{+63x} & = & \color{red}{-63x} +6 \color{blue}{+63x} \color{blue}{+98} \\\Leftrightarrow & -294x+63x& = & 6+98 \\\Leftrightarrow & \color{red}{-231} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-231} & & \\\Leftrightarrow & x = \frac{-104}{231} & & \\ & V = \left\{ \frac{-104}{231} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{5}{4})& = & 6x+\frac{2}{3} \\\Leftrightarrow & 25x+\frac{25}{4}& = & 6x+\frac{2}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{300}{ \color{blue}{12} }x+ \frac{75}{ \color{blue}{12} })& = & (\frac{72}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 300x \color{red}{+75} & = & \color{red}{72x} +8 \\\Leftrightarrow & 300x \color{red}{+75} \color{blue}{-75} \color{blue}{-72x} & = & \color{red}{72x} +8 \color{blue}{-72x} \color{blue}{-75} \\\Leftrightarrow & 300x-72x& = & 8-75 \\\Leftrightarrow & \color{red}{228} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{228} & & \\ & V = \left\{ \frac{-67}{228} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{3}{5})& = & -5x+\frac{7}{8} \\\Leftrightarrow & 24x+\frac{18}{5}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{960}{ \color{blue}{40} }x+ \frac{144}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 960x \color{red}{+144} & = & \color{red}{-200x} +35 \\\Leftrightarrow & 960x \color{red}{+144} \color{blue}{-144} \color{blue}{+200x} & = & \color{red}{-200x} +35 \color{blue}{+200x} \color{blue}{-144} \\\Leftrightarrow & 960x+200x& = & 35-144 \\\Leftrightarrow & \color{red}{1160} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{1160} & & \\ & V = \left\{ \frac{-109}{1160} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{7})& = & -3x+\frac{4}{7} \\\Leftrightarrow & 20x+\frac{20}{7}& = & -3x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{140}{ \color{blue}{7} }x+ \frac{20}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 140x \color{red}{+20} & = & \color{red}{-21x} +4 \\\Leftrightarrow & 140x \color{red}{+20} \color{blue}{-20} \color{blue}{+21x} & = & \color{red}{-21x} +4 \color{blue}{+21x} \color{blue}{-20} \\\Leftrightarrow & 140x+21x& = & 4-20 \\\Leftrightarrow & \color{red}{161} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{161} & & \\ & V = \left\{ \frac{-16}{161} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{3}{4})& = & 3x+\frac{4}{11} \\\Leftrightarrow & -14x-\frac{21}{4}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-616}{ \color{blue}{44} }x- \frac{231}{ \color{blue}{44} })& = & (\frac{132}{ \color{blue}{44} }x+ \frac{16}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -616x \color{red}{-231} & = & \color{red}{132x} +16 \\\Leftrightarrow & -616x \color{red}{-231} \color{blue}{+231} \color{blue}{-132x} & = & \color{red}{132x} +16 \color{blue}{-132x} \color{blue}{+231} \\\Leftrightarrow & -616x-132x& = & 16+231 \\\Leftrightarrow & \color{red}{-748} x& = & 247 \\\Leftrightarrow & x = \frac{247}{-748} & & \\\Leftrightarrow & x = \frac{-247}{748} & & \\ & V = \left\{ \frac{-247}{748} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{5}{11})& = & -5x+\frac{10}{9} \\\Leftrightarrow & -14x+\frac{35}{11}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1386}{ \color{blue}{99} }x+ \frac{315}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1386x \color{red}{+315} & = & \color{red}{-495x} +110 \\\Leftrightarrow & -1386x \color{red}{+315} \color{blue}{-315} \color{blue}{+495x} & = & \color{red}{-495x} +110 \color{blue}{+495x} \color{blue}{-315} \\\Leftrightarrow & -1386x+495x& = & 110-315 \\\Leftrightarrow & \color{red}{-891} x& = & -205 \\\Leftrightarrow & x = \frac{-205}{-891} & & \\\Leftrightarrow & x = \frac{205}{891} & & \\ & V = \left\{ \frac{205}{891} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{5}{7})& = & 9x+\frac{3}{7} \\\Leftrightarrow & 4x+\frac{10}{7}& = & 9x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{28}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{63}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 28x \color{red}{+10} & = & \color{red}{63x} +3 \\\Leftrightarrow & 28x \color{red}{+10} \color{blue}{-10} \color{blue}{-63x} & = & \color{red}{63x} +3 \color{blue}{-63x} \color{blue}{-10} \\\Leftrightarrow & 28x-63x& = & 3-10 \\\Leftrightarrow & \color{red}{-35} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-35} & & \\\Leftrightarrow & x = \frac{1}{5} & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{3})& = & -7x+\frac{5}{8} \\\Leftrightarrow & 15x-\frac{20}{3}& = & -7x+\frac{5}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{360}{ \color{blue}{24} }x- \frac{160}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 360x \color{red}{-160} & = & \color{red}{-168x} +15 \\\Leftrightarrow & 360x \color{red}{-160} \color{blue}{+160} \color{blue}{+168x} & = & \color{red}{-168x} +15 \color{blue}{+168x} \color{blue}{+160} \\\Leftrightarrow & 360x+168x& = & 15+160 \\\Leftrightarrow & \color{red}{528} x& = & 175 \\\Leftrightarrow & x = \frac{175}{528} & & \\ & V = \left\{ \frac{175}{528} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{3}{2})& = & 5x+\frac{7}{5} \\\Leftrightarrow & 6x+\frac{9}{2}& = & 5x+\frac{7}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{14}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{+45} & = & \color{red}{50x} +14 \\\Leftrightarrow & 60x \color{red}{+45} \color{blue}{-45} \color{blue}{-50x} & = & \color{red}{50x} +14 \color{blue}{-50x} \color{blue}{-45} \\\Leftrightarrow & 60x-50x& = & 14-45 \\\Leftrightarrow & \color{red}{10} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{10} & & \\ & V = \left\{ \frac{-31}{10} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{2}{3})& = & 3x+\frac{7}{8} \\\Leftrightarrow & 28x-\frac{14}{3}& = & 3x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{672}{ \color{blue}{24} }x- \frac{112}{ \color{blue}{24} })& = & (\frac{72}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 672x \color{red}{-112} & = & \color{red}{72x} +21 \\\Leftrightarrow & 672x \color{red}{-112} \color{blue}{+112} \color{blue}{-72x} & = & \color{red}{72x} +21 \color{blue}{-72x} \color{blue}{+112} \\\Leftrightarrow & 672x-72x& = & 21+112 \\\Leftrightarrow & \color{red}{600} x& = & 133 \\\Leftrightarrow & x = \frac{133}{600} & & \\ & V = \left\{ \frac{133}{600} \right\} & \\\end{align}\)
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