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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{2}{7})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 12x+\frac{6}{7}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{336}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 336x \color{red}{+24} & = & \color{red}{-140x} +63 \\\Leftrightarrow & 336x \color{red}{+24} \color{blue}{-24} \color{blue}{+140x} & = & \color{red}{-140x} +63 \color{blue}{+140x} \color{blue}{-24} \\\Leftrightarrow & 336x+140x& = & 63-24 \\\Leftrightarrow & \color{red}{476} x& = & 39 \\\Leftrightarrow & x = \frac{39}{476} & & \\ & V = \left\{ \frac{39}{476} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{4})& = & -2x+\frac{4}{5} \\\Leftrightarrow & 9x-\frac{15}{4}& = & -2x+\frac{4}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{180}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-40}{ \color{blue}{20} }x+ \frac{16}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 180x \color{red}{-75} & = & \color{red}{-40x} +16 \\\Leftrightarrow & 180x \color{red}{-75} \color{blue}{+75} \color{blue}{+40x} & = & \color{red}{-40x} +16 \color{blue}{+40x} \color{blue}{+75} \\\Leftrightarrow & 180x+40x& = & 16+75 \\\Leftrightarrow & \color{red}{220} x& = & 91 \\\Leftrightarrow & x = \frac{91}{220} & & \\ & V = \left\{ \frac{91}{220} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{2}{9})& = & 3x+\frac{3}{11} \\\Leftrightarrow & -14x+\frac{14}{9}& = & 3x+\frac{3}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1386}{ \color{blue}{99} }x+ \frac{154}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{27}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1386x \color{red}{+154} & = & \color{red}{297x} +27 \\\Leftrightarrow & -1386x \color{red}{+154} \color{blue}{-154} \color{blue}{-297x} & = & \color{red}{297x} +27 \color{blue}{-297x} \color{blue}{-154} \\\Leftrightarrow & -1386x-297x& = & 27-154 \\\Leftrightarrow & \color{red}{-1683} x& = & -127 \\\Leftrightarrow & x = \frac{-127}{-1683} & & \\\Leftrightarrow & x = \frac{127}{1683} & & \\ & V = \left\{ \frac{127}{1683} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{4}{7})& = & 3x+\frac{3}{2} \\\Leftrightarrow & -8x-\frac{16}{7}& = & 3x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-112}{ \color{blue}{14} }x- \frac{32}{ \color{blue}{14} })& = & (\frac{42}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -112x \color{red}{-32} & = & \color{red}{42x} +21 \\\Leftrightarrow & -112x \color{red}{-32} \color{blue}{+32} \color{blue}{-42x} & = & \color{red}{42x} +21 \color{blue}{-42x} \color{blue}{+32} \\\Leftrightarrow & -112x-42x& = & 21+32 \\\Leftrightarrow & \color{red}{-154} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-154} & & \\\Leftrightarrow & x = \frac{-53}{154} & & \\ & V = \left\{ \frac{-53}{154} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{3}{7})& = & -3x+\frac{5}{4} \\\Leftrightarrow & 4x-\frac{6}{7}& = & -3x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{112}{ \color{blue}{28} }x- \frac{24}{ \color{blue}{28} })& = & (\frac{-84}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 112x \color{red}{-24} & = & \color{red}{-84x} +35 \\\Leftrightarrow & 112x \color{red}{-24} \color{blue}{+24} \color{blue}{+84x} & = & \color{red}{-84x} +35 \color{blue}{+84x} \color{blue}{+24} \\\Leftrightarrow & 112x+84x& = & 35+24 \\\Leftrightarrow & \color{red}{196} x& = & 59 \\\Leftrightarrow & x = \frac{59}{196} & & \\ & V = \left\{ \frac{59}{196} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{4}{7})& = & -7x+\frac{7}{8} \\\Leftrightarrow & 10x+\frac{20}{7}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{560}{ \color{blue}{56} }x+ \frac{160}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 560x \color{red}{+160} & = & \color{red}{-392x} +49 \\\Leftrightarrow & 560x \color{red}{+160} \color{blue}{-160} \color{blue}{+392x} & = & \color{red}{-392x} +49 \color{blue}{+392x} \color{blue}{-160} \\\Leftrightarrow & 560x+392x& = & 49-160 \\\Leftrightarrow & \color{red}{952} x& = & -111 \\\Leftrightarrow & x = \frac{-111}{952} & & \\ & V = \left\{ \frac{-111}{952} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{5}{4})& = & -4x+\frac{9}{5} \\\Leftrightarrow & -15x+\frac{15}{4}& = & -4x+\frac{9}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-300}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{-80}{ \color{blue}{20} }x+ \frac{36}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -300x \color{red}{+75} & = & \color{red}{-80x} +36 \\\Leftrightarrow & -300x \color{red}{+75} \color{blue}{-75} \color{blue}{+80x} & = & \color{red}{-80x} +36 \color{blue}{+80x} \color{blue}{-75} \\\Leftrightarrow & -300x+80x& = & 36-75 \\\Leftrightarrow & \color{red}{-220} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{-220} & & \\\Leftrightarrow & x = \frac{39}{220} & & \\ & V = \left\{ \frac{39}{220} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & 2x+\frac{3}{10} \\\Leftrightarrow & 21x-\frac{14}{3}& = & 2x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{630}{ \color{blue}{30} }x- \frac{140}{ \color{blue}{30} })& = & (\frac{60}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 630x \color{red}{-140} & = & \color{red}{60x} +9 \\\Leftrightarrow & 630x \color{red}{-140} \color{blue}{+140} \color{blue}{-60x} & = & \color{red}{60x} +9 \color{blue}{-60x} \color{blue}{+140} \\\Leftrightarrow & 630x-60x& = & 9+140 \\\Leftrightarrow & \color{red}{570} x& = & 149 \\\Leftrightarrow & x = \frac{149}{570} & & \\ & V = \left\{ \frac{149}{570} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{2}{5})& = & 7x+\frac{9}{4} \\\Leftrightarrow & -6x+\frac{6}{5}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-120}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -120x \color{red}{+24} & = & \color{red}{140x} +45 \\\Leftrightarrow & -120x \color{red}{+24} \color{blue}{-24} \color{blue}{-140x} & = & \color{red}{140x} +45 \color{blue}{-140x} \color{blue}{-24} \\\Leftrightarrow & -120x-140x& = & 45-24 \\\Leftrightarrow & \color{red}{-260} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-260} & & \\\Leftrightarrow & x = \frac{-21}{260} & & \\ & V = \left\{ \frac{-21}{260} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{7})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1890}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1890x \color{red}{-270} & = & \color{red}{-441x} +28 \\\Leftrightarrow & -1890x \color{red}{-270} \color{blue}{+270} \color{blue}{+441x} & = & \color{red}{-441x} +28 \color{blue}{+441x} \color{blue}{+270} \\\Leftrightarrow & -1890x+441x& = & 28+270 \\\Leftrightarrow & \color{red}{-1449} x& = & 298 \\\Leftrightarrow & x = \frac{298}{-1449} & & \\\Leftrightarrow & x = \frac{-298}{1449} & & \\ & V = \left\{ \frac{-298}{1449} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{2}{3})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 8x+\frac{4}{3}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{+44} & = & \color{red}{-165x} +18 \\\Leftrightarrow & 264x \color{red}{+44} \color{blue}{-44} \color{blue}{+165x} & = & \color{red}{-165x} +18 \color{blue}{+165x} \color{blue}{-44} \\\Leftrightarrow & 264x+165x& = & 18-44 \\\Leftrightarrow & \color{red}{429} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{429} & & \\\Leftrightarrow & x = \frac{-2}{33} & & \\ & V = \left\{ \frac{-2}{33} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{5}{8})& = & -7x+\frac{3}{10} \\\Leftrightarrow & 15x-\frac{15}{8}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{600}{ \color{blue}{40} }x- \frac{75}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{12}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 600x \color{red}{-75} & = & \color{red}{-280x} +12 \\\Leftrightarrow & 600x \color{red}{-75} \color{blue}{+75} \color{blue}{+280x} & = & \color{red}{-280x} +12 \color{blue}{+280x} \color{blue}{+75} \\\Leftrightarrow & 600x+280x& = & 12+75 \\\Leftrightarrow & \color{red}{880} x& = & 87 \\\Leftrightarrow & x = \frac{87}{880} & & \\ & V = \left\{ \frac{87}{880} \right\} & \\\end{align}\)
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