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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{2}{11})& = & 7x+\frac{5}{11} \\\Leftrightarrow & -30x+\frac{12}{11}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-330}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -330x \color{red}{+12} & = & \color{red}{77x} +5 \\\Leftrightarrow & -330x \color{red}{+12} \color{blue}{-12} \color{blue}{-77x} & = & \color{red}{77x} +5 \color{blue}{-77x} \color{blue}{-12} \\\Leftrightarrow & -330x-77x& = & 5-12 \\\Leftrightarrow & \color{red}{-407} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-407} & & \\\Leftrightarrow & x = \frac{7}{407} & & \\ & V = \left\{ \frac{7}{407} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{3})& = & -7x+\frac{7}{9} \\\Leftrightarrow & 20x+\frac{8}{3}& = & -7x+\frac{7}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+24} & = & \color{red}{-63x} +7 \\\Leftrightarrow & 180x \color{red}{+24} \color{blue}{-24} \color{blue}{+63x} & = & \color{red}{-63x} +7 \color{blue}{+63x} \color{blue}{-24} \\\Leftrightarrow & 180x+63x& = & 7-24 \\\Leftrightarrow & \color{red}{243} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{243} & & \\ & V = \left\{ \frac{-17}{243} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{3})& = & -3x+\frac{4}{5} \\\Leftrightarrow & -35x-\frac{35}{3}& = & -3x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-525}{ \color{blue}{15} }x- \frac{175}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -525x \color{red}{-175} & = & \color{red}{-45x} +12 \\\Leftrightarrow & -525x \color{red}{-175} \color{blue}{+175} \color{blue}{+45x} & = & \color{red}{-45x} +12 \color{blue}{+45x} \color{blue}{+175} \\\Leftrightarrow & -525x+45x& = & 12+175 \\\Leftrightarrow & \color{red}{-480} x& = & 187 \\\Leftrightarrow & x = \frac{187}{-480} & & \\\Leftrightarrow & x = \frac{-187}{480} & & \\ & V = \left\{ \frac{-187}{480} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{5}{7})& = & -5x+\frac{10}{9} \\\Leftrightarrow & 4x+\frac{10}{7}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{252}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 252x \color{red}{+90} & = & \color{red}{-315x} +70 \\\Leftrightarrow & 252x \color{red}{+90} \color{blue}{-90} \color{blue}{+315x} & = & \color{red}{-315x} +70 \color{blue}{+315x} \color{blue}{-90} \\\Leftrightarrow & 252x+315x& = & 70-90 \\\Leftrightarrow & \color{red}{567} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{567} & & \\ & V = \left\{ \frac{-20}{567} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{5}{7})& = & 3x+\frac{7}{6} \\\Leftrightarrow & 20x-\frac{25}{7}& = & 3x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{840}{ \color{blue}{42} }x- \frac{150}{ \color{blue}{42} })& = & (\frac{126}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 840x \color{red}{-150} & = & \color{red}{126x} +49 \\\Leftrightarrow & 840x \color{red}{-150} \color{blue}{+150} \color{blue}{-126x} & = & \color{red}{126x} +49 \color{blue}{-126x} \color{blue}{+150} \\\Leftrightarrow & 840x-126x& = & 49+150 \\\Leftrightarrow & \color{red}{714} x& = & 199 \\\Leftrightarrow & x = \frac{199}{714} & & \\ & V = \left\{ \frac{199}{714} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{3}{8})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 15x-\frac{15}{8}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{840}{ \color{blue}{56} }x- \frac{105}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 840x \color{red}{-105} & = & \color{red}{-392x} +80 \\\Leftrightarrow & 840x \color{red}{-105} \color{blue}{+105} \color{blue}{+392x} & = & \color{red}{-392x} +80 \color{blue}{+392x} \color{blue}{+105} \\\Leftrightarrow & 840x+392x& = & 80+105 \\\Leftrightarrow & \color{red}{1232} x& = & 185 \\\Leftrightarrow & x = \frac{185}{1232} & & \\ & V = \left\{ \frac{185}{1232} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{4}{7})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 12x+\frac{16}{7}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x+ \frac{32}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{+32} & = & \color{red}{70x} +21 \\\Leftrightarrow & 168x \color{red}{+32} \color{blue}{-32} \color{blue}{-70x} & = & \color{red}{70x} +21 \color{blue}{-70x} \color{blue}{-32} \\\Leftrightarrow & 168x-70x& = & 21-32 \\\Leftrightarrow & \color{red}{98} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{98} & & \\ & V = \left\{ \frac{-11}{98} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{5}{3})& = & -8x+\frac{5}{7} \\\Leftrightarrow & 35x+\frac{35}{3}& = & -8x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{735}{ \color{blue}{21} }x+ \frac{245}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 735x \color{red}{+245} & = & \color{red}{-168x} +15 \\\Leftrightarrow & 735x \color{red}{+245} \color{blue}{-245} \color{blue}{+168x} & = & \color{red}{-168x} +15 \color{blue}{+168x} \color{blue}{-245} \\\Leftrightarrow & 735x+168x& = & 15-245 \\\Leftrightarrow & \color{red}{903} x& = & -230 \\\Leftrightarrow & x = \frac{-230}{903} & & \\ & V = \left\{ \frac{-230}{903} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{5})& = & -9x+\frac{6}{5} \\\Leftrightarrow & 8x-\frac{4}{5}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{40}{ \color{blue}{5} }x- \frac{4}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 40x \color{red}{-4} & = & \color{red}{-45x} +6 \\\Leftrightarrow & 40x \color{red}{-4} \color{blue}{+4} \color{blue}{+45x} & = & \color{red}{-45x} +6 \color{blue}{+45x} \color{blue}{+4} \\\Leftrightarrow & 40x+45x& = & 6+4 \\\Leftrightarrow & \color{red}{85} x& = & 10 \\\Leftrightarrow & x = \frac{10}{85} & & \\\Leftrightarrow & x = \frac{2}{17} & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{4}{5})& = & -4x+\frac{7}{10} \\\Leftrightarrow & -15x-\frac{12}{5}& = & -4x+\frac{7}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-150}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-40}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -150x \color{red}{-24} & = & \color{red}{-40x} +7 \\\Leftrightarrow & -150x \color{red}{-24} \color{blue}{+24} \color{blue}{+40x} & = & \color{red}{-40x} +7 \color{blue}{+40x} \color{blue}{+24} \\\Leftrightarrow & -150x+40x& = & 7+24 \\\Leftrightarrow & \color{red}{-110} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-110} & & \\\Leftrightarrow & x = \frac{-31}{110} & & \\ & V = \left\{ \frac{-31}{110} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{5})& = & 5x+\frac{7}{8} \\\Leftrightarrow & -12x+\frac{9}{5}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-480}{ \color{blue}{40} }x+ \frac{72}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -480x \color{red}{+72} & = & \color{red}{200x} +35 \\\Leftrightarrow & -480x \color{red}{+72} \color{blue}{-72} \color{blue}{-200x} & = & \color{red}{200x} +35 \color{blue}{-200x} \color{blue}{-72} \\\Leftrightarrow & -480x-200x& = & 35-72 \\\Leftrightarrow & \color{red}{-680} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-680} & & \\\Leftrightarrow & x = \frac{37}{680} & & \\ & V = \left\{ \frac{37}{680} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{2}{5})& = & -2x+\frac{7}{8} \\\Leftrightarrow & 15x-\frac{6}{5}& = & -2x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{600}{ \color{blue}{40} }x- \frac{48}{ \color{blue}{40} })& = & (\frac{-80}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 600x \color{red}{-48} & = & \color{red}{-80x} +35 \\\Leftrightarrow & 600x \color{red}{-48} \color{blue}{+48} \color{blue}{+80x} & = & \color{red}{-80x} +35 \color{blue}{+80x} \color{blue}{+48} \\\Leftrightarrow & 600x+80x& = & 35+48 \\\Leftrightarrow & \color{red}{680} x& = & 83 \\\Leftrightarrow & x = \frac{83}{680} & & \\ & V = \left\{ \frac{83}{680} \right\} & \\\end{align}\)
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