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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{3}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -10x-\frac{6}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-18} & = & \color{red}{147x} +14 \\\Leftrightarrow & -210x \color{red}{-18} \color{blue}{+18} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{+18} \\\Leftrightarrow & -210x-147x& = & 14+18 \\\Leftrightarrow & \color{red}{-357} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-357} & & \\\Leftrightarrow & x = \frac{-32}{357} & & \\ & V = \left\{ \frac{-32}{357} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{5}{7})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 18x+\frac{30}{7}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{378}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 378x \color{red}{+90} & = & \color{red}{105x} +28 \\\Leftrightarrow & 378x \color{red}{+90} \color{blue}{-90} \color{blue}{-105x} & = & \color{red}{105x} +28 \color{blue}{-105x} \color{blue}{-90} \\\Leftrightarrow & 378x-105x& = & 28-90 \\\Leftrightarrow & \color{red}{273} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{273} & & \\ & V = \left\{ \frac{-62}{273} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{2}{9})& = & 7x+\frac{9}{7} \\\Leftrightarrow & 8x+\frac{8}{9}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{+56} & = & \color{red}{441x} +81 \\\Leftrightarrow & 504x \color{red}{+56} \color{blue}{-56} \color{blue}{-441x} & = & \color{red}{441x} +81 \color{blue}{-441x} \color{blue}{-56} \\\Leftrightarrow & 504x-441x& = & 81-56 \\\Leftrightarrow & \color{red}{63} x& = & 25 \\\Leftrightarrow & x = \frac{25}{63} & & \\ & V = \left\{ \frac{25}{63} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{2})& = & 7x+\frac{3}{7} \\\Leftrightarrow & -10x+\frac{25}{2}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-140}{ \color{blue}{14} }x+ \frac{175}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{6}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -140x \color{red}{+175} & = & \color{red}{98x} +6 \\\Leftrightarrow & -140x \color{red}{+175} \color{blue}{-175} \color{blue}{-98x} & = & \color{red}{98x} +6 \color{blue}{-98x} \color{blue}{-175} \\\Leftrightarrow & -140x-98x& = & 6-175 \\\Leftrightarrow & \color{red}{-238} x& = & -169 \\\Leftrightarrow & x = \frac{-169}{-238} & & \\\Leftrightarrow & x = \frac{169}{238} & & \\ & V = \left\{ \frac{169}{238} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{5}{7})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 18x-\frac{30}{7}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{378}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 378x \color{red}{-90} & = & \color{red}{105x} +70 \\\Leftrightarrow & 378x \color{red}{-90} \color{blue}{+90} \color{blue}{-105x} & = & \color{red}{105x} +70 \color{blue}{-105x} \color{blue}{+90} \\\Leftrightarrow & 378x-105x& = & 70+90 \\\Leftrightarrow & \color{red}{273} x& = & 160 \\\Leftrightarrow & x = \frac{160}{273} & & \\ & V = \left\{ \frac{160}{273} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{3}{8})& = & -4x+\frac{10}{7} \\\Leftrightarrow & 25x+\frac{15}{8}& = & -4x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1400}{ \color{blue}{56} }x+ \frac{105}{ \color{blue}{56} })& = & (\frac{-224}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1400x \color{red}{+105} & = & \color{red}{-224x} +80 \\\Leftrightarrow & 1400x \color{red}{+105} \color{blue}{-105} \color{blue}{+224x} & = & \color{red}{-224x} +80 \color{blue}{+224x} \color{blue}{-105} \\\Leftrightarrow & 1400x+224x& = & 80-105 \\\Leftrightarrow & \color{red}{1624} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{1624} & & \\ & V = \left\{ \frac{-25}{1624} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{4}{7})& = & 5x+\frac{2}{9} \\\Leftrightarrow & 6x+\frac{8}{7}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{+72} & = & \color{red}{315x} +14 \\\Leftrightarrow & 378x \color{red}{+72} \color{blue}{-72} \color{blue}{-315x} & = & \color{red}{315x} +14 \color{blue}{-315x} \color{blue}{-72} \\\Leftrightarrow & 378x-315x& = & 14-72 \\\Leftrightarrow & \color{red}{63} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{63} & & \\ & V = \left\{ \frac{-58}{63} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{3}{7})& = & 9x+\frac{8}{11} \\\Leftrightarrow & 20x+\frac{12}{7}& = & 9x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x+ \frac{132}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{+132} & = & \color{red}{693x} +56 \\\Leftrightarrow & 1540x \color{red}{+132} \color{blue}{-132} \color{blue}{-693x} & = & \color{red}{693x} +56 \color{blue}{-693x} \color{blue}{-132} \\\Leftrightarrow & 1540x-693x& = & 56-132 \\\Leftrightarrow & \color{red}{847} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{847} & & \\ & V = \left\{ \frac{-76}{847} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{2}{7})& = & -2x+\frac{8}{3} \\\Leftrightarrow & 15x+\frac{6}{7}& = & -2x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-42}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{+18} & = & \color{red}{-42x} +56 \\\Leftrightarrow & 315x \color{red}{+18} \color{blue}{-18} \color{blue}{+42x} & = & \color{red}{-42x} +56 \color{blue}{+42x} \color{blue}{-18} \\\Leftrightarrow & 315x+42x& = & 56-18 \\\Leftrightarrow & \color{red}{357} x& = & 38 \\\Leftrightarrow & x = \frac{38}{357} & & \\ & V = \left\{ \frac{38}{357} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{4}{7})& = & -3x+\frac{10}{3} \\\Leftrightarrow & 10x+\frac{20}{7}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{+60} & = & \color{red}{-63x} +70 \\\Leftrightarrow & 210x \color{red}{+60} \color{blue}{-60} \color{blue}{+63x} & = & \color{red}{-63x} +70 \color{blue}{+63x} \color{blue}{-60} \\\Leftrightarrow & 210x+63x& = & 70-60 \\\Leftrightarrow & \color{red}{273} x& = & 10 \\\Leftrightarrow & x = \frac{10}{273} & & \\ & V = \left\{ \frac{10}{273} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{7})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 12x-\frac{12}{7}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x- \frac{24}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{-24} & = & \color{red}{70x} +21 \\\Leftrightarrow & 168x \color{red}{-24} \color{blue}{+24} \color{blue}{-70x} & = & \color{red}{70x} +21 \color{blue}{-70x} \color{blue}{+24} \\\Leftrightarrow & 168x-70x& = & 21+24 \\\Leftrightarrow & \color{red}{98} x& = & 45 \\\Leftrightarrow & x = \frac{45}{98} & & \\ & V = \left\{ \frac{45}{98} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{3}{5})& = & 3x+\frac{2}{7} \\\Leftrightarrow & 8x+\frac{6}{5}& = & 3x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{+42} & = & \color{red}{105x} +10 \\\Leftrightarrow & 280x \color{red}{+42} \color{blue}{-42} \color{blue}{-105x} & = & \color{red}{105x} +10 \color{blue}{-105x} \color{blue}{-42} \\\Leftrightarrow & 280x-105x& = & 10-42 \\\Leftrightarrow & \color{red}{175} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{175} & & \\ & V = \left\{ \frac{-32}{175} \right\} & \\\end{align}\)
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