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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{2}{5})& = & -7x+\frac{5}{8} \\\Leftrightarrow & -6x+\frac{4}{5}& = & -7x+\frac{5}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-240}{ \color{blue}{40} }x+ \frac{32}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{25}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -240x \color{red}{+32} & = & \color{red}{-280x} +25 \\\Leftrightarrow & -240x \color{red}{+32} \color{blue}{-32} \color{blue}{+280x} & = & \color{red}{-280x} +25 \color{blue}{+280x} \color{blue}{-32} \\\Leftrightarrow & -240x+280x& = & 25-32 \\\Leftrightarrow & \color{red}{40} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{40} & & \\ & V = \left\{ \frac{-7}{40} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{3}{5})& = & -5x+\frac{4}{7} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+84} & = & \color{red}{-175x} +20 \\\Leftrightarrow & 420x \color{red}{+84} \color{blue}{-84} \color{blue}{+175x} & = & \color{red}{-175x} +20 \color{blue}{+175x} \color{blue}{-84} \\\Leftrightarrow & 420x+175x& = & 20-84 \\\Leftrightarrow & \color{red}{595} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{595} & & \\ & V = \left\{ \frac{-64}{595} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{2}{11})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 12x+\frac{12}{11}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x+ \frac{36}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{+36} & = & \color{red}{-165x} +44 \\\Leftrightarrow & 396x \color{red}{+36} \color{blue}{-36} \color{blue}{+165x} & = & \color{red}{-165x} +44 \color{blue}{+165x} \color{blue}{-36} \\\Leftrightarrow & 396x+165x& = & 44-36 \\\Leftrightarrow & \color{red}{561} x& = & 8 \\\Leftrightarrow & x = \frac{8}{561} & & \\ & V = \left\{ \frac{8}{561} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{5}{8})& = & 8x+\frac{6}{5} \\\Leftrightarrow & -15x-\frac{15}{8}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-600}{ \color{blue}{40} }x- \frac{75}{ \color{blue}{40} })& = & (\frac{320}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -600x \color{red}{-75} & = & \color{red}{320x} +48 \\\Leftrightarrow & -600x \color{red}{-75} \color{blue}{+75} \color{blue}{-320x} & = & \color{red}{320x} +48 \color{blue}{-320x} \color{blue}{+75} \\\Leftrightarrow & -600x-320x& = & 48+75 \\\Leftrightarrow & \color{red}{-920} x& = & 123 \\\Leftrightarrow & x = \frac{123}{-920} & & \\\Leftrightarrow & x = \frac{-123}{920} & & \\ & V = \left\{ \frac{-123}{920} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{3})& = & -2x+\frac{9}{2} \\\Leftrightarrow & 21x+\frac{14}{3}& = & -2x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{126}{ \color{blue}{6} }x+ \frac{28}{ \color{blue}{6} })& = & (\frac{-12}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 126x \color{red}{+28} & = & \color{red}{-12x} +27 \\\Leftrightarrow & 126x \color{red}{+28} \color{blue}{-28} \color{blue}{+12x} & = & \color{red}{-12x} +27 \color{blue}{+12x} \color{blue}{-28} \\\Leftrightarrow & 126x+12x& = & 27-28 \\\Leftrightarrow & \color{red}{138} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{138} & & \\ & V = \left\{ \frac{-1}{138} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{3}{5})& = & 5x+\frac{8}{9} \\\Leftrightarrow & 18x-\frac{18}{5}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{810}{ \color{blue}{45} }x- \frac{162}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 810x \color{red}{-162} & = & \color{red}{225x} +40 \\\Leftrightarrow & 810x \color{red}{-162} \color{blue}{+162} \color{blue}{-225x} & = & \color{red}{225x} +40 \color{blue}{-225x} \color{blue}{+162} \\\Leftrightarrow & 810x-225x& = & 40+162 \\\Leftrightarrow & \color{red}{585} x& = & 202 \\\Leftrightarrow & x = \frac{202}{585} & & \\ & V = \left\{ \frac{202}{585} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{2}{11})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -12x-\frac{12}{11}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-264}{ \color{blue}{22} }x- \frac{24}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -264x \color{red}{-24} & = & \color{red}{-110x} +33 \\\Leftrightarrow & -264x \color{red}{-24} \color{blue}{+24} \color{blue}{+110x} & = & \color{red}{-110x} +33 \color{blue}{+110x} \color{blue}{+24} \\\Leftrightarrow & -264x+110x& = & 33+24 \\\Leftrightarrow & \color{red}{-154} x& = & 57 \\\Leftrightarrow & x = \frac{57}{-154} & & \\\Leftrightarrow & x = \frac{-57}{154} & & \\ & V = \left\{ \frac{-57}{154} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{2}{7})& = & 3x+\frac{8}{9} \\\Leftrightarrow & -20x+\frac{10}{7}& = & 3x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{+90} & = & \color{red}{189x} +56 \\\Leftrightarrow & -1260x \color{red}{+90} \color{blue}{-90} \color{blue}{-189x} & = & \color{red}{189x} +56 \color{blue}{-189x} \color{blue}{-90} \\\Leftrightarrow & -1260x-189x& = & 56-90 \\\Leftrightarrow & \color{red}{-1449} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-1449} & & \\\Leftrightarrow & x = \frac{34}{1449} & & \\ & V = \left\{ \frac{34}{1449} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{5}{3})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -10x-\frac{25}{3}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x- \frac{75}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{-75} & = & \color{red}{-63x} +10 \\\Leftrightarrow & -90x \color{red}{-75} \color{blue}{+75} \color{blue}{+63x} & = & \color{red}{-63x} +10 \color{blue}{+63x} \color{blue}{+75} \\\Leftrightarrow & -90x+63x& = & 10+75 \\\Leftrightarrow & \color{red}{-27} x& = & 85 \\\Leftrightarrow & x = \frac{85}{-27} & & \\\Leftrightarrow & x = \frac{-85}{27} & & \\ & V = \left\{ \frac{-85}{27} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{5}{8})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -20x-\frac{25}{8}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1120}{ \color{blue}{56} }x- \frac{175}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{32}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1120x \color{red}{-175} & = & \color{red}{392x} +32 \\\Leftrightarrow & -1120x \color{red}{-175} \color{blue}{+175} \color{blue}{-392x} & = & \color{red}{392x} +32 \color{blue}{-392x} \color{blue}{+175} \\\Leftrightarrow & -1120x-392x& = & 32+175 \\\Leftrightarrow & \color{red}{-1512} x& = & 207 \\\Leftrightarrow & x = \frac{207}{-1512} & & \\\Leftrightarrow & x = \frac{-23}{168} & & \\ & V = \left\{ \frac{-23}{168} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{3}{8})& = & -3x+\frac{5}{11} \\\Leftrightarrow & -14x+\frac{21}{8}& = & -3x+\frac{5}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1232}{ \color{blue}{88} }x+ \frac{231}{ \color{blue}{88} })& = & (\frac{-264}{ \color{blue}{88} }x+ \frac{40}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1232x \color{red}{+231} & = & \color{red}{-264x} +40 \\\Leftrightarrow & -1232x \color{red}{+231} \color{blue}{-231} \color{blue}{+264x} & = & \color{red}{-264x} +40 \color{blue}{+264x} \color{blue}{-231} \\\Leftrightarrow & -1232x+264x& = & 40-231 \\\Leftrightarrow & \color{red}{-968} x& = & -191 \\\Leftrightarrow & x = \frac{-191}{-968} & & \\\Leftrightarrow & x = \frac{191}{968} & & \\ & V = \left\{ \frac{191}{968} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{3}{7})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -8x+\frac{6}{7}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{+18} & = & \color{red}{-189x} +14 \\\Leftrightarrow & -168x \color{red}{+18} \color{blue}{-18} \color{blue}{+189x} & = & \color{red}{-189x} +14 \color{blue}{+189x} \color{blue}{-18} \\\Leftrightarrow & -168x+189x& = & 14-18 \\\Leftrightarrow & \color{red}{21} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{21} & & \\ & V = \left\{ \frac{-4}{21} \right\} & \\\end{align}\)
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