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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{4}{11})& = & 7x+\frac{4}{11} \\\Leftrightarrow & -6x-\frac{12}{11}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-66}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -66x \color{red}{-12} & = & \color{red}{77x} +4 \\\Leftrightarrow & -66x \color{red}{-12} \color{blue}{+12} \color{blue}{-77x} & = & \color{red}{77x} +4 \color{blue}{-77x} \color{blue}{+12} \\\Leftrightarrow & -66x-77x& = & 4+12 \\\Leftrightarrow & \color{red}{-143} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-143} & & \\\Leftrightarrow & x = \frac{-16}{143} & & \\ & V = \left\{ \frac{-16}{143} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{2}{5})& = & 8x+\frac{9}{5} \\\Leftrightarrow & -28x-\frac{14}{5}& = & 8x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-140}{ \color{blue}{5} }x- \frac{14}{ \color{blue}{5} })& = & (\frac{40}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -140x \color{red}{-14} & = & \color{red}{40x} +9 \\\Leftrightarrow & -140x \color{red}{-14} \color{blue}{+14} \color{blue}{-40x} & = & \color{red}{40x} +9 \color{blue}{-40x} \color{blue}{+14} \\\Leftrightarrow & -140x-40x& = & 9+14 \\\Leftrightarrow & \color{red}{-180} x& = & 23 \\\Leftrightarrow & x = \frac{23}{-180} & & \\\Leftrightarrow & x = \frac{-23}{180} & & \\ & V = \left\{ \frac{-23}{180} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{2}{9})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 20x-\frac{10}{9}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x- \frac{70}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{-70} & = & \color{red}{441x} +90 \\\Leftrightarrow & 1260x \color{red}{-70} \color{blue}{+70} \color{blue}{-441x} & = & \color{red}{441x} +90 \color{blue}{-441x} \color{blue}{+70} \\\Leftrightarrow & 1260x-441x& = & 90+70 \\\Leftrightarrow & \color{red}{819} x& = & 160 \\\Leftrightarrow & x = \frac{160}{819} & & \\ & V = \left\{ \frac{160}{819} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{11})& = & 5x+\frac{2}{7} \\\Leftrightarrow & -24x+\frac{24}{11}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x+ \frac{168}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{+168} & = & \color{red}{385x} +22 \\\Leftrightarrow & -1848x \color{red}{+168} \color{blue}{-168} \color{blue}{-385x} & = & \color{red}{385x} +22 \color{blue}{-385x} \color{blue}{-168} \\\Leftrightarrow & -1848x-385x& = & 22-168 \\\Leftrightarrow & \color{red}{-2233} x& = & -146 \\\Leftrightarrow & x = \frac{-146}{-2233} & & \\\Leftrightarrow & x = \frac{146}{2233} & & \\ & V = \left\{ \frac{146}{2233} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{3}{10})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 6x-\frac{9}{10}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x- \frac{9}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{-9} & = & \color{red}{50x} +12 \\\Leftrightarrow & 60x \color{red}{-9} \color{blue}{+9} \color{blue}{-50x} & = & \color{red}{50x} +12 \color{blue}{-50x} \color{blue}{+9} \\\Leftrightarrow & 60x-50x& = & 12+9 \\\Leftrightarrow & \color{red}{10} x& = & 21 \\\Leftrightarrow & x = \frac{21}{10} & & \\ & V = \left\{ \frac{21}{10} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{2}{9})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -16x-\frac{8}{9}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1008}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1008x \color{red}{-56} & = & \color{red}{-441x} +90 \\\Leftrightarrow & -1008x \color{red}{-56} \color{blue}{+56} \color{blue}{+441x} & = & \color{red}{-441x} +90 \color{blue}{+441x} \color{blue}{+56} \\\Leftrightarrow & -1008x+441x& = & 90+56 \\\Leftrightarrow & \color{red}{-567} x& = & 146 \\\Leftrightarrow & x = \frac{146}{-567} & & \\\Leftrightarrow & x = \frac{-146}{567} & & \\ & V = \left\{ \frac{-146}{567} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{2}{5})& = & 2x+\frac{8}{3} \\\Leftrightarrow & -18x+\frac{12}{5}& = & 2x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-270}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{30}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -270x \color{red}{+36} & = & \color{red}{30x} +40 \\\Leftrightarrow & -270x \color{red}{+36} \color{blue}{-36} \color{blue}{-30x} & = & \color{red}{30x} +40 \color{blue}{-30x} \color{blue}{-36} \\\Leftrightarrow & -270x-30x& = & 40-36 \\\Leftrightarrow & \color{red}{-300} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-300} & & \\\Leftrightarrow & x = \frac{-1}{75} & & \\ & V = \left\{ \frac{-1}{75} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{4}{5})& = & -5x+\frac{9}{2} \\\Leftrightarrow & -18x+\frac{24}{5}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-180}{ \color{blue}{10} }x+ \frac{48}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -180x \color{red}{+48} & = & \color{red}{-50x} +45 \\\Leftrightarrow & -180x \color{red}{+48} \color{blue}{-48} \color{blue}{+50x} & = & \color{red}{-50x} +45 \color{blue}{+50x} \color{blue}{-48} \\\Leftrightarrow & -180x+50x& = & 45-48 \\\Leftrightarrow & \color{red}{-130} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-130} & & \\\Leftrightarrow & x = \frac{3}{130} & & \\ & V = \left\{ \frac{3}{130} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{5})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{360}{ \color{blue}{30} }x+ \frac{72}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 360x \color{red}{+72} & = & \color{red}{-150x} +25 \\\Leftrightarrow & 360x \color{red}{+72} \color{blue}{-72} \color{blue}{+150x} & = & \color{red}{-150x} +25 \color{blue}{+150x} \color{blue}{-72} \\\Leftrightarrow & 360x+150x& = & 25-72 \\\Leftrightarrow & \color{red}{510} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{510} & & \\ & V = \left\{ \frac{-47}{510} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{5})& = & -5x+\frac{8}{7} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-84} & = & \color{red}{-175x} +40 \\\Leftrightarrow & 420x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +40 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & 420x+175x& = & 40+84 \\\Leftrightarrow & \color{red}{595} x& = & 124 \\\Leftrightarrow & x = \frac{124}{595} & & \\ & V = \left\{ \frac{124}{595} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & -5x+\frac{3}{7} \\\Leftrightarrow & -24x+\frac{18}{11}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{+126} & = & \color{red}{-385x} +33 \\\Leftrightarrow & -1848x \color{red}{+126} \color{blue}{-126} \color{blue}{+385x} & = & \color{red}{-385x} +33 \color{blue}{+385x} \color{blue}{-126} \\\Leftrightarrow & -1848x+385x& = & 33-126 \\\Leftrightarrow & \color{red}{-1463} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{-1463} & & \\\Leftrightarrow & x = \frac{93}{1463} & & \\ & V = \left\{ \frac{93}{1463} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{5}{7})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 10x-\frac{10}{7}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{140}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 140x \color{red}{-20} & = & \color{red}{-98x} +21 \\\Leftrightarrow & 140x \color{red}{-20} \color{blue}{+20} \color{blue}{+98x} & = & \color{red}{-98x} +21 \color{blue}{+98x} \color{blue}{+20} \\\Leftrightarrow & 140x+98x& = & 21+20 \\\Leftrightarrow & \color{red}{238} x& = & 41 \\\Leftrightarrow & x = \frac{41}{238} & & \\ & V = \left\{ \frac{41}{238} \right\} & \\\end{align}\)
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