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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{7})& = & -3x+\frac{8}{7} \\\Leftrightarrow & -20x-\frac{16}{7}& = & -3x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-140}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -140x \color{red}{-16} & = & \color{red}{-21x} +8 \\\Leftrightarrow & -140x \color{red}{-16} \color{blue}{+16} \color{blue}{+21x} & = & \color{red}{-21x} +8 \color{blue}{+21x} \color{blue}{+16} \\\Leftrightarrow & -140x+21x& = & 8+16 \\\Leftrightarrow & \color{red}{-119} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-119} & & \\\Leftrightarrow & x = \frac{-24}{119} & & \\ & V = \left\{ \frac{-24}{119} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{3}{5})& = & -7x+\frac{7}{5} \\\Leftrightarrow & -16x+\frac{12}{5}& = & -7x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-80}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -80x \color{red}{+12} & = & \color{red}{-35x} +7 \\\Leftrightarrow & -80x \color{red}{+12} \color{blue}{-12} \color{blue}{+35x} & = & \color{red}{-35x} +7 \color{blue}{+35x} \color{blue}{-12} \\\Leftrightarrow & -80x+35x& = & 7-12 \\\Leftrightarrow & \color{red}{-45} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-45} & & \\\Leftrightarrow & x = \frac{1}{9} & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{2}{3})& = & 2x+\frac{9}{2} \\\Leftrightarrow & 35x+\frac{14}{3}& = & 2x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{210}{ \color{blue}{6} }x+ \frac{28}{ \color{blue}{6} })& = & (\frac{12}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 210x \color{red}{+28} & = & \color{red}{12x} +27 \\\Leftrightarrow & 210x \color{red}{+28} \color{blue}{-28} \color{blue}{-12x} & = & \color{red}{12x} +27 \color{blue}{-12x} \color{blue}{-28} \\\Leftrightarrow & 210x-12x& = & 27-28 \\\Leftrightarrow & \color{red}{198} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{198} & & \\ & V = \left\{ \frac{-1}{198} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{5}{11})& = & 7x+\frac{9}{8} \\\Leftrightarrow & 10x+\frac{10}{11}& = & 7x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{880}{ \color{blue}{88} }x+ \frac{80}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 880x \color{red}{+80} & = & \color{red}{616x} +99 \\\Leftrightarrow & 880x \color{red}{+80} \color{blue}{-80} \color{blue}{-616x} & = & \color{red}{616x} +99 \color{blue}{-616x} \color{blue}{-80} \\\Leftrightarrow & 880x-616x& = & 99-80 \\\Leftrightarrow & \color{red}{264} x& = & 19 \\\Leftrightarrow & x = \frac{19}{264} & & \\ & V = \left\{ \frac{19}{264} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{2}{7})& = & -2x+\frac{5}{6} \\\Leftrightarrow & 9x+\frac{6}{7}& = & -2x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{378}{ \color{blue}{42} }x+ \frac{36}{ \color{blue}{42} })& = & (\frac{-84}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 378x \color{red}{+36} & = & \color{red}{-84x} +35 \\\Leftrightarrow & 378x \color{red}{+36} \color{blue}{-36} \color{blue}{+84x} & = & \color{red}{-84x} +35 \color{blue}{+84x} \color{blue}{-36} \\\Leftrightarrow & 378x+84x& = & 35-36 \\\Leftrightarrow & \color{red}{462} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{462} & & \\ & V = \left\{ \frac{-1}{462} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{3}{10})& = & 8x+\frac{6}{5} \\\Leftrightarrow & -21x-\frac{21}{10}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-210}{ \color{blue}{10} }x- \frac{21}{ \color{blue}{10} })& = & (\frac{80}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -210x \color{red}{-21} & = & \color{red}{80x} +12 \\\Leftrightarrow & -210x \color{red}{-21} \color{blue}{+21} \color{blue}{-80x} & = & \color{red}{80x} +12 \color{blue}{-80x} \color{blue}{+21} \\\Leftrightarrow & -210x-80x& = & 12+21 \\\Leftrightarrow & \color{red}{-290} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-290} & & \\\Leftrightarrow & x = \frac{-33}{290} & & \\ & V = \left\{ \frac{-33}{290} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{5}{2})& = & -7x+\frac{7}{8} \\\Leftrightarrow & -28x-\frac{35}{2}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-224}{ \color{blue}{8} }x- \frac{140}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -224x \color{red}{-140} & = & \color{red}{-56x} +7 \\\Leftrightarrow & -224x \color{red}{-140} \color{blue}{+140} \color{blue}{+56x} & = & \color{red}{-56x} +7 \color{blue}{+56x} \color{blue}{+140} \\\Leftrightarrow & -224x+56x& = & 7+140 \\\Leftrightarrow & \color{red}{-168} x& = & 147 \\\Leftrightarrow & x = \frac{147}{-168} & & \\\Leftrightarrow & x = \frac{-7}{8} & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{2}{5})& = & 5x+\frac{7}{2} \\\Leftrightarrow & -9x+\frac{6}{5}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-90}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -90x \color{red}{+12} & = & \color{red}{50x} +35 \\\Leftrightarrow & -90x \color{red}{+12} \color{blue}{-12} \color{blue}{-50x} & = & \color{red}{50x} +35 \color{blue}{-50x} \color{blue}{-12} \\\Leftrightarrow & -90x-50x& = & 35-12 \\\Leftrightarrow & \color{red}{-140} x& = & 23 \\\Leftrightarrow & x = \frac{23}{-140} & & \\\Leftrightarrow & x = \frac{-23}{140} & & \\ & V = \left\{ \frac{-23}{140} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{4}{5})& = & 4x+\frac{4}{5} \\\Leftrightarrow & -15x+\frac{12}{5}& = & 4x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-75}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{20}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -75x \color{red}{+12} & = & \color{red}{20x} +4 \\\Leftrightarrow & -75x \color{red}{+12} \color{blue}{-12} \color{blue}{-20x} & = & \color{red}{20x} +4 \color{blue}{-20x} \color{blue}{-12} \\\Leftrightarrow & -75x-20x& = & 4-12 \\\Leftrightarrow & \color{red}{-95} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-95} & & \\\Leftrightarrow & x = \frac{8}{95} & & \\ & V = \left\{ \frac{8}{95} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{3}{7})& = & 9x+\frac{4}{11} \\\Leftrightarrow & 4x+\frac{6}{7}& = & 9x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{308}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 308x \color{red}{+66} & = & \color{red}{693x} +28 \\\Leftrightarrow & 308x \color{red}{+66} \color{blue}{-66} \color{blue}{-693x} & = & \color{red}{693x} +28 \color{blue}{-693x} \color{blue}{-66} \\\Leftrightarrow & 308x-693x& = & 28-66 \\\Leftrightarrow & \color{red}{-385} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-385} & & \\\Leftrightarrow & x = \frac{38}{385} & & \\ & V = \left\{ \frac{38}{385} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{2}{3})& = & -7x+\frac{5}{8} \\\Leftrightarrow & 16x+\frac{8}{3}& = & -7x+\frac{5}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{384}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 384x \color{red}{+64} & = & \color{red}{-168x} +15 \\\Leftrightarrow & 384x \color{red}{+64} \color{blue}{-64} \color{blue}{+168x} & = & \color{red}{-168x} +15 \color{blue}{+168x} \color{blue}{-64} \\\Leftrightarrow & 384x+168x& = & 15-64 \\\Leftrightarrow & \color{red}{552} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{552} & & \\ & V = \left\{ \frac{-49}{552} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{3}{11})& = & -9x+\frac{5}{8} \\\Leftrightarrow & 4x+\frac{6}{11}& = & -9x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{352}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} })& = & (\frac{-792}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 352x \color{red}{+48} & = & \color{red}{-792x} +55 \\\Leftrightarrow & 352x \color{red}{+48} \color{blue}{-48} \color{blue}{+792x} & = & \color{red}{-792x} +55 \color{blue}{+792x} \color{blue}{-48} \\\Leftrightarrow & 352x+792x& = & 55-48 \\\Leftrightarrow & \color{red}{1144} x& = & 7 \\\Leftrightarrow & x = \frac{7}{1144} & & \\ & V = \left\{ \frac{7}{1144} \right\} & \\\end{align}\)
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