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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{4}{3})& = & -5x+\frac{7}{8} \\\Leftrightarrow & -4x-\frac{8}{3}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-96}{ \color{blue}{24} }x- \frac{64}{ \color{blue}{24} })& = & (\frac{-120}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -96x \color{red}{-64} & = & \color{red}{-120x} +21 \\\Leftrightarrow & -96x \color{red}{-64} \color{blue}{+64} \color{blue}{+120x} & = & \color{red}{-120x} +21 \color{blue}{+120x} \color{blue}{+64} \\\Leftrightarrow & -96x+120x& = & 21+64 \\\Leftrightarrow & \color{red}{24} x& = & 85 \\\Leftrightarrow & x = \frac{85}{24} & & \\ & V = \left\{ \frac{85}{24} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{4}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 6x-\frac{12}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{30}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 30x \color{red}{-12} & = & \color{red}{-35x} +6 \\\Leftrightarrow & 30x \color{red}{-12} \color{blue}{+12} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{+12} \\\Leftrightarrow & 30x+35x& = & 6+12 \\\Leftrightarrow & \color{red}{65} x& = & 18 \\\Leftrightarrow & x = \frac{18}{65} & & \\ & V = \left\{ \frac{18}{65} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & 2x+\frac{2}{11} \\\Leftrightarrow & 21x-\frac{14}{3}& = & 2x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{693}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{66}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 693x \color{red}{-154} & = & \color{red}{66x} +6 \\\Leftrightarrow & 693x \color{red}{-154} \color{blue}{+154} \color{blue}{-66x} & = & \color{red}{66x} +6 \color{blue}{-66x} \color{blue}{+154} \\\Leftrightarrow & 693x-66x& = & 6+154 \\\Leftrightarrow & \color{red}{627} x& = & 160 \\\Leftrightarrow & x = \frac{160}{627} & & \\ & V = \left\{ \frac{160}{627} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{2}{7})& = & 7x+\frac{9}{5} \\\Leftrightarrow & 12x-\frac{6}{7}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-30} & = & \color{red}{245x} +63 \\\Leftrightarrow & 420x \color{red}{-30} \color{blue}{+30} \color{blue}{-245x} & = & \color{red}{245x} +63 \color{blue}{-245x} \color{blue}{+30} \\\Leftrightarrow & 420x-245x& = & 63+30 \\\Leftrightarrow & \color{red}{175} x& = & 93 \\\Leftrightarrow & x = \frac{93}{175} & & \\ & V = \left\{ \frac{93}{175} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{4}{7})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -10x+\frac{20}{7}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{+220} & = & \color{red}{539x} +70 \\\Leftrightarrow & -770x \color{red}{+220} \color{blue}{-220} \color{blue}{-539x} & = & \color{red}{539x} +70 \color{blue}{-539x} \color{blue}{-220} \\\Leftrightarrow & -770x-539x& = & 70-220 \\\Leftrightarrow & \color{red}{-1309} x& = & -150 \\\Leftrightarrow & x = \frac{-150}{-1309} & & \\\Leftrightarrow & x = \frac{150}{1309} & & \\ & V = \left\{ \frac{150}{1309} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{6})& = & 3x+\frac{7}{4} \\\Leftrightarrow & 10x-\frac{25}{6}& = & 3x+\frac{7}{4} \\ & & & \text{kgv van noemers 6 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{120}{ \color{blue}{12} }x- \frac{50}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{21}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 120x \color{red}{-50} & = & \color{red}{36x} +21 \\\Leftrightarrow & 120x \color{red}{-50} \color{blue}{+50} \color{blue}{-36x} & = & \color{red}{36x} +21 \color{blue}{-36x} \color{blue}{+50} \\\Leftrightarrow & 120x-36x& = & 21+50 \\\Leftrightarrow & \color{red}{84} x& = & 71 \\\Leftrightarrow & x = \frac{71}{84} & & \\ & V = \left\{ \frac{71}{84} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{3}{10})& = & -2x+\frac{8}{11} \\\Leftrightarrow & -28x-\frac{21}{10}& = & -2x+\frac{8}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-3080}{ \color{blue}{110} }x- \frac{231}{ \color{blue}{110} })& = & (\frac{-220}{ \color{blue}{110} }x+ \frac{80}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -3080x \color{red}{-231} & = & \color{red}{-220x} +80 \\\Leftrightarrow & -3080x \color{red}{-231} \color{blue}{+231} \color{blue}{+220x} & = & \color{red}{-220x} +80 \color{blue}{+220x} \color{blue}{+231} \\\Leftrightarrow & -3080x+220x& = & 80+231 \\\Leftrightarrow & \color{red}{-2860} x& = & 311 \\\Leftrightarrow & x = \frac{311}{-2860} & & \\\Leftrightarrow & x = \frac{-311}{2860} & & \\ & V = \left\{ \frac{-311}{2860} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{2}{5})& = & 8x+\frac{9}{8} \\\Leftrightarrow & -28x+\frac{14}{5}& = & 8x+\frac{9}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1120}{ \color{blue}{40} }x+ \frac{112}{ \color{blue}{40} })& = & (\frac{320}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1120x \color{red}{+112} & = & \color{red}{320x} +45 \\\Leftrightarrow & -1120x \color{red}{+112} \color{blue}{-112} \color{blue}{-320x} & = & \color{red}{320x} +45 \color{blue}{-320x} \color{blue}{-112} \\\Leftrightarrow & -1120x-320x& = & 45-112 \\\Leftrightarrow & \color{red}{-1440} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{-1440} & & \\\Leftrightarrow & x = \frac{67}{1440} & & \\ & V = \left\{ \frac{67}{1440} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{3}{4})& = & 2x+\frac{9}{10} \\\Leftrightarrow & 25x-\frac{15}{4}& = & 2x+\frac{9}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{500}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{40}{ \color{blue}{20} }x+ \frac{18}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 500x \color{red}{-75} & = & \color{red}{40x} +18 \\\Leftrightarrow & 500x \color{red}{-75} \color{blue}{+75} \color{blue}{-40x} & = & \color{red}{40x} +18 \color{blue}{-40x} \color{blue}{+75} \\\Leftrightarrow & 500x-40x& = & 18+75 \\\Leftrightarrow & \color{red}{460} x& = & 93 \\\Leftrightarrow & x = \frac{93}{460} & & \\ & V = \left\{ \frac{93}{460} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{5}{7})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -6x-\frac{15}{7}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{45}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-45} & = & \color{red}{-147x} +28 \\\Leftrightarrow & -126x \color{red}{-45} \color{blue}{+45} \color{blue}{+147x} & = & \color{red}{-147x} +28 \color{blue}{+147x} \color{blue}{+45} \\\Leftrightarrow & -126x+147x& = & 28+45 \\\Leftrightarrow & \color{red}{21} x& = & 73 \\\Leftrightarrow & x = \frac{73}{21} & & \\ & V = \left\{ \frac{73}{21} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{2}{11})& = & -7x+\frac{5}{7} \\\Leftrightarrow & 10x-\frac{4}{11}& = & -7x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{28}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-28} & = & \color{red}{-539x} +55 \\\Leftrightarrow & 770x \color{red}{-28} \color{blue}{+28} \color{blue}{+539x} & = & \color{red}{-539x} +55 \color{blue}{+539x} \color{blue}{+28} \\\Leftrightarrow & 770x+539x& = & 55+28 \\\Leftrightarrow & \color{red}{1309} x& = & 83 \\\Leftrightarrow & x = \frac{83}{1309} & & \\ & V = \left\{ \frac{83}{1309} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{5}{8})& = & -7x+\frac{7}{8} \\\Leftrightarrow & -20x-\frac{25}{8}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-160}{ \color{blue}{8} }x- \frac{25}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -160x \color{red}{-25} & = & \color{red}{-56x} +7 \\\Leftrightarrow & -160x \color{red}{-25} \color{blue}{+25} \color{blue}{+56x} & = & \color{red}{-56x} +7 \color{blue}{+56x} \color{blue}{+25} \\\Leftrightarrow & -160x+56x& = & 7+25 \\\Leftrightarrow & \color{red}{-104} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-104} & & \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
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