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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{5}{12})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 10x+\frac{25}{12}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 12 en 7 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{840}{ \color{blue}{84} }x+ \frac{175}{ \color{blue}{84} })& = & (\frac{588}{ \color{blue}{84} }x+ \frac{120}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 840x \color{red}{+175} & = & \color{red}{588x} +120 \\\Leftrightarrow & 840x \color{red}{+175} \color{blue}{-175} \color{blue}{-588x} & = & \color{red}{588x} +120 \color{blue}{-588x} \color{blue}{-175} \\\Leftrightarrow & 840x-588x& = & 120-175 \\\Leftrightarrow & \color{red}{252} x& = & -55 \\\Leftrightarrow & x = \frac{-55}{252} & & \\ & V = \left\{ \frac{-55}{252} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{3}{7})& = & -8x+\frac{5}{7} \\\Leftrightarrow & -15x+\frac{15}{7}& = & -8x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-105}{ \color{blue}{7} }x+ \frac{15}{ \color{blue}{7} })& = & (\frac{-56}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -105x \color{red}{+15} & = & \color{red}{-56x} +5 \\\Leftrightarrow & -105x \color{red}{+15} \color{blue}{-15} \color{blue}{+56x} & = & \color{red}{-56x} +5 \color{blue}{+56x} \color{blue}{-15} \\\Leftrightarrow & -105x+56x& = & 5-15 \\\Leftrightarrow & \color{red}{-49} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-49} & & \\\Leftrightarrow & x = \frac{10}{49} & & \\ & V = \left\{ \frac{10}{49} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{7})& = & -7x+\frac{4}{5} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-50} & = & \color{red}{-245x} +28 \\\Leftrightarrow & -350x \color{red}{-50} \color{blue}{+50} \color{blue}{+245x} & = & \color{red}{-245x} +28 \color{blue}{+245x} \color{blue}{+50} \\\Leftrightarrow & -350x+245x& = & 28+50 \\\Leftrightarrow & \color{red}{-105} x& = & 78 \\\Leftrightarrow & x = \frac{78}{-105} & & \\\Leftrightarrow & x = \frac{-26}{35} & & \\ & V = \left\{ \frac{-26}{35} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{3}{8})& = & 3x+\frac{3}{8} \\\Leftrightarrow & 14x+\frac{21}{8}& = & 3x+\frac{3}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{112}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{24}{ \color{blue}{8} }x+ \frac{3}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 112x \color{red}{+21} & = & \color{red}{24x} +3 \\\Leftrightarrow & 112x \color{red}{+21} \color{blue}{-21} \color{blue}{-24x} & = & \color{red}{24x} +3 \color{blue}{-24x} \color{blue}{-21} \\\Leftrightarrow & 112x-24x& = & 3-21 \\\Leftrightarrow & \color{red}{88} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{88} & & \\\Leftrightarrow & x = \frac{-9}{44} & & \\ & V = \left\{ \frac{-9}{44} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{3}{5})& = & -2x+\frac{9}{11} \\\Leftrightarrow & 9x+\frac{9}{5}& = & -2x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{495}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} })& = & (\frac{-110}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 495x \color{red}{+99} & = & \color{red}{-110x} +45 \\\Leftrightarrow & 495x \color{red}{+99} \color{blue}{-99} \color{blue}{+110x} & = & \color{red}{-110x} +45 \color{blue}{+110x} \color{blue}{-99} \\\Leftrightarrow & 495x+110x& = & 45-99 \\\Leftrightarrow & \color{red}{605} x& = & -54 \\\Leftrightarrow & x = \frac{-54}{605} & & \\ & V = \left\{ \frac{-54}{605} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{7})& = & -3x+\frac{4}{3} \\\Leftrightarrow & 8x+\frac{8}{7}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{+24} & = & \color{red}{-63x} +28 \\\Leftrightarrow & 168x \color{red}{+24} \color{blue}{-24} \color{blue}{+63x} & = & \color{red}{-63x} +28 \color{blue}{+63x} \color{blue}{-24} \\\Leftrightarrow & 168x+63x& = & 28-24 \\\Leftrightarrow & \color{red}{231} x& = & 4 \\\Leftrightarrow & x = \frac{4}{231} & & \\ & V = \left\{ \frac{4}{231} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{4})& = & 3x+\frac{3}{11} \\\Leftrightarrow & -20x-\frac{15}{4}& = & 3x+\frac{3}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-880}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{132}{ \color{blue}{44} }x+ \frac{12}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -880x \color{red}{-165} & = & \color{red}{132x} +12 \\\Leftrightarrow & -880x \color{red}{-165} \color{blue}{+165} \color{blue}{-132x} & = & \color{red}{132x} +12 \color{blue}{-132x} \color{blue}{+165} \\\Leftrightarrow & -880x-132x& = & 12+165 \\\Leftrightarrow & \color{red}{-1012} x& = & 177 \\\Leftrightarrow & x = \frac{177}{-1012} & & \\\Leftrightarrow & x = \frac{-177}{1012} & & \\ & V = \left\{ \frac{-177}{1012} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{3}{7})& = & 7x+\frac{9}{10} \\\Leftrightarrow & 15x+\frac{9}{7}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1050}{ \color{blue}{70} }x+ \frac{90}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1050x \color{red}{+90} & = & \color{red}{490x} +63 \\\Leftrightarrow & 1050x \color{red}{+90} \color{blue}{-90} \color{blue}{-490x} & = & \color{red}{490x} +63 \color{blue}{-490x} \color{blue}{-90} \\\Leftrightarrow & 1050x-490x& = & 63-90 \\\Leftrightarrow & \color{red}{560} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{560} & & \\ & V = \left\{ \frac{-27}{560} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{2}{9})& = & 5x+\frac{8}{9} \\\Leftrightarrow & -12x+\frac{8}{9}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-108}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -108x \color{red}{+8} & = & \color{red}{45x} +8 \\\Leftrightarrow & -108x \color{red}{+8} \color{blue}{-8} \color{blue}{-45x} & = & \color{red}{45x} +8 \color{blue}{-45x} \color{blue}{-8} \\\Leftrightarrow & -108x-45x& = & 8-8 \\\Leftrightarrow & \color{red}{-153} x& = & 0 \\\Leftrightarrow & x = \frac{0}{-153} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{5}{4})& = & -4x+\frac{8}{11} \\\Leftrightarrow & -15x-\frac{15}{4}& = & -4x+\frac{8}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-660}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{-176}{ \color{blue}{44} }x+ \frac{32}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -660x \color{red}{-165} & = & \color{red}{-176x} +32 \\\Leftrightarrow & -660x \color{red}{-165} \color{blue}{+165} \color{blue}{+176x} & = & \color{red}{-176x} +32 \color{blue}{+176x} \color{blue}{+165} \\\Leftrightarrow & -660x+176x& = & 32+165 \\\Leftrightarrow & \color{red}{-484} x& = & 197 \\\Leftrightarrow & x = \frac{197}{-484} & & \\\Leftrightarrow & x = \frac{-197}{484} & & \\ & V = \left\{ \frac{-197}{484} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{6})& = & -3x+\frac{8}{11} \\\Leftrightarrow & 14x-\frac{35}{6}& = & -3x+\frac{8}{11} \\ & & & \text{kgv van noemers 6 en 11 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{924}{ \color{blue}{66} }x- \frac{385}{ \color{blue}{66} })& = & (\frac{-198}{ \color{blue}{66} }x+ \frac{48}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 924x \color{red}{-385} & = & \color{red}{-198x} +48 \\\Leftrightarrow & 924x \color{red}{-385} \color{blue}{+385} \color{blue}{+198x} & = & \color{red}{-198x} +48 \color{blue}{+198x} \color{blue}{+385} \\\Leftrightarrow & 924x+198x& = & 48+385 \\\Leftrightarrow & \color{red}{1122} x& = & 433 \\\Leftrightarrow & x = \frac{433}{1122} & & \\ & V = \left\{ \frac{433}{1122} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{3})& = & 8x+\frac{10}{9} \\\Leftrightarrow & -21x-\frac{14}{3}& = & 8x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-189}{ \color{blue}{9} }x- \frac{42}{ \color{blue}{9} })& = & (\frac{72}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -189x \color{red}{-42} & = & \color{red}{72x} +10 \\\Leftrightarrow & -189x \color{red}{-42} \color{blue}{+42} \color{blue}{-72x} & = & \color{red}{72x} +10 \color{blue}{-72x} \color{blue}{+42} \\\Leftrightarrow & -189x-72x& = & 10+42 \\\Leftrightarrow & \color{red}{-261} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-261} & & \\\Leftrightarrow & x = \frac{-52}{261} & & \\ & V = \left\{ \frac{-52}{261} \right\} & \\\end{align}\)
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