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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{4}{3})& = & -9x+\frac{7}{4} \\\Leftrightarrow & -8x-\frac{8}{3}& = & -9x+\frac{7}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-96}{ \color{blue}{12} }x- \frac{32}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{21}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -96x \color{red}{-32} & = & \color{red}{-108x} +21 \\\Leftrightarrow & -96x \color{red}{-32} \color{blue}{+32} \color{blue}{+108x} & = & \color{red}{-108x} +21 \color{blue}{+108x} \color{blue}{+32} \\\Leftrightarrow & -96x+108x& = & 21+32 \\\Leftrightarrow & \color{red}{12} x& = & 53 \\\Leftrightarrow & x = \frac{53}{12} & & \\ & V = \left\{ \frac{53}{12} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{2}{9})& = & 9x+\frac{2}{5} \\\Leftrightarrow & -4x-\frac{4}{9}& = & 9x+\frac{2}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-180}{ \color{blue}{45} }x- \frac{20}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{18}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -180x \color{red}{-20} & = & \color{red}{405x} +18 \\\Leftrightarrow & -180x \color{red}{-20} \color{blue}{+20} \color{blue}{-405x} & = & \color{red}{405x} +18 \color{blue}{-405x} \color{blue}{+20} \\\Leftrightarrow & -180x-405x& = & 18+20 \\\Leftrightarrow & \color{red}{-585} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-585} & & \\\Leftrightarrow & x = \frac{-38}{585} & & \\ & V = \left\{ \frac{-38}{585} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{2}{7})& = & 5x+\frac{7}{10} \\\Leftrightarrow & -12x-\frac{6}{7}& = & 5x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-840}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -840x \color{red}{-60} & = & \color{red}{350x} +49 \\\Leftrightarrow & -840x \color{red}{-60} \color{blue}{+60} \color{blue}{-350x} & = & \color{red}{350x} +49 \color{blue}{-350x} \color{blue}{+60} \\\Leftrightarrow & -840x-350x& = & 49+60 \\\Leftrightarrow & \color{red}{-1190} x& = & 109 \\\Leftrightarrow & x = \frac{109}{-1190} & & \\\Leftrightarrow & x = \frac{-109}{1190} & & \\ & V = \left\{ \frac{-109}{1190} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{4}{5})& = & -7x+\frac{10}{11} \\\Leftrightarrow & 9x-\frac{12}{5}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{495}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 495x \color{red}{-132} & = & \color{red}{-385x} +50 \\\Leftrightarrow & 495x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +50 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & 495x+385x& = & 50+132 \\\Leftrightarrow & \color{red}{880} x& = & 182 \\\Leftrightarrow & x = \frac{182}{880} & & \\\Leftrightarrow & x = \frac{91}{440} & & \\ & V = \left\{ \frac{91}{440} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{3})& = & -3x+\frac{5}{11} \\\Leftrightarrow & 14x+\frac{14}{3}& = & -3x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{+154} & = & \color{red}{-99x} +15 \\\Leftrightarrow & 462x \color{red}{+154} \color{blue}{-154} \color{blue}{+99x} & = & \color{red}{-99x} +15 \color{blue}{+99x} \color{blue}{-154} \\\Leftrightarrow & 462x+99x& = & 15-154 \\\Leftrightarrow & \color{red}{561} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{561} & & \\ & V = \left\{ \frac{-139}{561} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{4}{11})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -28x+\frac{28}{11}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-308}{ \color{blue}{11} }x+ \frac{28}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -308x \color{red}{+28} & = & \color{red}{55x} +2 \\\Leftrightarrow & -308x \color{red}{+28} \color{blue}{-28} \color{blue}{-55x} & = & \color{red}{55x} +2 \color{blue}{-55x} \color{blue}{-28} \\\Leftrightarrow & -308x-55x& = & 2-28 \\\Leftrightarrow & \color{red}{-363} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-363} & & \\\Leftrightarrow & x = \frac{26}{363} & & \\ & V = \left\{ \frac{26}{363} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{5}{7})& = & 3x+\frac{10}{11} \\\Leftrightarrow & -20x+\frac{20}{7}& = & 3x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{+220} & = & \color{red}{231x} +70 \\\Leftrightarrow & -1540x \color{red}{+220} \color{blue}{-220} \color{blue}{-231x} & = & \color{red}{231x} +70 \color{blue}{-231x} \color{blue}{-220} \\\Leftrightarrow & -1540x-231x& = & 70-220 \\\Leftrightarrow & \color{red}{-1771} x& = & -150 \\\Leftrightarrow & x = \frac{-150}{-1771} & & \\\Leftrightarrow & x = \frac{150}{1771} & & \\ & V = \left\{ \frac{150}{1771} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{4}{11})& = & 3x+\frac{5}{2} \\\Leftrightarrow & 10x-\frac{8}{11}& = & 3x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{220}{ \color{blue}{22} }x- \frac{16}{ \color{blue}{22} })& = & (\frac{66}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 220x \color{red}{-16} & = & \color{red}{66x} +55 \\\Leftrightarrow & 220x \color{red}{-16} \color{blue}{+16} \color{blue}{-66x} & = & \color{red}{66x} +55 \color{blue}{-66x} \color{blue}{+16} \\\Leftrightarrow & 220x-66x& = & 55+16 \\\Leftrightarrow & \color{red}{154} x& = & 71 \\\Leftrightarrow & x = \frac{71}{154} & & \\ & V = \left\{ \frac{71}{154} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{1}{2})& = & 8x+\frac{2}{5} \\\Leftrightarrow & -25x+\frac{5}{2}& = & 8x+\frac{2}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-250}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} })& = & (\frac{80}{ \color{blue}{10} }x+ \frac{4}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -250x \color{red}{+25} & = & \color{red}{80x} +4 \\\Leftrightarrow & -250x \color{red}{+25} \color{blue}{-25} \color{blue}{-80x} & = & \color{red}{80x} +4 \color{blue}{-80x} \color{blue}{-25} \\\Leftrightarrow & -250x-80x& = & 4-25 \\\Leftrightarrow & \color{red}{-330} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-330} & & \\\Leftrightarrow & x = \frac{7}{110} & & \\ & V = \left\{ \frac{7}{110} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{2}{7})& = & -9x+\frac{4}{11} \\\Leftrightarrow & 10x-\frac{4}{7}& = & -9x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{44}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-44} & = & \color{red}{-693x} +28 \\\Leftrightarrow & 770x \color{red}{-44} \color{blue}{+44} \color{blue}{+693x} & = & \color{red}{-693x} +28 \color{blue}{+693x} \color{blue}{+44} \\\Leftrightarrow & 770x+693x& = & 28+44 \\\Leftrightarrow & \color{red}{1463} x& = & 72 \\\Leftrightarrow & x = \frac{72}{1463} & & \\ & V = \left\{ \frac{72}{1463} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{4}{7})& = & 5x+\frac{3}{7} \\\Leftrightarrow & 12x-\frac{16}{7}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{-16} & = & \color{red}{35x} +3 \\\Leftrightarrow & 84x \color{red}{-16} \color{blue}{+16} \color{blue}{-35x} & = & \color{red}{35x} +3 \color{blue}{-35x} \color{blue}{+16} \\\Leftrightarrow & 84x-35x& = & 3+16 \\\Leftrightarrow & \color{red}{49} x& = & 19 \\\Leftrightarrow & x = \frac{19}{49} & & \\ & V = \left\{ \frac{19}{49} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{5})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -6x+\frac{12}{5}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{+108} & = & \color{red}{-315x} +20 \\\Leftrightarrow & -270x \color{red}{+108} \color{blue}{-108} \color{blue}{+315x} & = & \color{red}{-315x} +20 \color{blue}{+315x} \color{blue}{-108} \\\Leftrightarrow & -270x+315x& = & 20-108 \\\Leftrightarrow & \color{red}{45} x& = & -88 \\\Leftrightarrow & x = \frac{-88}{45} & & \\ & V = \left\{ \frac{-88}{45} \right\} & \\\end{align}\)
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