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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{2}{11})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 9x-\frac{6}{11}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{198}{ \color{blue}{22} }x- \frac{12}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 198x \color{red}{-12} & = & \color{red}{-154x} +99 \\\Leftrightarrow & 198x \color{red}{-12} \color{blue}{+12} \color{blue}{+154x} & = & \color{red}{-154x} +99 \color{blue}{+154x} \color{blue}{+12} \\\Leftrightarrow & 198x+154x& = & 99+12 \\\Leftrightarrow & \color{red}{352} x& = & 111 \\\Leftrightarrow & x = \frac{111}{352} & & \\ & V = \left\{ \frac{111}{352} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{2})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -12x-\frac{15}{2}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-264}{ \color{blue}{22} }x- \frac{165}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{12}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -264x \color{red}{-165} & = & \color{red}{-110x} +12 \\\Leftrightarrow & -264x \color{red}{-165} \color{blue}{+165} \color{blue}{+110x} & = & \color{red}{-110x} +12 \color{blue}{+110x} \color{blue}{+165} \\\Leftrightarrow & -264x+110x& = & 12+165 \\\Leftrightarrow & \color{red}{-154} x& = & 177 \\\Leftrightarrow & x = \frac{177}{-154} & & \\\Leftrightarrow & x = \frac{-177}{154} & & \\ & V = \left\{ \frac{-177}{154} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{5}{11})& = & -3x+\frac{4}{11} \\\Leftrightarrow & 8x-\frac{10}{11}& = & -3x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{88}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 88x \color{red}{-10} & = & \color{red}{-33x} +4 \\\Leftrightarrow & 88x \color{red}{-10} \color{blue}{+10} \color{blue}{+33x} & = & \color{red}{-33x} +4 \color{blue}{+33x} \color{blue}{+10} \\\Leftrightarrow & 88x+33x& = & 4+10 \\\Leftrightarrow & \color{red}{121} x& = & 14 \\\Leftrightarrow & x = \frac{14}{121} & & \\ & V = \left\{ \frac{14}{121} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{4}{11})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -12x+\frac{16}{11}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{112}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+112} & = & \color{red}{-385x} +110 \\\Leftrightarrow & -924x \color{red}{+112} \color{blue}{-112} \color{blue}{+385x} & = & \color{red}{-385x} +110 \color{blue}{+385x} \color{blue}{-112} \\\Leftrightarrow & -924x+385x& = & 110-112 \\\Leftrightarrow & \color{red}{-539} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-539} & & \\\Leftrightarrow & x = \frac{2}{539} & & \\ & V = \left\{ \frac{2}{539} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{2}{11})& = & -7x+\frac{7}{5} \\\Leftrightarrow & -9x+\frac{6}{11}& = & -7x+\frac{7}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{77}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{+30} & = & \color{red}{-385x} +77 \\\Leftrightarrow & -495x \color{red}{+30} \color{blue}{-30} \color{blue}{+385x} & = & \color{red}{-385x} +77 \color{blue}{+385x} \color{blue}{-30} \\\Leftrightarrow & -495x+385x& = & 77-30 \\\Leftrightarrow & \color{red}{-110} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-110} & & \\\Leftrightarrow & x = \frac{-47}{110} & & \\ & V = \left\{ \frac{-47}{110} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{3}{4})& = & 4x+\frac{5}{6} \\\Leftrightarrow & -15x+\frac{9}{4}& = & 4x+\frac{5}{6} \\ & & & \text{kgv van noemers 4 en 6 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} })& = & (\frac{48}{ \color{blue}{12} }x+ \frac{10}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{+27} & = & \color{red}{48x} +10 \\\Leftrightarrow & -180x \color{red}{+27} \color{blue}{-27} \color{blue}{-48x} & = & \color{red}{48x} +10 \color{blue}{-48x} \color{blue}{-27} \\\Leftrightarrow & -180x-48x& = & 10-27 \\\Leftrightarrow & \color{red}{-228} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-228} & & \\\Leftrightarrow & x = \frac{17}{228} & & \\ & V = \left\{ \frac{17}{228} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{4}{5})& = & -7x+\frac{9}{4} \\\Leftrightarrow & 6x+\frac{12}{5}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{120}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 120x \color{red}{+48} & = & \color{red}{-140x} +45 \\\Leftrightarrow & 120x \color{red}{+48} \color{blue}{-48} \color{blue}{+140x} & = & \color{red}{-140x} +45 \color{blue}{+140x} \color{blue}{-48} \\\Leftrightarrow & 120x+140x& = & 45-48 \\\Leftrightarrow & \color{red}{260} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{260} & & \\ & V = \left\{ \frac{-3}{260} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{5}{4})& = & -2x+\frac{7}{3} \\\Leftrightarrow & 15x-\frac{15}{4}& = & -2x+\frac{7}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{-24}{ \color{blue}{12} }x+ \frac{28}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{-45} & = & \color{red}{-24x} +28 \\\Leftrightarrow & 180x \color{red}{-45} \color{blue}{+45} \color{blue}{+24x} & = & \color{red}{-24x} +28 \color{blue}{+24x} \color{blue}{+45} \\\Leftrightarrow & 180x+24x& = & 28+45 \\\Leftrightarrow & \color{red}{204} x& = & 73 \\\Leftrightarrow & x = \frac{73}{204} & & \\ & V = \left\{ \frac{73}{204} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{3})& = & -9x+\frac{3}{2} \\\Leftrightarrow & -4x+\frac{8}{3}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-24}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -24x \color{red}{+16} & = & \color{red}{-54x} +9 \\\Leftrightarrow & -24x \color{red}{+16} \color{blue}{-16} \color{blue}{+54x} & = & \color{red}{-54x} +9 \color{blue}{+54x} \color{blue}{-16} \\\Leftrightarrow & -24x+54x& = & 9-16 \\\Leftrightarrow & \color{red}{30} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{30} & & \\ & V = \left\{ \frac{-7}{30} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{3}{11})& = & 5x+\frac{8}{9} \\\Leftrightarrow & 24x+\frac{18}{11}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2376}{ \color{blue}{99} }x+ \frac{162}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2376x \color{red}{+162} & = & \color{red}{495x} +88 \\\Leftrightarrow & 2376x \color{red}{+162} \color{blue}{-162} \color{blue}{-495x} & = & \color{red}{495x} +88 \color{blue}{-495x} \color{blue}{-162} \\\Leftrightarrow & 2376x-495x& = & 88-162 \\\Leftrightarrow & \color{red}{1881} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{1881} & & \\ & V = \left\{ \frac{-74}{1881} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{2}{3})& = & 9x+\frac{9}{11} \\\Leftrightarrow & -28x-\frac{14}{3}& = & 9x+\frac{9}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-924}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{27}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -924x \color{red}{-154} & = & \color{red}{297x} +27 \\\Leftrightarrow & -924x \color{red}{-154} \color{blue}{+154} \color{blue}{-297x} & = & \color{red}{297x} +27 \color{blue}{-297x} \color{blue}{+154} \\\Leftrightarrow & -924x-297x& = & 27+154 \\\Leftrightarrow & \color{red}{-1221} x& = & 181 \\\Leftrightarrow & x = \frac{181}{-1221} & & \\\Leftrightarrow & x = \frac{-181}{1221} & & \\ & V = \left\{ \frac{-181}{1221} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{3}{5})& = & 7x+\frac{9}{11} \\\Leftrightarrow & 12x+\frac{18}{5}& = & 7x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{198}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+198} & = & \color{red}{385x} +45 \\\Leftrightarrow & 660x \color{red}{+198} \color{blue}{-198} \color{blue}{-385x} & = & \color{red}{385x} +45 \color{blue}{-385x} \color{blue}{-198} \\\Leftrightarrow & 660x-385x& = & 45-198 \\\Leftrightarrow & \color{red}{275} x& = & -153 \\\Leftrightarrow & x = \frac{-153}{275} & & \\ & V = \left\{ \frac{-153}{275} \right\} & \\\end{align}\)
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