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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{4}{7})& = & -7x+\frac{4}{11} \\\Leftrightarrow & 6x+\frac{12}{7}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x+ \frac{132}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{+132} & = & \color{red}{-539x} +28 \\\Leftrightarrow & 462x \color{red}{+132} \color{blue}{-132} \color{blue}{+539x} & = & \color{red}{-539x} +28 \color{blue}{+539x} \color{blue}{-132} \\\Leftrightarrow & 462x+539x& = & 28-132 \\\Leftrightarrow & \color{red}{1001} x& = & -104 \\\Leftrightarrow & x = \frac{-104}{1001} & & \\\Leftrightarrow & x = \frac{-8}{77} & & \\ & V = \left\{ \frac{-8}{77} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{3}{5})& = & -5x+\frac{9}{10} \\\Leftrightarrow & -12x-\frac{18}{5}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x- \frac{36}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{-36} & = & \color{red}{-50x} +9 \\\Leftrightarrow & -120x \color{red}{-36} \color{blue}{+36} \color{blue}{+50x} & = & \color{red}{-50x} +9 \color{blue}{+50x} \color{blue}{+36} \\\Leftrightarrow & -120x+50x& = & 9+36 \\\Leftrightarrow & \color{red}{-70} x& = & 45 \\\Leftrightarrow & x = \frac{45}{-70} & & \\\Leftrightarrow & x = \frac{-9}{14} & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{5}{11})& = & 7x+\frac{5}{11} \\\Leftrightarrow & 18x-\frac{30}{11}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{198}{ \color{blue}{11} }x- \frac{30}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 198x \color{red}{-30} & = & \color{red}{77x} +5 \\\Leftrightarrow & 198x \color{red}{-30} \color{blue}{+30} \color{blue}{-77x} & = & \color{red}{77x} +5 \color{blue}{-77x} \color{blue}{+30} \\\Leftrightarrow & 198x-77x& = & 5+30 \\\Leftrightarrow & \color{red}{121} x& = & 35 \\\Leftrightarrow & x = \frac{35}{121} & & \\ & V = \left\{ \frac{35}{121} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & -5x+\frac{7}{3} \\\Leftrightarrow & -12x-\frac{18}{11}& = & -5x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-54} & = & \color{red}{-165x} +77 \\\Leftrightarrow & -396x \color{red}{-54} \color{blue}{+54} \color{blue}{+165x} & = & \color{red}{-165x} +77 \color{blue}{+165x} \color{blue}{+54} \\\Leftrightarrow & -396x+165x& = & 77+54 \\\Leftrightarrow & \color{red}{-231} x& = & 131 \\\Leftrightarrow & x = \frac{131}{-231} & & \\\Leftrightarrow & x = \frac{-131}{231} & & \\ & V = \left\{ \frac{-131}{231} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{5}{11})& = & 3x+\frac{5}{12} \\\Leftrightarrow & -28x-\frac{35}{11}& = & 3x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-3696}{ \color{blue}{132} }x- \frac{420}{ \color{blue}{132} })& = & (\frac{396}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -3696x \color{red}{-420} & = & \color{red}{396x} +55 \\\Leftrightarrow & -3696x \color{red}{-420} \color{blue}{+420} \color{blue}{-396x} & = & \color{red}{396x} +55 \color{blue}{-396x} \color{blue}{+420} \\\Leftrightarrow & -3696x-396x& = & 55+420 \\\Leftrightarrow & \color{red}{-4092} x& = & 475 \\\Leftrightarrow & x = \frac{475}{-4092} & & \\\Leftrightarrow & x = \frac{-475}{4092} & & \\ & V = \left\{ \frac{-475}{4092} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{3}{11})& = & 9x+\frac{10}{7} \\\Leftrightarrow & -18x-\frac{18}{11}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{-126} & = & \color{red}{693x} +110 \\\Leftrightarrow & -1386x \color{red}{-126} \color{blue}{+126} \color{blue}{-693x} & = & \color{red}{693x} +110 \color{blue}{-693x} \color{blue}{+126} \\\Leftrightarrow & -1386x-693x& = & 110+126 \\\Leftrightarrow & \color{red}{-2079} x& = & 236 \\\Leftrightarrow & x = \frac{236}{-2079} & & \\\Leftrightarrow & x = \frac{-236}{2079} & & \\ & V = \left\{ \frac{-236}{2079} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{5}{3})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 6x-\frac{10}{3}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{18}{ \color{blue}{3} }x- \frac{10}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 18x \color{red}{-10} & = & \color{red}{21x} +4 \\\Leftrightarrow & 18x \color{red}{-10} \color{blue}{+10} \color{blue}{-21x} & = & \color{red}{21x} +4 \color{blue}{-21x} \color{blue}{+10} \\\Leftrightarrow & 18x-21x& = & 4+10 \\\Leftrightarrow & \color{red}{-3} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-3} & & \\\Leftrightarrow & x = \frac{-14}{3} & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{5}{7})& = & -7x+\frac{4}{9} \\\Leftrightarrow & 20x+\frac{20}{7}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x+ \frac{180}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{+180} & = & \color{red}{-441x} +28 \\\Leftrightarrow & 1260x \color{red}{+180} \color{blue}{-180} \color{blue}{+441x} & = & \color{red}{-441x} +28 \color{blue}{+441x} \color{blue}{-180} \\\Leftrightarrow & 1260x+441x& = & 28-180 \\\Leftrightarrow & \color{red}{1701} x& = & -152 \\\Leftrightarrow & x = \frac{-152}{1701} & & \\ & V = \left\{ \frac{-152}{1701} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{3})& = & 2x+\frac{6}{11} \\\Leftrightarrow & 15x-\frac{20}{3}& = & 2x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{66}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{-220} & = & \color{red}{66x} +18 \\\Leftrightarrow & 495x \color{red}{-220} \color{blue}{+220} \color{blue}{-66x} & = & \color{red}{66x} +18 \color{blue}{-66x} \color{blue}{+220} \\\Leftrightarrow & 495x-66x& = & 18+220 \\\Leftrightarrow & \color{red}{429} x& = & 238 \\\Leftrightarrow & x = \frac{238}{429} & & \\ & V = \left\{ \frac{238}{429} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{9})& = & -3x+\frac{4}{3} \\\Leftrightarrow & -20x+\frac{16}{9}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x+ \frac{16}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{+16} & = & \color{red}{-27x} +12 \\\Leftrightarrow & -180x \color{red}{+16} \color{blue}{-16} \color{blue}{+27x} & = & \color{red}{-27x} +12 \color{blue}{+27x} \color{blue}{-16} \\\Leftrightarrow & -180x+27x& = & 12-16 \\\Leftrightarrow & \color{red}{-153} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-153} & & \\\Leftrightarrow & x = \frac{4}{153} & & \\ & V = \left\{ \frac{4}{153} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{11})& = & -7x+\frac{8}{7} \\\Leftrightarrow & -30x-\frac{30}{11}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x- \frac{210}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{-210} & = & \color{red}{-539x} +88 \\\Leftrightarrow & -2310x \color{red}{-210} \color{blue}{+210} \color{blue}{+539x} & = & \color{red}{-539x} +88 \color{blue}{+539x} \color{blue}{+210} \\\Leftrightarrow & -2310x+539x& = & 88+210 \\\Leftrightarrow & \color{red}{-1771} x& = & 298 \\\Leftrightarrow & x = \frac{298}{-1771} & & \\\Leftrightarrow & x = \frac{-298}{1771} & & \\ & V = \left\{ \frac{-298}{1771} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{5}{3})& = & 9x+\frac{7}{5} \\\Leftrightarrow & -20x+\frac{20}{3}& = & 9x+\frac{7}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{21}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{+100} & = & \color{red}{135x} +21 \\\Leftrightarrow & -300x \color{red}{+100} \color{blue}{-100} \color{blue}{-135x} & = & \color{red}{135x} +21 \color{blue}{-135x} \color{blue}{-100} \\\Leftrightarrow & -300x-135x& = & 21-100 \\\Leftrightarrow & \color{red}{-435} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{-435} & & \\\Leftrightarrow & x = \frac{79}{435} & & \\ & V = \left\{ \frac{79}{435} \right\} & \\\end{align}\)
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