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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{5}{7})& = & -7x+\frac{7}{12} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-2520}{ \color{blue}{84} }x- \frac{360}{ \color{blue}{84} })& = & (\frac{-588}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -2520x \color{red}{-360} & = & \color{red}{-588x} +49 \\\Leftrightarrow & -2520x \color{red}{-360} \color{blue}{+360} \color{blue}{+588x} & = & \color{red}{-588x} +49 \color{blue}{+588x} \color{blue}{+360} \\\Leftrightarrow & -2520x+588x& = & 49+360 \\\Leftrightarrow & \color{red}{-1932} x& = & 409 \\\Leftrightarrow & x = \frac{409}{-1932} & & \\\Leftrightarrow & x = \frac{-409}{1932} & & \\ & V = \left\{ \frac{-409}{1932} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{5}{9})& = & -3x+\frac{4}{3} \\\Leftrightarrow & -14x+\frac{35}{9}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-126}{ \color{blue}{9} }x+ \frac{35}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -126x \color{red}{+35} & = & \color{red}{-27x} +12 \\\Leftrightarrow & -126x \color{red}{+35} \color{blue}{-35} \color{blue}{+27x} & = & \color{red}{-27x} +12 \color{blue}{+27x} \color{blue}{-35} \\\Leftrightarrow & -126x+27x& = & 12-35 \\\Leftrightarrow & \color{red}{-99} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-99} & & \\\Leftrightarrow & x = \frac{23}{99} & & \\ & V = \left\{ \frac{23}{99} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{5})& = & 4x+\frac{8}{5} \\\Leftrightarrow & -15x-\frac{6}{5}& = & 4x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-75}{ \color{blue}{5} }x- \frac{6}{ \color{blue}{5} })& = & (\frac{20}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -75x \color{red}{-6} & = & \color{red}{20x} +8 \\\Leftrightarrow & -75x \color{red}{-6} \color{blue}{+6} \color{blue}{-20x} & = & \color{red}{20x} +8 \color{blue}{-20x} \color{blue}{+6} \\\Leftrightarrow & -75x-20x& = & 8+6 \\\Leftrightarrow & \color{red}{-95} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-95} & & \\\Leftrightarrow & x = \frac{-14}{95} & & \\ & V = \left\{ \frac{-14}{95} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{2}{9})& = & -7x+\frac{7}{5} \\\Leftrightarrow & 4x+\frac{4}{9}& = & -7x+\frac{7}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{180}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{63}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 180x \color{red}{+20} & = & \color{red}{-315x} +63 \\\Leftrightarrow & 180x \color{red}{+20} \color{blue}{-20} \color{blue}{+315x} & = & \color{red}{-315x} +63 \color{blue}{+315x} \color{blue}{-20} \\\Leftrightarrow & 180x+315x& = & 63-20 \\\Leftrightarrow & \color{red}{495} x& = & 43 \\\Leftrightarrow & x = \frac{43}{495} & & \\ & V = \left\{ \frac{43}{495} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{2}{9})& = & -7x+\frac{7}{11} \\\Leftrightarrow & -16x-\frac{8}{9}& = & -7x+\frac{7}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1584}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{63}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1584x \color{red}{-88} & = & \color{red}{-693x} +63 \\\Leftrightarrow & -1584x \color{red}{-88} \color{blue}{+88} \color{blue}{+693x} & = & \color{red}{-693x} +63 \color{blue}{+693x} \color{blue}{+88} \\\Leftrightarrow & -1584x+693x& = & 63+88 \\\Leftrightarrow & \color{red}{-891} x& = & 151 \\\Leftrightarrow & x = \frac{151}{-891} & & \\\Leftrightarrow & x = \frac{-151}{891} & & \\ & V = \left\{ \frac{-151}{891} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{4}{3})& = & -8x+\frac{2}{5} \\\Leftrightarrow & -15x-\frac{20}{3}& = & -8x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x- \frac{100}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{-100} & = & \color{red}{-120x} +6 \\\Leftrightarrow & -225x \color{red}{-100} \color{blue}{+100} \color{blue}{+120x} & = & \color{red}{-120x} +6 \color{blue}{+120x} \color{blue}{+100} \\\Leftrightarrow & -225x+120x& = & 6+100 \\\Leftrightarrow & \color{red}{-105} x& = & 106 \\\Leftrightarrow & x = \frac{106}{-105} & & \\\Leftrightarrow & x = \frac{-106}{105} & & \\ & V = \left\{ \frac{-106}{105} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{2}{5})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -30x-\frac{12}{5}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{-132} & = & \color{red}{385x} +30 \\\Leftrightarrow & -1650x \color{red}{-132} \color{blue}{+132} \color{blue}{-385x} & = & \color{red}{385x} +30 \color{blue}{-385x} \color{blue}{+132} \\\Leftrightarrow & -1650x-385x& = & 30+132 \\\Leftrightarrow & \color{red}{-2035} x& = & 162 \\\Leftrightarrow & x = \frac{162}{-2035} & & \\\Leftrightarrow & x = \frac{-162}{2035} & & \\ & V = \left\{ \frac{-162}{2035} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{2}{9})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 8x-\frac{8}{9}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{144}{ \color{blue}{18} }x- \frac{16}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 144x \color{red}{-16} & = & \color{red}{-126x} +81 \\\Leftrightarrow & 144x \color{red}{-16} \color{blue}{+16} \color{blue}{+126x} & = & \color{red}{-126x} +81 \color{blue}{+126x} \color{blue}{+16} \\\Leftrightarrow & 144x+126x& = & 81+16 \\\Leftrightarrow & \color{red}{270} x& = & 97 \\\Leftrightarrow & x = \frac{97}{270} & & \\ & V = \left\{ \frac{97}{270} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{7})& = & 3x+\frac{6}{7} \\\Leftrightarrow & -20x-\frac{16}{7}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-140}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -140x \color{red}{-16} & = & \color{red}{21x} +6 \\\Leftrightarrow & -140x \color{red}{-16} \color{blue}{+16} \color{blue}{-21x} & = & \color{red}{21x} +6 \color{blue}{-21x} \color{blue}{+16} \\\Leftrightarrow & -140x-21x& = & 6+16 \\\Leftrightarrow & \color{red}{-161} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-161} & & \\\Leftrightarrow & x = \frac{-22}{161} & & \\ & V = \left\{ \frac{-22}{161} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{7})& = & -7x+\frac{3}{5} \\\Leftrightarrow & 20x-\frac{20}{7}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{-100} & = & \color{red}{-245x} +21 \\\Leftrightarrow & 700x \color{red}{-100} \color{blue}{+100} \color{blue}{+245x} & = & \color{red}{-245x} +21 \color{blue}{+245x} \color{blue}{+100} \\\Leftrightarrow & 700x+245x& = & 21+100 \\\Leftrightarrow & \color{red}{945} x& = & 121 \\\Leftrightarrow & x = \frac{121}{945} & & \\ & V = \left\{ \frac{121}{945} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{2}{3})& = & -9x+\frac{3}{5} \\\Leftrightarrow & -8x-\frac{4}{3}& = & -9x+\frac{3}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x- \frac{20}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{9}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{-20} & = & \color{red}{-135x} +9 \\\Leftrightarrow & -120x \color{red}{-20} \color{blue}{+20} \color{blue}{+135x} & = & \color{red}{-135x} +9 \color{blue}{+135x} \color{blue}{+20} \\\Leftrightarrow & -120x+135x& = & 9+20 \\\Leftrightarrow & \color{red}{15} x& = & 29 \\\Leftrightarrow & x = \frac{29}{15} & & \\ & V = \left\{ \frac{29}{15} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{5}{11})& = & -7x+\frac{9}{4} \\\Leftrightarrow & 30x+\frac{30}{11}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1320}{ \color{blue}{44} }x+ \frac{120}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1320x \color{red}{+120} & = & \color{red}{-308x} +99 \\\Leftrightarrow & 1320x \color{red}{+120} \color{blue}{-120} \color{blue}{+308x} & = & \color{red}{-308x} +99 \color{blue}{+308x} \color{blue}{-120} \\\Leftrightarrow & 1320x+308x& = & 99-120 \\\Leftrightarrow & \color{red}{1628} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{1628} & & \\ & V = \left\{ \frac{-21}{1628} \right\} & \\\end{align}\)
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