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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{2}{7})& = & -8x+\frac{2}{9} \\\Leftrightarrow & -18x+\frac{12}{7}& = & -8x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1134}{ \color{blue}{63} }x+ \frac{108}{ \color{blue}{63} })& = & (\frac{-504}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1134x \color{red}{+108} & = & \color{red}{-504x} +14 \\\Leftrightarrow & -1134x \color{red}{+108} \color{blue}{-108} \color{blue}{+504x} & = & \color{red}{-504x} +14 \color{blue}{+504x} \color{blue}{-108} \\\Leftrightarrow & -1134x+504x& = & 14-108 \\\Leftrightarrow & \color{red}{-630} x& = & -94 \\\Leftrightarrow & x = \frac{-94}{-630} & & \\\Leftrightarrow & x = \frac{47}{315} & & \\ & V = \left\{ \frac{47}{315} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{5}{7})& = & -9x+\frac{2}{7} \\\Leftrightarrow & -4x-\frac{10}{7}& = & -9x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-28}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-63}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -28x \color{red}{-10} & = & \color{red}{-63x} +2 \\\Leftrightarrow & -28x \color{red}{-10} \color{blue}{+10} \color{blue}{+63x} & = & \color{red}{-63x} +2 \color{blue}{+63x} \color{blue}{+10} \\\Leftrightarrow & -28x+63x& = & 2+10 \\\Leftrightarrow & \color{red}{35} x& = & 12 \\\Leftrightarrow & x = \frac{12}{35} & & \\ & V = \left\{ \frac{12}{35} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{5}{12})& = & -3x+\frac{4}{7} \\\Leftrightarrow & -14x-\frac{35}{12}& = & -3x+\frac{4}{7} \\ & & & \text{kgv van noemers 12 en 7 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-1176}{ \color{blue}{84} }x- \frac{245}{ \color{blue}{84} })& = & (\frac{-252}{ \color{blue}{84} }x+ \frac{48}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -1176x \color{red}{-245} & = & \color{red}{-252x} +48 \\\Leftrightarrow & -1176x \color{red}{-245} \color{blue}{+245} \color{blue}{+252x} & = & \color{red}{-252x} +48 \color{blue}{+252x} \color{blue}{+245} \\\Leftrightarrow & -1176x+252x& = & 48+245 \\\Leftrightarrow & \color{red}{-924} x& = & 293 \\\Leftrightarrow & x = \frac{293}{-924} & & \\\Leftrightarrow & x = \frac{-293}{924} & & \\ & V = \left\{ \frac{-293}{924} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{4}{11})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 4x-\frac{8}{11}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{132}{ \color{blue}{33} }x- \frac{24}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 132x \color{red}{-24} & = & \color{red}{165x} +110 \\\Leftrightarrow & 132x \color{red}{-24} \color{blue}{+24} \color{blue}{-165x} & = & \color{red}{165x} +110 \color{blue}{-165x} \color{blue}{+24} \\\Leftrightarrow & 132x-165x& = & 110+24 \\\Leftrightarrow & \color{red}{-33} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-33} & & \\\Leftrightarrow & x = \frac{-134}{33} & & \\ & V = \left\{ \frac{-134}{33} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & 7x+\frac{8}{9} \\\Leftrightarrow & 30x+\frac{12}{5}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1350}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1350x \color{red}{+108} & = & \color{red}{315x} +40 \\\Leftrightarrow & 1350x \color{red}{+108} \color{blue}{-108} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{-108} \\\Leftrightarrow & 1350x-315x& = & 40-108 \\\Leftrightarrow & \color{red}{1035} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{1035} & & \\ & V = \left\{ \frac{-68}{1035} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{2}{3})& = & -3x+\frac{9}{2} \\\Leftrightarrow & 16x-\frac{8}{3}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{96}{ \color{blue}{6} }x- \frac{16}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 96x \color{red}{-16} & = & \color{red}{-18x} +27 \\\Leftrightarrow & 96x \color{red}{-16} \color{blue}{+16} \color{blue}{+18x} & = & \color{red}{-18x} +27 \color{blue}{+18x} \color{blue}{+16} \\\Leftrightarrow & 96x+18x& = & 27+16 \\\Leftrightarrow & \color{red}{114} x& = & 43 \\\Leftrightarrow & x = \frac{43}{114} & & \\ & V = \left\{ \frac{43}{114} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{11})& = & 7x+\frac{7}{3} \\\Leftrightarrow & -6x+\frac{15}{11}& = & 7x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-198}{ \color{blue}{33} }x+ \frac{45}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -198x \color{red}{+45} & = & \color{red}{231x} +77 \\\Leftrightarrow & -198x \color{red}{+45} \color{blue}{-45} \color{blue}{-231x} & = & \color{red}{231x} +77 \color{blue}{-231x} \color{blue}{-45} \\\Leftrightarrow & -198x-231x& = & 77-45 \\\Leftrightarrow & \color{red}{-429} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-429} & & \\\Leftrightarrow & x = \frac{-32}{429} & & \\ & V = \left\{ \frac{-32}{429} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{9})& = & -2x+\frac{6}{7} \\\Leftrightarrow & 21x+\frac{14}{9}& = & -2x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1323}{ \color{blue}{63} }x+ \frac{98}{ \color{blue}{63} })& = & (\frac{-126}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1323x \color{red}{+98} & = & \color{red}{-126x} +54 \\\Leftrightarrow & 1323x \color{red}{+98} \color{blue}{-98} \color{blue}{+126x} & = & \color{red}{-126x} +54 \color{blue}{+126x} \color{blue}{-98} \\\Leftrightarrow & 1323x+126x& = & 54-98 \\\Leftrightarrow & \color{red}{1449} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{1449} & & \\ & V = \left\{ \frac{-44}{1449} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{5})& = & -6x+\frac{10}{9} \\\Leftrightarrow & -28x-\frac{28}{5}& = & -6x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1260}{ \color{blue}{45} }x- \frac{252}{ \color{blue}{45} })& = & (\frac{-270}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1260x \color{red}{-252} & = & \color{red}{-270x} +50 \\\Leftrightarrow & -1260x \color{red}{-252} \color{blue}{+252} \color{blue}{+270x} & = & \color{red}{-270x} +50 \color{blue}{+270x} \color{blue}{+252} \\\Leftrightarrow & -1260x+270x& = & 50+252 \\\Leftrightarrow & \color{red}{-990} x& = & 302 \\\Leftrightarrow & x = \frac{302}{-990} & & \\\Leftrightarrow & x = \frac{-151}{495} & & \\ & V = \left\{ \frac{-151}{495} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{11})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -6x+\frac{12}{11}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-132}{ \color{blue}{22} }x+ \frac{24}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -132x \color{red}{+24} & = & \color{red}{154x} +99 \\\Leftrightarrow & -132x \color{red}{+24} \color{blue}{-24} \color{blue}{-154x} & = & \color{red}{154x} +99 \color{blue}{-154x} \color{blue}{-24} \\\Leftrightarrow & -132x-154x& = & 99-24 \\\Leftrightarrow & \color{red}{-286} x& = & 75 \\\Leftrightarrow & x = \frac{75}{-286} & & \\\Leftrightarrow & x = \frac{-75}{286} & & \\ & V = \left\{ \frac{-75}{286} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{5}{8})& = & -3x+\frac{8}{5} \\\Leftrightarrow & 25x+\frac{25}{8}& = & -3x+\frac{8}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{1000}{ \color{blue}{40} }x+ \frac{125}{ \color{blue}{40} })& = & (\frac{-120}{ \color{blue}{40} }x+ \frac{64}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 1000x \color{red}{+125} & = & \color{red}{-120x} +64 \\\Leftrightarrow & 1000x \color{red}{+125} \color{blue}{-125} \color{blue}{+120x} & = & \color{red}{-120x} +64 \color{blue}{+120x} \color{blue}{-125} \\\Leftrightarrow & 1000x+120x& = & 64-125 \\\Leftrightarrow & \color{red}{1120} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{1120} & & \\ & V = \left\{ \frac{-61}{1120} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{5}{7})& = & 7x+\frac{3}{10} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{700}{ \color{blue}{70} }x- \frac{100}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 700x \color{red}{-100} & = & \color{red}{490x} +21 \\\Leftrightarrow & 700x \color{red}{-100} \color{blue}{+100} \color{blue}{-490x} & = & \color{red}{490x} +21 \color{blue}{-490x} \color{blue}{+100} \\\Leftrightarrow & 700x-490x& = & 21+100 \\\Leftrightarrow & \color{red}{210} x& = & 121 \\\Leftrightarrow & x = \frac{121}{210} & & \\ & V = \left\{ \frac{121}{210} \right\} & \\\end{align}\)
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