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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{3}{11})& = & -9x+\frac{5}{3} \\\Leftrightarrow & -8x+\frac{6}{11}& = & -9x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+18} & = & \color{red}{-297x} +55 \\\Leftrightarrow & -264x \color{red}{+18} \color{blue}{-18} \color{blue}{+297x} & = & \color{red}{-297x} +55 \color{blue}{+297x} \color{blue}{-18} \\\Leftrightarrow & -264x+297x& = & 55-18 \\\Leftrightarrow & \color{red}{33} x& = & 37 \\\Leftrightarrow & x = \frac{37}{33} & & \\ & V = \left\{ \frac{37}{33} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{2}{11})& = & -5x+\frac{5}{9} \\\Leftrightarrow & -12x-\frac{8}{11}& = & -5x+\frac{5}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x- \frac{72}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{55}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{-72} & = & \color{red}{-495x} +55 \\\Leftrightarrow & -1188x \color{red}{-72} \color{blue}{+72} \color{blue}{+495x} & = & \color{red}{-495x} +55 \color{blue}{+495x} \color{blue}{+72} \\\Leftrightarrow & -1188x+495x& = & 55+72 \\\Leftrightarrow & \color{red}{-693} x& = & 127 \\\Leftrightarrow & x = \frac{127}{-693} & & \\\Leftrightarrow & x = \frac{-127}{693} & & \\ & V = \left\{ \frac{-127}{693} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{2}{3})& = & 8x+\frac{2}{5} \\\Leftrightarrow & 21x+\frac{14}{3}& = & 8x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{+70} & = & \color{red}{120x} +6 \\\Leftrightarrow & 315x \color{red}{+70} \color{blue}{-70} \color{blue}{-120x} & = & \color{red}{120x} +6 \color{blue}{-120x} \color{blue}{-70} \\\Leftrightarrow & 315x-120x& = & 6-70 \\\Leftrightarrow & \color{red}{195} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{195} & & \\ & V = \left\{ \frac{-64}{195} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{5}{3})& = & -3x+\frac{10}{7} \\\Leftrightarrow & 16x-\frac{20}{3}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{-140} & = & \color{red}{-63x} +30 \\\Leftrightarrow & 336x \color{red}{-140} \color{blue}{+140} \color{blue}{+63x} & = & \color{red}{-63x} +30 \color{blue}{+63x} \color{blue}{+140} \\\Leftrightarrow & 336x+63x& = & 30+140 \\\Leftrightarrow & \color{red}{399} x& = & 170 \\\Leftrightarrow & x = \frac{170}{399} & & \\ & V = \left\{ \frac{170}{399} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{3}{4})& = & 3x+\frac{5}{2} \\\Leftrightarrow & 25x+\frac{15}{4}& = & 3x+\frac{5}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{100}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{12}{ \color{blue}{4} }x+ \frac{10}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 100x \color{red}{+15} & = & \color{red}{12x} +10 \\\Leftrightarrow & 100x \color{red}{+15} \color{blue}{-15} \color{blue}{-12x} & = & \color{red}{12x} +10 \color{blue}{-12x} \color{blue}{-15} \\\Leftrightarrow & 100x-12x& = & 10-15 \\\Leftrightarrow & \color{red}{88} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{88} & & \\ & V = \left\{ \frac{-5}{88} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{2}{5})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 24x+\frac{12}{5}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{720}{ \color{blue}{30} }x+ \frac{72}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 720x \color{red}{+72} & = & \color{red}{-150x} +25 \\\Leftrightarrow & 720x \color{red}{+72} \color{blue}{-72} \color{blue}{+150x} & = & \color{red}{-150x} +25 \color{blue}{+150x} \color{blue}{-72} \\\Leftrightarrow & 720x+150x& = & 25-72 \\\Leftrightarrow & \color{red}{870} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{870} & & \\ & V = \left\{ \frac{-47}{870} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{5})& = & -9x+\frac{7}{12} \\\Leftrightarrow & -20x-\frac{12}{5}& = & -9x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1200}{ \color{blue}{60} }x- \frac{144}{ \color{blue}{60} })& = & (\frac{-540}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1200x \color{red}{-144} & = & \color{red}{-540x} +35 \\\Leftrightarrow & -1200x \color{red}{-144} \color{blue}{+144} \color{blue}{+540x} & = & \color{red}{-540x} +35 \color{blue}{+540x} \color{blue}{+144} \\\Leftrightarrow & -1200x+540x& = & 35+144 \\\Leftrightarrow & \color{red}{-660} x& = & 179 \\\Leftrightarrow & x = \frac{179}{-660} & & \\\Leftrightarrow & x = \frac{-179}{660} & & \\ & V = \left\{ \frac{-179}{660} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{3}{5})& = & -7x+\frac{3}{7} \\\Leftrightarrow & 6x+\frac{6}{5}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{+42} & = & \color{red}{-245x} +15 \\\Leftrightarrow & 210x \color{red}{+42} \color{blue}{-42} \color{blue}{+245x} & = & \color{red}{-245x} +15 \color{blue}{+245x} \color{blue}{-42} \\\Leftrightarrow & 210x+245x& = & 15-42 \\\Leftrightarrow & \color{red}{455} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{455} & & \\ & V = \left\{ \frac{-27}{455} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{3}{11})& = & 9x+\frac{8}{3} \\\Leftrightarrow & -35x-\frac{21}{11}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x- \frac{63}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{-63} & = & \color{red}{297x} +88 \\\Leftrightarrow & -1155x \color{red}{-63} \color{blue}{+63} \color{blue}{-297x} & = & \color{red}{297x} +88 \color{blue}{-297x} \color{blue}{+63} \\\Leftrightarrow & -1155x-297x& = & 88+63 \\\Leftrightarrow & \color{red}{-1452} x& = & 151 \\\Leftrightarrow & x = \frac{151}{-1452} & & \\\Leftrightarrow & x = \frac{-151}{1452} & & \\ & V = \left\{ \frac{-151}{1452} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{5}{7})& = & -8x+\frac{2}{9} \\\Leftrightarrow & 15x+\frac{25}{7}& = & -8x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x+ \frac{225}{ \color{blue}{63} })& = & (\frac{-504}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{+225} & = & \color{red}{-504x} +14 \\\Leftrightarrow & 945x \color{red}{+225} \color{blue}{-225} \color{blue}{+504x} & = & \color{red}{-504x} +14 \color{blue}{+504x} \color{blue}{-225} \\\Leftrightarrow & 945x+504x& = & 14-225 \\\Leftrightarrow & \color{red}{1449} x& = & -211 \\\Leftrightarrow & x = \frac{-211}{1449} & & \\ & V = \left\{ \frac{-211}{1449} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{5}{9})& = & 5x+\frac{3}{10} \\\Leftrightarrow & 28x+\frac{35}{9}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{2520}{ \color{blue}{90} }x+ \frac{350}{ \color{blue}{90} })& = & (\frac{450}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 2520x \color{red}{+350} & = & \color{red}{450x} +27 \\\Leftrightarrow & 2520x \color{red}{+350} \color{blue}{-350} \color{blue}{-450x} & = & \color{red}{450x} +27 \color{blue}{-450x} \color{blue}{-350} \\\Leftrightarrow & 2520x-450x& = & 27-350 \\\Leftrightarrow & \color{red}{2070} x& = & -323 \\\Leftrightarrow & x = \frac{-323}{2070} & & \\ & V = \left\{ \frac{-323}{2070} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{7})& = & 7x+\frac{7}{12} \\\Leftrightarrow & -20x-\frac{10}{7}& = & 7x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-1680}{ \color{blue}{84} }x- \frac{120}{ \color{blue}{84} })& = & (\frac{588}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -1680x \color{red}{-120} & = & \color{red}{588x} +49 \\\Leftrightarrow & -1680x \color{red}{-120} \color{blue}{+120} \color{blue}{-588x} & = & \color{red}{588x} +49 \color{blue}{-588x} \color{blue}{+120} \\\Leftrightarrow & -1680x-588x& = & 49+120 \\\Leftrightarrow & \color{red}{-2268} x& = & 169 \\\Leftrightarrow & x = \frac{169}{-2268} & & \\\Leftrightarrow & x = \frac{-169}{2268} & & \\ & V = \left\{ \frac{-169}{2268} \right\} & \\\end{align}\)
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