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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{4}{7})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -12x-\frac{24}{7}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{72}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-72} & = & \color{red}{105x} +28 \\\Leftrightarrow & -252x \color{red}{-72} \color{blue}{+72} \color{blue}{-105x} & = & \color{red}{105x} +28 \color{blue}{-105x} \color{blue}{+72} \\\Leftrightarrow & -252x-105x& = & 28+72 \\\Leftrightarrow & \color{red}{-357} x& = & 100 \\\Leftrightarrow & x = \frac{100}{-357} & & \\\Leftrightarrow & x = \frac{-100}{357} & & \\ & V = \left\{ \frac{-100}{357} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{3}{11})& = & 2x+\frac{7}{8} \\\Leftrightarrow & -18x+\frac{18}{11}& = & 2x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1584}{ \color{blue}{88} }x+ \frac{144}{ \color{blue}{88} })& = & (\frac{176}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1584x \color{red}{+144} & = & \color{red}{176x} +77 \\\Leftrightarrow & -1584x \color{red}{+144} \color{blue}{-144} \color{blue}{-176x} & = & \color{red}{176x} +77 \color{blue}{-176x} \color{blue}{-144} \\\Leftrightarrow & -1584x-176x& = & 77-144 \\\Leftrightarrow & \color{red}{-1760} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{-1760} & & \\\Leftrightarrow & x = \frac{67}{1760} & & \\ & V = \left\{ \frac{67}{1760} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{5}{7})& = & -7x+\frac{5}{12} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-2520}{ \color{blue}{84} }x- \frac{360}{ \color{blue}{84} })& = & (\frac{-588}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -2520x \color{red}{-360} & = & \color{red}{-588x} +35 \\\Leftrightarrow & -2520x \color{red}{-360} \color{blue}{+360} \color{blue}{+588x} & = & \color{red}{-588x} +35 \color{blue}{+588x} \color{blue}{+360} \\\Leftrightarrow & -2520x+588x& = & 35+360 \\\Leftrightarrow & \color{red}{-1932} x& = & 395 \\\Leftrightarrow & x = \frac{395}{-1932} & & \\\Leftrightarrow & x = \frac{-395}{1932} & & \\ & V = \left\{ \frac{-395}{1932} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{4}{11})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 12x+\frac{24}{11}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x+ \frac{72}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{+72} & = & \color{red}{-165x} +22 \\\Leftrightarrow & 396x \color{red}{+72} \color{blue}{-72} \color{blue}{+165x} & = & \color{red}{-165x} +22 \color{blue}{+165x} \color{blue}{-72} \\\Leftrightarrow & 396x+165x& = & 22-72 \\\Leftrightarrow & \color{red}{561} x& = & -50 \\\Leftrightarrow & x = \frac{-50}{561} & & \\ & V = \left\{ \frac{-50}{561} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{3}{4})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 35x-\frac{21}{4}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{420}{ \color{blue}{12} }x- \frac{63}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 420x \color{red}{-63} & = & \color{red}{36x} +16 \\\Leftrightarrow & 420x \color{red}{-63} \color{blue}{+63} \color{blue}{-36x} & = & \color{red}{36x} +16 \color{blue}{-36x} \color{blue}{+63} \\\Leftrightarrow & 420x-36x& = & 16+63 \\\Leftrightarrow & \color{red}{384} x& = & 79 \\\Leftrightarrow & x = \frac{79}{384} & & \\ & V = \left\{ \frac{79}{384} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{2}{11})& = & 2x+\frac{3}{2} \\\Leftrightarrow & 25x-\frac{10}{11}& = & 2x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{550}{ \color{blue}{22} }x- \frac{20}{ \color{blue}{22} })& = & (\frac{44}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 550x \color{red}{-20} & = & \color{red}{44x} +33 \\\Leftrightarrow & 550x \color{red}{-20} \color{blue}{+20} \color{blue}{-44x} & = & \color{red}{44x} +33 \color{blue}{-44x} \color{blue}{+20} \\\Leftrightarrow & 550x-44x& = & 33+20 \\\Leftrightarrow & \color{red}{506} x& = & 53 \\\Leftrightarrow & x = \frac{53}{506} & & \\ & V = \left\{ \frac{53}{506} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{2}{7})& = & -5x+\frac{8}{5} \\\Leftrightarrow & 12x-\frac{12}{7}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{60}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-60} & = & \color{red}{-175x} +56 \\\Leftrightarrow & 420x \color{red}{-60} \color{blue}{+60} \color{blue}{+175x} & = & \color{red}{-175x} +56 \color{blue}{+175x} \color{blue}{+60} \\\Leftrightarrow & 420x+175x& = & 56+60 \\\Leftrightarrow & \color{red}{595} x& = & 116 \\\Leftrightarrow & x = \frac{116}{595} & & \\ & V = \left\{ \frac{116}{595} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{5}{3})& = & 9x+\frac{5}{12} \\\Leftrightarrow & 20x-\frac{25}{3}& = & 9x+\frac{5}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{240}{ \color{blue}{12} }x- \frac{100}{ \color{blue}{12} })& = & (\frac{108}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 240x \color{red}{-100} & = & \color{red}{108x} +5 \\\Leftrightarrow & 240x \color{red}{-100} \color{blue}{+100} \color{blue}{-108x} & = & \color{red}{108x} +5 \color{blue}{-108x} \color{blue}{+100} \\\Leftrightarrow & 240x-108x& = & 5+100 \\\Leftrightarrow & \color{red}{132} x& = & 105 \\\Leftrightarrow & x = \frac{105}{132} & & \\\Leftrightarrow & x = \frac{35}{44} & & \\ & V = \left\{ \frac{35}{44} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{4}{9})& = & 9x+\frac{2}{3} \\\Leftrightarrow & -8x+\frac{16}{9}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x+ \frac{16}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{+16} & = & \color{red}{81x} +6 \\\Leftrightarrow & -72x \color{red}{+16} \color{blue}{-16} \color{blue}{-81x} & = & \color{red}{81x} +6 \color{blue}{-81x} \color{blue}{-16} \\\Leftrightarrow & -72x-81x& = & 6-16 \\\Leftrightarrow & \color{red}{-153} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-153} & & \\\Leftrightarrow & x = \frac{10}{153} & & \\ & V = \left\{ \frac{10}{153} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{7})& = & 3x+\frac{2}{3} \\\Leftrightarrow & 4x+\frac{8}{7}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{+24} & = & \color{red}{63x} +14 \\\Leftrightarrow & 84x \color{red}{+24} \color{blue}{-24} \color{blue}{-63x} & = & \color{red}{63x} +14 \color{blue}{-63x} \color{blue}{-24} \\\Leftrightarrow & 84x-63x& = & 14-24 \\\Leftrightarrow & \color{red}{21} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{21} & & \\ & V = \left\{ \frac{-10}{21} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{9})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 21x+\frac{14}{9}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2079}{ \color{blue}{99} }x+ \frac{154}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2079x \color{red}{+154} & = & \color{red}{-495x} +54 \\\Leftrightarrow & 2079x \color{red}{+154} \color{blue}{-154} \color{blue}{+495x} & = & \color{red}{-495x} +54 \color{blue}{+495x} \color{blue}{-154} \\\Leftrightarrow & 2079x+495x& = & 54-154 \\\Leftrightarrow & \color{red}{2574} x& = & -100 \\\Leftrightarrow & x = \frac{-100}{2574} & & \\\Leftrightarrow & x = \frac{-50}{1287} & & \\ & V = \left\{ \frac{-50}{1287} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{5}{7})& = & 7x+\frac{9}{4} \\\Leftrightarrow & -6x-\frac{10}{7}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-168}{ \color{blue}{28} }x- \frac{40}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -168x \color{red}{-40} & = & \color{red}{196x} +63 \\\Leftrightarrow & -168x \color{red}{-40} \color{blue}{+40} \color{blue}{-196x} & = & \color{red}{196x} +63 \color{blue}{-196x} \color{blue}{+40} \\\Leftrightarrow & -168x-196x& = & 63+40 \\\Leftrightarrow & \color{red}{-364} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-364} & & \\\Leftrightarrow & x = \frac{-103}{364} & & \\ & V = \left\{ \frac{-103}{364} \right\} & \\\end{align}\)
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