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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{3}{11})& = & 7x+\frac{3}{7} \\\Leftrightarrow & 18x+\frac{18}{11}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{+126} & = & \color{red}{539x} +33 \\\Leftrightarrow & 1386x \color{red}{+126} \color{blue}{-126} \color{blue}{-539x} & = & \color{red}{539x} +33 \color{blue}{-539x} \color{blue}{-126} \\\Leftrightarrow & 1386x-539x& = & 33-126 \\\Leftrightarrow & \color{red}{847} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{847} & & \\ & V = \left\{ \frac{-93}{847} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{3}{7})& = & -5x+\frac{8}{5} \\\Leftrightarrow & 12x-\frac{12}{7}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{60}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-60} & = & \color{red}{-175x} +56 \\\Leftrightarrow & 420x \color{red}{-60} \color{blue}{+60} \color{blue}{+175x} & = & \color{red}{-175x} +56 \color{blue}{+175x} \color{blue}{+60} \\\Leftrightarrow & 420x+175x& = & 56+60 \\\Leftrightarrow & \color{red}{595} x& = & 116 \\\Leftrightarrow & x = \frac{116}{595} & & \\ & V = \left\{ \frac{116}{595} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{4}{3})& = & -7x+\frac{7}{9} \\\Leftrightarrow & 10x-\frac{20}{3}& = & -7x+\frac{7}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x- \frac{60}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{-60} & = & \color{red}{-63x} +7 \\\Leftrightarrow & 90x \color{red}{-60} \color{blue}{+60} \color{blue}{+63x} & = & \color{red}{-63x} +7 \color{blue}{+63x} \color{blue}{+60} \\\Leftrightarrow & 90x+63x& = & 7+60 \\\Leftrightarrow & \color{red}{153} x& = & 67 \\\Leftrightarrow & x = \frac{67}{153} & & \\ & V = \left\{ \frac{67}{153} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{3}{5})& = & 3x+\frac{9}{2} \\\Leftrightarrow & -8x+\frac{6}{5}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} })& = & (\frac{30}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{+12} & = & \color{red}{30x} +45 \\\Leftrightarrow & -80x \color{red}{+12} \color{blue}{-12} \color{blue}{-30x} & = & \color{red}{30x} +45 \color{blue}{-30x} \color{blue}{-12} \\\Leftrightarrow & -80x-30x& = & 45-12 \\\Leftrightarrow & \color{red}{-110} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-110} & & \\\Leftrightarrow & x = \frac{-3}{10} & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{3}{4})& = & 8x+\frac{8}{3} \\\Leftrightarrow & -25x-\frac{15}{4}& = & 8x+\frac{8}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-300}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -300x \color{red}{-45} & = & \color{red}{96x} +32 \\\Leftrightarrow & -300x \color{red}{-45} \color{blue}{+45} \color{blue}{-96x} & = & \color{red}{96x} +32 \color{blue}{-96x} \color{blue}{+45} \\\Leftrightarrow & -300x-96x& = & 32+45 \\\Leftrightarrow & \color{red}{-396} x& = & 77 \\\Leftrightarrow & x = \frac{77}{-396} & & \\\Leftrightarrow & x = \frac{-7}{36} & & \\ & V = \left\{ \frac{-7}{36} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{5}{12})& = & -2x+\frac{8}{3} \\\Leftrightarrow & -25x+\frac{25}{12}& = & -2x+\frac{8}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-300}{ \color{blue}{12} }x+ \frac{25}{ \color{blue}{12} })& = & (\frac{-24}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -300x \color{red}{+25} & = & \color{red}{-24x} +32 \\\Leftrightarrow & -300x \color{red}{+25} \color{blue}{-25} \color{blue}{+24x} & = & \color{red}{-24x} +32 \color{blue}{+24x} \color{blue}{-25} \\\Leftrightarrow & -300x+24x& = & 32-25 \\\Leftrightarrow & \color{red}{-276} x& = & 7 \\\Leftrightarrow & x = \frac{7}{-276} & & \\\Leftrightarrow & x = \frac{-7}{276} & & \\ & V = \left\{ \frac{-7}{276} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{4}{3})& = & -6x+\frac{9}{2} \\\Leftrightarrow & -35x-\frac{28}{3}& = & -6x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-210}{ \color{blue}{6} }x- \frac{56}{ \color{blue}{6} })& = & (\frac{-36}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -210x \color{red}{-56} & = & \color{red}{-36x} +27 \\\Leftrightarrow & -210x \color{red}{-56} \color{blue}{+56} \color{blue}{+36x} & = & \color{red}{-36x} +27 \color{blue}{+36x} \color{blue}{+56} \\\Leftrightarrow & -210x+36x& = & 27+56 \\\Leftrightarrow & \color{red}{-174} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-174} & & \\\Leftrightarrow & x = \frac{-83}{174} & & \\ & V = \left\{ \frac{-83}{174} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{3}{2})& = & -8x+\frac{7}{8} \\\Leftrightarrow & 15x-\frac{9}{2}& = & -8x+\frac{7}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{120}{ \color{blue}{8} }x- \frac{36}{ \color{blue}{8} })& = & (\frac{-64}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 120x \color{red}{-36} & = & \color{red}{-64x} +7 \\\Leftrightarrow & 120x \color{red}{-36} \color{blue}{+36} \color{blue}{+64x} & = & \color{red}{-64x} +7 \color{blue}{+64x} \color{blue}{+36} \\\Leftrightarrow & 120x+64x& = & 7+36 \\\Leftrightarrow & \color{red}{184} x& = & 43 \\\Leftrightarrow & x = \frac{43}{184} & & \\ & V = \left\{ \frac{43}{184} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{4})& = & -9x+\frac{7}{8} \\\Leftrightarrow & 20x-\frac{25}{4}& = & -9x+\frac{7}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{160}{ \color{blue}{8} }x- \frac{50}{ \color{blue}{8} })& = & (\frac{-72}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 160x \color{red}{-50} & = & \color{red}{-72x} +7 \\\Leftrightarrow & 160x \color{red}{-50} \color{blue}{+50} \color{blue}{+72x} & = & \color{red}{-72x} +7 \color{blue}{+72x} \color{blue}{+50} \\\Leftrightarrow & 160x+72x& = & 7+50 \\\Leftrightarrow & \color{red}{232} x& = & 57 \\\Leftrightarrow & x = \frac{57}{232} & & \\ & V = \left\{ \frac{57}{232} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{5}{7})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 12x-\frac{30}{7}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{336}{ \color{blue}{28} }x- \frac{120}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 336x \color{red}{-120} & = & \color{red}{-140x} +63 \\\Leftrightarrow & 336x \color{red}{-120} \color{blue}{+120} \color{blue}{+140x} & = & \color{red}{-140x} +63 \color{blue}{+140x} \color{blue}{+120} \\\Leftrightarrow & 336x+140x& = & 63+120 \\\Leftrightarrow & \color{red}{476} x& = & 183 \\\Leftrightarrow & x = \frac{183}{476} & & \\ & V = \left\{ \frac{183}{476} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{3}{11})& = & -8x+\frac{9}{2} \\\Leftrightarrow & -21x-\frac{21}{11}& = & -8x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-462}{ \color{blue}{22} }x- \frac{42}{ \color{blue}{22} })& = & (\frac{-176}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -462x \color{red}{-42} & = & \color{red}{-176x} +99 \\\Leftrightarrow & -462x \color{red}{-42} \color{blue}{+42} \color{blue}{+176x} & = & \color{red}{-176x} +99 \color{blue}{+176x} \color{blue}{+42} \\\Leftrightarrow & -462x+176x& = & 99+42 \\\Leftrightarrow & \color{red}{-286} x& = & 141 \\\Leftrightarrow & x = \frac{141}{-286} & & \\\Leftrightarrow & x = \frac{-141}{286} & & \\ & V = \left\{ \frac{-141}{286} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{3}{10})& = & -5x+\frac{4}{7} \\\Leftrightarrow & -12x-\frac{9}{10}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 10 en 7 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-840}{ \color{blue}{70} }x- \frac{63}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{40}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -840x \color{red}{-63} & = & \color{red}{-350x} +40 \\\Leftrightarrow & -840x \color{red}{-63} \color{blue}{+63} \color{blue}{+350x} & = & \color{red}{-350x} +40 \color{blue}{+350x} \color{blue}{+63} \\\Leftrightarrow & -840x+350x& = & 40+63 \\\Leftrightarrow & \color{red}{-490} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-490} & & \\\Leftrightarrow & x = \frac{-103}{490} & & \\ & V = \left\{ \frac{-103}{490} \right\} & \\\end{align}\)
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