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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{3}{5})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -6x-\frac{9}{5}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x- \frac{18}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{-18} & = & \color{red}{70x} +15 \\\Leftrightarrow & -60x \color{red}{-18} \color{blue}{+18} \color{blue}{-70x} & = & \color{red}{70x} +15 \color{blue}{-70x} \color{blue}{+18} \\\Leftrightarrow & -60x-70x& = & 15+18 \\\Leftrightarrow & \color{red}{-130} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-130} & & \\\Leftrightarrow & x = \frac{-33}{130} & & \\ & V = \left\{ \frac{-33}{130} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{3}{4})& = & -2x+\frac{6}{7} \\\Leftrightarrow & 15x-\frac{15}{4}& = & -2x+\frac{6}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{420}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-56}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 420x \color{red}{-105} & = & \color{red}{-56x} +24 \\\Leftrightarrow & 420x \color{red}{-105} \color{blue}{+105} \color{blue}{+56x} & = & \color{red}{-56x} +24 \color{blue}{+56x} \color{blue}{+105} \\\Leftrightarrow & 420x+56x& = & 24+105 \\\Leftrightarrow & \color{red}{476} x& = & 129 \\\Leftrightarrow & x = \frac{129}{476} & & \\ & V = \left\{ \frac{129}{476} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{2}{3})& = & 2x+\frac{3}{2} \\\Leftrightarrow & -28x-\frac{14}{3}& = & 2x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-168}{ \color{blue}{6} }x- \frac{28}{ \color{blue}{6} })& = & (\frac{12}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -168x \color{red}{-28} & = & \color{red}{12x} +9 \\\Leftrightarrow & -168x \color{red}{-28} \color{blue}{+28} \color{blue}{-12x} & = & \color{red}{12x} +9 \color{blue}{-12x} \color{blue}{+28} \\\Leftrightarrow & -168x-12x& = & 9+28 \\\Leftrightarrow & \color{red}{-180} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-180} & & \\\Leftrightarrow & x = \frac{-37}{180} & & \\ & V = \left\{ \frac{-37}{180} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{5}{12})& = & 3x+\frac{5}{6} \\\Leftrightarrow & -14x-\frac{35}{12}& = & 3x+\frac{5}{6} \\ & & & \text{kgv van noemers 12 en 6 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-168}{ \color{blue}{12} }x- \frac{35}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{10}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -168x \color{red}{-35} & = & \color{red}{36x} +10 \\\Leftrightarrow & -168x \color{red}{-35} \color{blue}{+35} \color{blue}{-36x} & = & \color{red}{36x} +10 \color{blue}{-36x} \color{blue}{+35} \\\Leftrightarrow & -168x-36x& = & 10+35 \\\Leftrightarrow & \color{red}{-204} x& = & 45 \\\Leftrightarrow & x = \frac{45}{-204} & & \\\Leftrightarrow & x = \frac{-15}{68} & & \\ & V = \left\{ \frac{-15}{68} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{4}{3})& = & 4x+\frac{10}{7} \\\Leftrightarrow & 15x+\frac{20}{3}& = & 4x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{84}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{+140} & = & \color{red}{84x} +30 \\\Leftrightarrow & 315x \color{red}{+140} \color{blue}{-140} \color{blue}{-84x} & = & \color{red}{84x} +30 \color{blue}{-84x} \color{blue}{-140} \\\Leftrightarrow & 315x-84x& = & 30-140 \\\Leftrightarrow & \color{red}{231} x& = & -110 \\\Leftrightarrow & x = \frac{-110}{231} & & \\\Leftrightarrow & x = \frac{-10}{21} & & \\ & V = \left\{ \frac{-10}{21} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{4}{3})& = & -7x+\frac{5}{6} \\\Leftrightarrow & -10x-\frac{8}{3}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-60}{ \color{blue}{6} }x- \frac{16}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -60x \color{red}{-16} & = & \color{red}{-42x} +5 \\\Leftrightarrow & -60x \color{red}{-16} \color{blue}{+16} \color{blue}{+42x} & = & \color{red}{-42x} +5 \color{blue}{+42x} \color{blue}{+16} \\\Leftrightarrow & -60x+42x& = & 5+16 \\\Leftrightarrow & \color{red}{-18} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-18} & & \\\Leftrightarrow & x = \frac{-7}{6} & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{3}{11})& = & -8x+\frac{10}{7} \\\Leftrightarrow & -21x-\frac{21}{11}& = & -8x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1617}{ \color{blue}{77} }x- \frac{147}{ \color{blue}{77} })& = & (\frac{-616}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1617x \color{red}{-147} & = & \color{red}{-616x} +110 \\\Leftrightarrow & -1617x \color{red}{-147} \color{blue}{+147} \color{blue}{+616x} & = & \color{red}{-616x} +110 \color{blue}{+616x} \color{blue}{+147} \\\Leftrightarrow & -1617x+616x& = & 110+147 \\\Leftrightarrow & \color{red}{-1001} x& = & 257 \\\Leftrightarrow & x = \frac{257}{-1001} & & \\\Leftrightarrow & x = \frac{-257}{1001} & & \\ & V = \left\{ \frac{-257}{1001} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{2}{11})& = & -9x+\frac{10}{3} \\\Leftrightarrow & -4x-\frac{4}{11}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-132}{ \color{blue}{33} }x- \frac{12}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -132x \color{red}{-12} & = & \color{red}{-297x} +110 \\\Leftrightarrow & -132x \color{red}{-12} \color{blue}{+12} \color{blue}{+297x} & = & \color{red}{-297x} +110 \color{blue}{+297x} \color{blue}{+12} \\\Leftrightarrow & -132x+297x& = & 110+12 \\\Leftrightarrow & \color{red}{165} x& = & 122 \\\Leftrightarrow & x = \frac{122}{165} & & \\ & V = \left\{ \frac{122}{165} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{2}{9})& = & 4x+\frac{6}{11} \\\Leftrightarrow & 25x+\frac{10}{9}& = & 4x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2475}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} })& = & (\frac{396}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2475x \color{red}{+110} & = & \color{red}{396x} +54 \\\Leftrightarrow & 2475x \color{red}{+110} \color{blue}{-110} \color{blue}{-396x} & = & \color{red}{396x} +54 \color{blue}{-396x} \color{blue}{-110} \\\Leftrightarrow & 2475x-396x& = & 54-110 \\\Leftrightarrow & \color{red}{2079} x& = & -56 \\\Leftrightarrow & x = \frac{-56}{2079} & & \\\Leftrightarrow & x = \frac{-8}{297} & & \\ & V = \left\{ \frac{-8}{297} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{3})& = & 9x+\frac{10}{9} \\\Leftrightarrow & -8x+\frac{8}{3}& = & 9x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{+24} & = & \color{red}{81x} +10 \\\Leftrightarrow & -72x \color{red}{+24} \color{blue}{-24} \color{blue}{-81x} & = & \color{red}{81x} +10 \color{blue}{-81x} \color{blue}{-24} \\\Leftrightarrow & -72x-81x& = & 10-24 \\\Leftrightarrow & \color{red}{-153} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-153} & & \\\Leftrightarrow & x = \frac{14}{153} & & \\ & V = \left\{ \frac{14}{153} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{4}{11})& = & -5x+\frac{3}{10} \\\Leftrightarrow & 12x-\frac{24}{11}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1320}{ \color{blue}{110} }x- \frac{240}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1320x \color{red}{-240} & = & \color{red}{-550x} +33 \\\Leftrightarrow & 1320x \color{red}{-240} \color{blue}{+240} \color{blue}{+550x} & = & \color{red}{-550x} +33 \color{blue}{+550x} \color{blue}{+240} \\\Leftrightarrow & 1320x+550x& = & 33+240 \\\Leftrightarrow & \color{red}{1870} x& = & 273 \\\Leftrightarrow & x = \frac{273}{1870} & & \\ & V = \left\{ \frac{273}{1870} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{4}{7})& = & 7x+\frac{5}{2} \\\Leftrightarrow & 20x-\frac{16}{7}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{280}{ \color{blue}{14} }x- \frac{32}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 280x \color{red}{-32} & = & \color{red}{98x} +35 \\\Leftrightarrow & 280x \color{red}{-32} \color{blue}{+32} \color{blue}{-98x} & = & \color{red}{98x} +35 \color{blue}{-98x} \color{blue}{+32} \\\Leftrightarrow & 280x-98x& = & 35+32 \\\Leftrightarrow & \color{red}{182} x& = & 67 \\\Leftrightarrow & x = \frac{67}{182} & & \\ & V = \left\{ \frac{67}{182} \right\} & \\\end{align}\)
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