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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{2}{5})& = & -7x+\frac{7}{10} \\\Leftrightarrow & 9x-\frac{6}{5}& = & -7x+\frac{7}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{90}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 90x \color{red}{-12} & = & \color{red}{-70x} +7 \\\Leftrightarrow & 90x \color{red}{-12} \color{blue}{+12} \color{blue}{+70x} & = & \color{red}{-70x} +7 \color{blue}{+70x} \color{blue}{+12} \\\Leftrightarrow & 90x+70x& = & 7+12 \\\Leftrightarrow & \color{red}{160} x& = & 19 \\\Leftrightarrow & x = \frac{19}{160} & & \\ & V = \left\{ \frac{19}{160} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{3}{5})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -16x+\frac{12}{5}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-880}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -880x \color{red}{+132} & = & \color{red}{-385x} +25 \\\Leftrightarrow & -880x \color{red}{+132} \color{blue}{-132} \color{blue}{+385x} & = & \color{red}{-385x} +25 \color{blue}{+385x} \color{blue}{-132} \\\Leftrightarrow & -880x+385x& = & 25-132 \\\Leftrightarrow & \color{red}{-495} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{-495} & & \\\Leftrightarrow & x = \frac{107}{495} & & \\ & V = \left\{ \frac{107}{495} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{11})& = & -7x+\frac{7}{3} \\\Leftrightarrow & -30x-\frac{18}{11}& = & -7x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-990}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -990x \color{red}{-54} & = & \color{red}{-231x} +77 \\\Leftrightarrow & -990x \color{red}{-54} \color{blue}{+54} \color{blue}{+231x} & = & \color{red}{-231x} +77 \color{blue}{+231x} \color{blue}{+54} \\\Leftrightarrow & -990x+231x& = & 77+54 \\\Leftrightarrow & \color{red}{-759} x& = & 131 \\\Leftrightarrow & x = \frac{131}{-759} & & \\\Leftrightarrow & x = \frac{-131}{759} & & \\ & V = \left\{ \frac{-131}{759} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{2}{7})& = & 4x+\frac{6}{11} \\\Leftrightarrow & -15x+\frac{10}{7}& = & 4x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{308}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{+110} & = & \color{red}{308x} +42 \\\Leftrightarrow & -1155x \color{red}{+110} \color{blue}{-110} \color{blue}{-308x} & = & \color{red}{308x} +42 \color{blue}{-308x} \color{blue}{-110} \\\Leftrightarrow & -1155x-308x& = & 42-110 \\\Leftrightarrow & \color{red}{-1463} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{-1463} & & \\\Leftrightarrow & x = \frac{68}{1463} & & \\ & V = \left\{ \frac{68}{1463} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{4}{3})& = & -9x+\frac{4}{7} \\\Leftrightarrow & -8x-\frac{8}{3}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{-56} & = & \color{red}{-189x} +12 \\\Leftrightarrow & -168x \color{red}{-56} \color{blue}{+56} \color{blue}{+189x} & = & \color{red}{-189x} +12 \color{blue}{+189x} \color{blue}{+56} \\\Leftrightarrow & -168x+189x& = & 12+56 \\\Leftrightarrow & \color{red}{21} x& = & 68 \\\Leftrightarrow & x = \frac{68}{21} & & \\ & V = \left\{ \frac{68}{21} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{4}{5})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 18x-\frac{24}{5}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x- \frac{168}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{-168} & = & \color{red}{175x} +10 \\\Leftrightarrow & 630x \color{red}{-168} \color{blue}{+168} \color{blue}{-175x} & = & \color{red}{175x} +10 \color{blue}{-175x} \color{blue}{+168} \\\Leftrightarrow & 630x-175x& = & 10+168 \\\Leftrightarrow & \color{red}{455} x& = & 178 \\\Leftrightarrow & x = \frac{178}{455} & & \\ & V = \left\{ \frac{178}{455} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{3}{11})& = & 2x+\frac{5}{11} \\\Leftrightarrow & 9x-\frac{9}{11}& = & 2x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{99}{ \color{blue}{11} }x- \frac{9}{ \color{blue}{11} })& = & (\frac{22}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 99x \color{red}{-9} & = & \color{red}{22x} +5 \\\Leftrightarrow & 99x \color{red}{-9} \color{blue}{+9} \color{blue}{-22x} & = & \color{red}{22x} +5 \color{blue}{-22x} \color{blue}{+9} \\\Leftrightarrow & 99x-22x& = & 5+9 \\\Leftrightarrow & \color{red}{77} x& = & 14 \\\Leftrightarrow & x = \frac{14}{77} & & \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{5}{9})& = & -3x+\frac{3}{2} \\\Leftrightarrow & -35x+\frac{35}{9}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-630}{ \color{blue}{18} }x+ \frac{70}{ \color{blue}{18} })& = & (\frac{-54}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -630x \color{red}{+70} & = & \color{red}{-54x} +27 \\\Leftrightarrow & -630x \color{red}{+70} \color{blue}{-70} \color{blue}{+54x} & = & \color{red}{-54x} +27 \color{blue}{+54x} \color{blue}{-70} \\\Leftrightarrow & -630x+54x& = & 27-70 \\\Leftrightarrow & \color{red}{-576} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-576} & & \\\Leftrightarrow & x = \frac{43}{576} & & \\ & V = \left\{ \frac{43}{576} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{3}{5})& = & 9x+\frac{9}{7} \\\Leftrightarrow & -8x-\frac{6}{5}& = & 9x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{-42} & = & \color{red}{315x} +45 \\\Leftrightarrow & -280x \color{red}{-42} \color{blue}{+42} \color{blue}{-315x} & = & \color{red}{315x} +45 \color{blue}{-315x} \color{blue}{+42} \\\Leftrightarrow & -280x-315x& = & 45+42 \\\Leftrightarrow & \color{red}{-595} x& = & 87 \\\Leftrightarrow & x = \frac{87}{-595} & & \\\Leftrightarrow & x = \frac{-87}{595} & & \\ & V = \left\{ \frac{-87}{595} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{4}{5})& = & 2x+\frac{9}{4} \\\Leftrightarrow & 9x-\frac{12}{5}& = & 2x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{180}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{40}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 180x \color{red}{-48} & = & \color{red}{40x} +45 \\\Leftrightarrow & 180x \color{red}{-48} \color{blue}{+48} \color{blue}{-40x} & = & \color{red}{40x} +45 \color{blue}{-40x} \color{blue}{+48} \\\Leftrightarrow & 180x-40x& = & 45+48 \\\Leftrightarrow & \color{red}{140} x& = & 93 \\\Leftrightarrow & x = \frac{93}{140} & & \\ & V = \left\{ \frac{93}{140} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{4}{11})& = & 3x+\frac{4}{7} \\\Leftrightarrow & 20x-\frac{16}{11}& = & 3x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x- \frac{112}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{-112} & = & \color{red}{231x} +44 \\\Leftrightarrow & 1540x \color{red}{-112} \color{blue}{+112} \color{blue}{-231x} & = & \color{red}{231x} +44 \color{blue}{-231x} \color{blue}{+112} \\\Leftrightarrow & 1540x-231x& = & 44+112 \\\Leftrightarrow & \color{red}{1309} x& = & 156 \\\Leftrightarrow & x = \frac{156}{1309} & & \\ & V = \left\{ \frac{156}{1309} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{5}{7})& = & 5x+\frac{3}{7} \\\Leftrightarrow & 4x+\frac{10}{7}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{28}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 28x \color{red}{+10} & = & \color{red}{35x} +3 \\\Leftrightarrow & 28x \color{red}{+10} \color{blue}{-10} \color{blue}{-35x} & = & \color{red}{35x} +3 \color{blue}{-35x} \color{blue}{-10} \\\Leftrightarrow & 28x-35x& = & 3-10 \\\Leftrightarrow & \color{red}{-7} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-7} & & \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
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