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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{3}{5})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -18x-\frac{18}{5}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-270}{ \color{blue}{15} }x- \frac{54}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -270x \color{red}{-54} & = & \color{red}{75x} +10 \\\Leftrightarrow & -270x \color{red}{-54} \color{blue}{+54} \color{blue}{-75x} & = & \color{red}{75x} +10 \color{blue}{-75x} \color{blue}{+54} \\\Leftrightarrow & -270x-75x& = & 10+54 \\\Leftrightarrow & \color{red}{-345} x& = & 64 \\\Leftrightarrow & x = \frac{64}{-345} & & \\\Leftrightarrow & x = \frac{-64}{345} & & \\ & V = \left\{ \frac{-64}{345} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{11})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -28x-\frac{28}{11}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-616}{ \color{blue}{22} }x- \frac{56}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -616x \color{red}{-56} & = & \color{red}{154x} +33 \\\Leftrightarrow & -616x \color{red}{-56} \color{blue}{+56} \color{blue}{-154x} & = & \color{red}{154x} +33 \color{blue}{-154x} \color{blue}{+56} \\\Leftrightarrow & -616x-154x& = & 33+56 \\\Leftrightarrow & \color{red}{-770} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-770} & & \\\Leftrightarrow & x = \frac{-89}{770} & & \\ & V = \left\{ \frac{-89}{770} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{3}{11})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -24x+\frac{18}{11}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-264}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -264x \color{red}{+18} & = & \color{red}{55x} +2 \\\Leftrightarrow & -264x \color{red}{+18} \color{blue}{-18} \color{blue}{-55x} & = & \color{red}{55x} +2 \color{blue}{-55x} \color{blue}{-18} \\\Leftrightarrow & -264x-55x& = & 2-18 \\\Leftrightarrow & \color{red}{-319} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-319} & & \\\Leftrightarrow & x = \frac{16}{319} & & \\ & V = \left\{ \frac{16}{319} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{4}{3})& = & -8x+\frac{3}{7} \\\Leftrightarrow & 21x+\frac{28}{3}& = & -8x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{441}{ \color{blue}{21} }x+ \frac{196}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 441x \color{red}{+196} & = & \color{red}{-168x} +9 \\\Leftrightarrow & 441x \color{red}{+196} \color{blue}{-196} \color{blue}{+168x} & = & \color{red}{-168x} +9 \color{blue}{+168x} \color{blue}{-196} \\\Leftrightarrow & 441x+168x& = & 9-196 \\\Leftrightarrow & \color{red}{609} x& = & -187 \\\Leftrightarrow & x = \frac{-187}{609} & & \\ & V = \left\{ \frac{-187}{609} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{2}{9})& = & -8x+\frac{10}{3} \\\Leftrightarrow & -21x+\frac{14}{9}& = & -8x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-189}{ \color{blue}{9} }x+ \frac{14}{ \color{blue}{9} })& = & (\frac{-72}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -189x \color{red}{+14} & = & \color{red}{-72x} +30 \\\Leftrightarrow & -189x \color{red}{+14} \color{blue}{-14} \color{blue}{+72x} & = & \color{red}{-72x} +30 \color{blue}{+72x} \color{blue}{-14} \\\Leftrightarrow & -189x+72x& = & 30-14 \\\Leftrightarrow & \color{red}{-117} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-117} & & \\\Leftrightarrow & x = \frac{-16}{117} & & \\ & V = \left\{ \frac{-16}{117} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{3}{2})& = & 6x+\frac{10}{3} \\\Leftrightarrow & 25x+\frac{15}{2}& = & 6x+\frac{10}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{150}{ \color{blue}{6} }x+ \frac{45}{ \color{blue}{6} })& = & (\frac{36}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 150x \color{red}{+45} & = & \color{red}{36x} +20 \\\Leftrightarrow & 150x \color{red}{+45} \color{blue}{-45} \color{blue}{-36x} & = & \color{red}{36x} +20 \color{blue}{-36x} \color{blue}{-45} \\\Leftrightarrow & 150x-36x& = & 20-45 \\\Leftrightarrow & \color{red}{114} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{114} & & \\ & V = \left\{ \frac{-25}{114} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{2}{11})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -30x+\frac{12}{11}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x+ \frac{60}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{+60} & = & \color{red}{385x} +66 \\\Leftrightarrow & -1650x \color{red}{+60} \color{blue}{-60} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{-60} \\\Leftrightarrow & -1650x-385x& = & 66-60 \\\Leftrightarrow & \color{red}{-2035} x& = & 6 \\\Leftrightarrow & x = \frac{6}{-2035} & & \\\Leftrightarrow & x = \frac{-6}{2035} & & \\ & V = \left\{ \frac{-6}{2035} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{4}{5})& = & 5x+\frac{5}{3} \\\Leftrightarrow & 6x-\frac{12}{5}& = & 5x+\frac{5}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{90}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{25}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 90x \color{red}{-36} & = & \color{red}{75x} +25 \\\Leftrightarrow & 90x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +25 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & 90x-75x& = & 25+36 \\\Leftrightarrow & \color{red}{15} x& = & 61 \\\Leftrightarrow & x = \frac{61}{15} & & \\ & V = \left\{ \frac{61}{15} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{5}{12})& = & -5x+\frac{5}{11} \\\Leftrightarrow & -28x-\frac{35}{12}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 12 en 11 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-3696}{ \color{blue}{132} }x- \frac{385}{ \color{blue}{132} })& = & (\frac{-660}{ \color{blue}{132} }x+ \frac{60}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -3696x \color{red}{-385} & = & \color{red}{-660x} +60 \\\Leftrightarrow & -3696x \color{red}{-385} \color{blue}{+385} \color{blue}{+660x} & = & \color{red}{-660x} +60 \color{blue}{+660x} \color{blue}{+385} \\\Leftrightarrow & -3696x+660x& = & 60+385 \\\Leftrightarrow & \color{red}{-3036} x& = & 445 \\\Leftrightarrow & x = \frac{445}{-3036} & & \\\Leftrightarrow & x = \frac{-445}{3036} & & \\ & V = \left\{ \frac{-445}{3036} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{5})& = & 3x+\frac{6}{5} \\\Leftrightarrow & -8x+\frac{8}{5}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-40}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} })& = & (\frac{15}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -40x \color{red}{+8} & = & \color{red}{15x} +6 \\\Leftrightarrow & -40x \color{red}{+8} \color{blue}{-8} \color{blue}{-15x} & = & \color{red}{15x} +6 \color{blue}{-15x} \color{blue}{-8} \\\Leftrightarrow & -40x-15x& = & 6-8 \\\Leftrightarrow & \color{red}{-55} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-55} & & \\\Leftrightarrow & x = \frac{2}{55} & & \\ & V = \left\{ \frac{2}{55} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{5}{6})& = & -7x+\frac{7}{12} \\\Leftrightarrow & -10x-\frac{25}{6}& = & -7x+\frac{7}{12} \\ & & & \text{kgv van noemers 6 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-120}{ \color{blue}{12} }x- \frac{50}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -120x \color{red}{-50} & = & \color{red}{-84x} +7 \\\Leftrightarrow & -120x \color{red}{-50} \color{blue}{+50} \color{blue}{+84x} & = & \color{red}{-84x} +7 \color{blue}{+84x} \color{blue}{+50} \\\Leftrightarrow & -120x+84x& = & 7+50 \\\Leftrightarrow & \color{red}{-36} x& = & 57 \\\Leftrightarrow & x = \frac{57}{-36} & & \\\Leftrightarrow & x = \frac{-19}{12} & & \\ & V = \left\{ \frac{-19}{12} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{5}{2})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 6x-\frac{15}{2}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x- \frac{75}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{-75} & = & \color{red}{-50x} +12 \\\Leftrightarrow & 60x \color{red}{-75} \color{blue}{+75} \color{blue}{+50x} & = & \color{red}{-50x} +12 \color{blue}{+50x} \color{blue}{+75} \\\Leftrightarrow & 60x+50x& = & 12+75 \\\Leftrightarrow & \color{red}{110} x& = & 87 \\\Leftrightarrow & x = \frac{87}{110} & & \\ & V = \left\{ \frac{87}{110} \right\} & \\\end{align}\)
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