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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{2}{11})& = & 2x+\frac{4}{5} \\\Leftrightarrow & 15x-\frac{6}{11}& = & 2x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x- \frac{30}{ \color{blue}{55} })& = & (\frac{110}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{-30} & = & \color{red}{110x} +44 \\\Leftrightarrow & 825x \color{red}{-30} \color{blue}{+30} \color{blue}{-110x} & = & \color{red}{110x} +44 \color{blue}{-110x} \color{blue}{+30} \\\Leftrightarrow & 825x-110x& = & 44+30 \\\Leftrightarrow & \color{red}{715} x& = & 74 \\\Leftrightarrow & x = \frac{74}{715} & & \\ & V = \left\{ \frac{74}{715} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{9})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -28x-\frac{28}{9}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-252}{ \color{blue}{9} }x- \frac{28}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -252x \color{red}{-28} & = & \color{red}{-63x} +30 \\\Leftrightarrow & -252x \color{red}{-28} \color{blue}{+28} \color{blue}{+63x} & = & \color{red}{-63x} +30 \color{blue}{+63x} \color{blue}{+28} \\\Leftrightarrow & -252x+63x& = & 30+28 \\\Leftrightarrow & \color{red}{-189} x& = & 58 \\\Leftrightarrow & x = \frac{58}{-189} & & \\\Leftrightarrow & x = \frac{-58}{189} & & \\ & V = \left\{ \frac{-58}{189} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{2}{5})& = & -5x+\frac{4}{9} \\\Leftrightarrow & -18x+\frac{12}{5}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-810}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -810x \color{red}{+108} & = & \color{red}{-225x} +20 \\\Leftrightarrow & -810x \color{red}{+108} \color{blue}{-108} \color{blue}{+225x} & = & \color{red}{-225x} +20 \color{blue}{+225x} \color{blue}{-108} \\\Leftrightarrow & -810x+225x& = & 20-108 \\\Leftrightarrow & \color{red}{-585} x& = & -88 \\\Leftrightarrow & x = \frac{-88}{-585} & & \\\Leftrightarrow & x = \frac{88}{585} & & \\ & V = \left\{ \frac{88}{585} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{2}{3})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 8x+\frac{8}{3}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{96}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 96x \color{red}{+32} & = & \color{red}{-60x} +27 \\\Leftrightarrow & 96x \color{red}{+32} \color{blue}{-32} \color{blue}{+60x} & = & \color{red}{-60x} +27 \color{blue}{+60x} \color{blue}{-32} \\\Leftrightarrow & 96x+60x& = & 27-32 \\\Leftrightarrow & \color{red}{156} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{156} & & \\ & V = \left\{ \frac{-5}{156} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{5})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -30x-\frac{18}{5}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-450}{ \color{blue}{15} }x- \frac{54}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -450x \color{red}{-54} & = & \color{red}{-105x} +10 \\\Leftrightarrow & -450x \color{red}{-54} \color{blue}{+54} \color{blue}{+105x} & = & \color{red}{-105x} +10 \color{blue}{+105x} \color{blue}{+54} \\\Leftrightarrow & -450x+105x& = & 10+54 \\\Leftrightarrow & \color{red}{-345} x& = & 64 \\\Leftrightarrow & x = \frac{64}{-345} & & \\\Leftrightarrow & x = \frac{-64}{345} & & \\ & V = \left\{ \frac{-64}{345} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{4}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -9x+\frac{12}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-45}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -45x \color{red}{+12} & = & \color{red}{-25x} +6 \\\Leftrightarrow & -45x \color{red}{+12} \color{blue}{-12} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{-12} \\\Leftrightarrow & -45x+25x& = & 6-12 \\\Leftrightarrow & \color{red}{-20} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-20} & & \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{4}{7})& = & -7x+\frac{5}{7} \\\Leftrightarrow & -16x+\frac{16}{7}& = & -7x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-112}{ \color{blue}{7} }x+ \frac{16}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -112x \color{red}{+16} & = & \color{red}{-49x} +5 \\\Leftrightarrow & -112x \color{red}{+16} \color{blue}{-16} \color{blue}{+49x} & = & \color{red}{-49x} +5 \color{blue}{+49x} \color{blue}{-16} \\\Leftrightarrow & -112x+49x& = & 5-16 \\\Leftrightarrow & \color{red}{-63} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-63} & & \\\Leftrightarrow & x = \frac{11}{63} & & \\ & V = \left\{ \frac{11}{63} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{2}{5})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 24x-\frac{12}{5}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{840}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 840x \color{red}{-84} & = & \color{red}{-175x} +15 \\\Leftrightarrow & 840x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +15 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & 840x+175x& = & 15+84 \\\Leftrightarrow & \color{red}{1015} x& = & 99 \\\Leftrightarrow & x = \frac{99}{1015} & & \\ & V = \left\{ \frac{99}{1015} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{3}{5})& = & -5x+\frac{8}{9} \\\Leftrightarrow & -4x-\frac{6}{5}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-180}{ \color{blue}{45} }x- \frac{54}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -180x \color{red}{-54} & = & \color{red}{-225x} +40 \\\Leftrightarrow & -180x \color{red}{-54} \color{blue}{+54} \color{blue}{+225x} & = & \color{red}{-225x} +40 \color{blue}{+225x} \color{blue}{+54} \\\Leftrightarrow & -180x+225x& = & 40+54 \\\Leftrightarrow & \color{red}{45} x& = & 94 \\\Leftrightarrow & x = \frac{94}{45} & & \\ & V = \left\{ \frac{94}{45} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{2}{7})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 6x-\frac{6}{7}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{84}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 84x \color{red}{-12} & = & \color{red}{70x} +21 \\\Leftrightarrow & 84x \color{red}{-12} \color{blue}{+12} \color{blue}{-70x} & = & \color{red}{70x} +21 \color{blue}{-70x} \color{blue}{+12} \\\Leftrightarrow & 84x-70x& = & 21+12 \\\Leftrightarrow & \color{red}{14} x& = & 33 \\\Leftrightarrow & x = \frac{33}{14} & & \\ & V = \left\{ \frac{33}{14} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{5}{3})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -16x+\frac{20}{3}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-48}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -48x \color{red}{+20} & = & \color{red}{21x} +2 \\\Leftrightarrow & -48x \color{red}{+20} \color{blue}{-20} \color{blue}{-21x} & = & \color{red}{21x} +2 \color{blue}{-21x} \color{blue}{-20} \\\Leftrightarrow & -48x-21x& = & 2-20 \\\Leftrightarrow & \color{red}{-69} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-69} & & \\\Leftrightarrow & x = \frac{6}{23} & & \\ & V = \left\{ \frac{6}{23} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{4}{9})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 6x+\frac{8}{9}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{108}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 108x \color{red}{+16} & = & \color{red}{-90x} +15 \\\Leftrightarrow & 108x \color{red}{+16} \color{blue}{-16} \color{blue}{+90x} & = & \color{red}{-90x} +15 \color{blue}{+90x} \color{blue}{-16} \\\Leftrightarrow & 108x+90x& = & 15-16 \\\Leftrightarrow & \color{red}{198} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{198} & & \\ & V = \left\{ \frac{-1}{198} \right\} & \\\end{align}\)
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