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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{4}{11})& = & 9x+\frac{2}{3} \\\Leftrightarrow & 4x-\frac{8}{11}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{132}{ \color{blue}{33} }x- \frac{24}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 132x \color{red}{-24} & = & \color{red}{297x} +22 \\\Leftrightarrow & 132x \color{red}{-24} \color{blue}{+24} \color{blue}{-297x} & = & \color{red}{297x} +22 \color{blue}{-297x} \color{blue}{+24} \\\Leftrightarrow & 132x-297x& = & 22+24 \\\Leftrightarrow & \color{red}{-165} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-165} & & \\\Leftrightarrow & x = \frac{-46}{165} & & \\ & V = \left\{ \frac{-46}{165} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{4}{7})& = & 9x+\frac{7}{6} \\\Leftrightarrow & -35x-4& = & 9x+\frac{7}{6} \\ & & & \text{kgv van noemers 1 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-210}{ \color{blue}{6} }x- \frac{24}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -210x \color{red}{-24} & = & \color{red}{54x} +7 \\\Leftrightarrow & -210x \color{red}{-24} \color{blue}{+24} \color{blue}{-54x} & = & \color{red}{54x} +7 \color{blue}{-54x} \color{blue}{+24} \\\Leftrightarrow & -210x-54x& = & 7+24 \\\Leftrightarrow & \color{red}{-264} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-264} & & \\\Leftrightarrow & x = \frac{-31}{264} & & \\ & V = \left\{ \frac{-31}{264} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{2})& = & 7x+\frac{8}{9} \\\Leftrightarrow & -28x+\frac{21}{2}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-504}{ \color{blue}{18} }x+ \frac{189}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -504x \color{red}{+189} & = & \color{red}{126x} +16 \\\Leftrightarrow & -504x \color{red}{+189} \color{blue}{-189} \color{blue}{-126x} & = & \color{red}{126x} +16 \color{blue}{-126x} \color{blue}{-189} \\\Leftrightarrow & -504x-126x& = & 16-189 \\\Leftrightarrow & \color{red}{-630} x& = & -173 \\\Leftrightarrow & x = \frac{-173}{-630} & & \\\Leftrightarrow & x = \frac{173}{630} & & \\ & V = \left\{ \frac{173}{630} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{3}{11})& = & -7x+\frac{3}{7} \\\Leftrightarrow & 30x+\frac{18}{11}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2310}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2310x \color{red}{+126} & = & \color{red}{-539x} +33 \\\Leftrightarrow & 2310x \color{red}{+126} \color{blue}{-126} \color{blue}{+539x} & = & \color{red}{-539x} +33 \color{blue}{+539x} \color{blue}{-126} \\\Leftrightarrow & 2310x+539x& = & 33-126 \\\Leftrightarrow & \color{red}{2849} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{2849} & & \\ & V = \left\{ \frac{-93}{2849} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{4}{11})& = & 3x+\frac{3}{4} \\\Leftrightarrow & 10x-\frac{20}{11}& = & 3x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{440}{ \color{blue}{44} }x- \frac{80}{ \color{blue}{44} })& = & (\frac{132}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 440x \color{red}{-80} & = & \color{red}{132x} +33 \\\Leftrightarrow & 440x \color{red}{-80} \color{blue}{+80} \color{blue}{-132x} & = & \color{red}{132x} +33 \color{blue}{-132x} \color{blue}{+80} \\\Leftrightarrow & 440x-132x& = & 33+80 \\\Leftrightarrow & \color{red}{308} x& = & 113 \\\Leftrightarrow & x = \frac{113}{308} & & \\ & V = \left\{ \frac{113}{308} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{9})& = & 9x+\frac{8}{7} \\\Leftrightarrow & 20x-\frac{20}{9}& = & 9x+\frac{8}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{-140} & = & \color{red}{567x} +72 \\\Leftrightarrow & 1260x \color{red}{-140} \color{blue}{+140} \color{blue}{-567x} & = & \color{red}{567x} +72 \color{blue}{-567x} \color{blue}{+140} \\\Leftrightarrow & 1260x-567x& = & 72+140 \\\Leftrightarrow & \color{red}{693} x& = & 212 \\\Leftrightarrow & x = \frac{212}{693} & & \\ & V = \left\{ \frac{212}{693} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{2}{9})& = & -7x+\frac{5}{12} \\\Leftrightarrow & -6x+\frac{4}{9}& = & -7x+\frac{5}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-216}{ \color{blue}{36} }x+ \frac{16}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{15}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -216x \color{red}{+16} & = & \color{red}{-252x} +15 \\\Leftrightarrow & -216x \color{red}{+16} \color{blue}{-16} \color{blue}{+252x} & = & \color{red}{-252x} +15 \color{blue}{+252x} \color{blue}{-16} \\\Leftrightarrow & -216x+252x& = & 15-16 \\\Leftrightarrow & \color{red}{36} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{36} & & \\ & V = \left\{ \frac{-1}{36} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{3}{8})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -14x+\frac{21}{8}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-560}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -560x \color{red}{+105} & = & \color{red}{-200x} +48 \\\Leftrightarrow & -560x \color{red}{+105} \color{blue}{-105} \color{blue}{+200x} & = & \color{red}{-200x} +48 \color{blue}{+200x} \color{blue}{-105} \\\Leftrightarrow & -560x+200x& = & 48-105 \\\Leftrightarrow & \color{red}{-360} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{-360} & & \\\Leftrightarrow & x = \frac{19}{120} & & \\ & V = \left\{ \frac{19}{120} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{3}{10})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -9x+\frac{9}{10}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-990}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{20}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -990x \color{red}{+99} & = & \color{red}{550x} +20 \\\Leftrightarrow & -990x \color{red}{+99} \color{blue}{-99} \color{blue}{-550x} & = & \color{red}{550x} +20 \color{blue}{-550x} \color{blue}{-99} \\\Leftrightarrow & -990x-550x& = & 20-99 \\\Leftrightarrow & \color{red}{-1540} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{-1540} & & \\\Leftrightarrow & x = \frac{79}{1540} & & \\ & V = \left\{ \frac{79}{1540} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{5}{4})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -9x+\frac{15}{4}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-108}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -108x \color{red}{+45} & = & \color{red}{60x} +40 \\\Leftrightarrow & -108x \color{red}{+45} \color{blue}{-45} \color{blue}{-60x} & = & \color{red}{60x} +40 \color{blue}{-60x} \color{blue}{-45} \\\Leftrightarrow & -108x-60x& = & 40-45 \\\Leftrightarrow & \color{red}{-168} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-168} & & \\\Leftrightarrow & x = \frac{5}{168} & & \\ & V = \left\{ \frac{5}{168} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{3}{4})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 20x-\frac{15}{4}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{240}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 240x \color{red}{-45} & = & \color{red}{36x} +16 \\\Leftrightarrow & 240x \color{red}{-45} \color{blue}{+45} \color{blue}{-36x} & = & \color{red}{36x} +16 \color{blue}{-36x} \color{blue}{+45} \\\Leftrightarrow & 240x-36x& = & 16+45 \\\Leftrightarrow & \color{red}{204} x& = & 61 \\\Leftrightarrow & x = \frac{61}{204} & & \\ & V = \left\{ \frac{61}{204} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{3}{2})& = & -3x+\frac{2}{11} \\\Leftrightarrow & 10x+\frac{15}{2}& = & -3x+\frac{2}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{220}{ \color{blue}{22} }x+ \frac{165}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{4}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 220x \color{red}{+165} & = & \color{red}{-66x} +4 \\\Leftrightarrow & 220x \color{red}{+165} \color{blue}{-165} \color{blue}{+66x} & = & \color{red}{-66x} +4 \color{blue}{+66x} \color{blue}{-165} \\\Leftrightarrow & 220x+66x& = & 4-165 \\\Leftrightarrow & \color{red}{286} x& = & -161 \\\Leftrightarrow & x = \frac{-161}{286} & & \\ & V = \left\{ \frac{-161}{286} \right\} & \\\end{align}\)
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