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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{7})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 20x+\frac{10}{7}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{280}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 280x \color{red}{+20} & = & \color{red}{98x} +63 \\\Leftrightarrow & 280x \color{red}{+20} \color{blue}{-20} \color{blue}{-98x} & = & \color{red}{98x} +63 \color{blue}{-98x} \color{blue}{-20} \\\Leftrightarrow & 280x-98x& = & 63-20 \\\Leftrightarrow & \color{red}{182} x& = & 43 \\\Leftrightarrow & x = \frac{43}{182} & & \\ & V = \left\{ \frac{43}{182} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{3}{8})& = & 4x+\frac{6}{11} \\\Leftrightarrow & -28x-\frac{21}{8}& = & 4x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2464}{ \color{blue}{88} }x- \frac{231}{ \color{blue}{88} })& = & (\frac{352}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2464x \color{red}{-231} & = & \color{red}{352x} +48 \\\Leftrightarrow & -2464x \color{red}{-231} \color{blue}{+231} \color{blue}{-352x} & = & \color{red}{352x} +48 \color{blue}{-352x} \color{blue}{+231} \\\Leftrightarrow & -2464x-352x& = & 48+231 \\\Leftrightarrow & \color{red}{-2816} x& = & 279 \\\Leftrightarrow & x = \frac{279}{-2816} & & \\\Leftrightarrow & x = \frac{-279}{2816} & & \\ & V = \left\{ \frac{-279}{2816} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{2}{3})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 10x-\frac{10}{3}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{150}{ \color{blue}{15} }x- \frac{50}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 150x \color{red}{-50} & = & \color{red}{-45x} +18 \\\Leftrightarrow & 150x \color{red}{-50} \color{blue}{+50} \color{blue}{+45x} & = & \color{red}{-45x} +18 \color{blue}{+45x} \color{blue}{+50} \\\Leftrightarrow & 150x+45x& = & 18+50 \\\Leftrightarrow & \color{red}{195} x& = & 68 \\\Leftrightarrow & x = \frac{68}{195} & & \\ & V = \left\{ \frac{68}{195} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{4}{3})& = & -5x+\frac{4}{11} \\\Leftrightarrow & -28x+\frac{28}{3}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-924}{ \color{blue}{33} }x+ \frac{308}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -924x \color{red}{+308} & = & \color{red}{-165x} +12 \\\Leftrightarrow & -924x \color{red}{+308} \color{blue}{-308} \color{blue}{+165x} & = & \color{red}{-165x} +12 \color{blue}{+165x} \color{blue}{-308} \\\Leftrightarrow & -924x+165x& = & 12-308 \\\Leftrightarrow & \color{red}{-759} x& = & -296 \\\Leftrightarrow & x = \frac{-296}{-759} & & \\\Leftrightarrow & x = \frac{296}{759} & & \\ & V = \left\{ \frac{296}{759} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{3}{2})& = & -4x+\frac{9}{11} \\\Leftrightarrow & 25x-\frac{15}{2}& = & -4x+\frac{9}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{550}{ \color{blue}{22} }x- \frac{165}{ \color{blue}{22} })& = & (\frac{-88}{ \color{blue}{22} }x+ \frac{18}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 550x \color{red}{-165} & = & \color{red}{-88x} +18 \\\Leftrightarrow & 550x \color{red}{-165} \color{blue}{+165} \color{blue}{+88x} & = & \color{red}{-88x} +18 \color{blue}{+88x} \color{blue}{+165} \\\Leftrightarrow & 550x+88x& = & 18+165 \\\Leftrightarrow & \color{red}{638} x& = & 183 \\\Leftrightarrow & x = \frac{183}{638} & & \\ & V = \left\{ \frac{183}{638} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{2}{5})& = & 9x+\frac{8}{3} \\\Leftrightarrow & -4x-\frac{4}{5}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-60}{ \color{blue}{15} }x- \frac{12}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -60x \color{red}{-12} & = & \color{red}{135x} +40 \\\Leftrightarrow & -60x \color{red}{-12} \color{blue}{+12} \color{blue}{-135x} & = & \color{red}{135x} +40 \color{blue}{-135x} \color{blue}{+12} \\\Leftrightarrow & -60x-135x& = & 40+12 \\\Leftrightarrow & \color{red}{-195} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-195} & & \\\Leftrightarrow & x = \frac{-4}{15} & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{3})& = & 7x+\frac{5}{3} \\\Leftrightarrow & -16x+\frac{8}{3}& = & 7x+\frac{5}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-48}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{5}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -48x \color{red}{+8} & = & \color{red}{21x} +5 \\\Leftrightarrow & -48x \color{red}{+8} \color{blue}{-8} \color{blue}{-21x} & = & \color{red}{21x} +5 \color{blue}{-21x} \color{blue}{-8} \\\Leftrightarrow & -48x-21x& = & 5-8 \\\Leftrightarrow & \color{red}{-69} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-69} & & \\\Leftrightarrow & x = \frac{1}{23} & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{11})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -30x-\frac{18}{11}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-660}{ \color{blue}{22} }x- \frac{36}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -660x \color{red}{-36} & = & \color{red}{-154x} +99 \\\Leftrightarrow & -660x \color{red}{-36} \color{blue}{+36} \color{blue}{+154x} & = & \color{red}{-154x} +99 \color{blue}{+154x} \color{blue}{+36} \\\Leftrightarrow & -660x+154x& = & 99+36 \\\Leftrightarrow & \color{red}{-506} x& = & 135 \\\Leftrightarrow & x = \frac{135}{-506} & & \\\Leftrightarrow & x = \frac{-135}{506} & & \\ & V = \left\{ \frac{-135}{506} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{2}{9})& = & -3x+\frac{10}{3} \\\Leftrightarrow & -14x-\frac{14}{9}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-126}{ \color{blue}{9} }x- \frac{14}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -126x \color{red}{-14} & = & \color{red}{-27x} +30 \\\Leftrightarrow & -126x \color{red}{-14} \color{blue}{+14} \color{blue}{+27x} & = & \color{red}{-27x} +30 \color{blue}{+27x} \color{blue}{+14} \\\Leftrightarrow & -126x+27x& = & 30+14 \\\Leftrightarrow & \color{red}{-99} x& = & 44 \\\Leftrightarrow & x = \frac{44}{-99} & & \\\Leftrightarrow & x = \frac{-4}{9} & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{5}{12})& = & 8x+\frac{8}{3} \\\Leftrightarrow & -15x+\frac{25}{12}& = & 8x+\frac{8}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x+ \frac{25}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{+25} & = & \color{red}{96x} +32 \\\Leftrightarrow & -180x \color{red}{+25} \color{blue}{-25} \color{blue}{-96x} & = & \color{red}{96x} +32 \color{blue}{-96x} \color{blue}{-25} \\\Leftrightarrow & -180x-96x& = & 32-25 \\\Leftrightarrow & \color{red}{-276} x& = & 7 \\\Leftrightarrow & x = \frac{7}{-276} & & \\\Leftrightarrow & x = \frac{-7}{276} & & \\ & V = \left\{ \frac{-7}{276} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{2}{3})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 10x-\frac{4}{3}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{150}{ \color{blue}{15} }x- \frac{20}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 150x \color{red}{-20} & = & \color{red}{-105x} +18 \\\Leftrightarrow & 150x \color{red}{-20} \color{blue}{+20} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{+20} \\\Leftrightarrow & 150x+105x& = & 18+20 \\\Leftrightarrow & \color{red}{255} x& = & 38 \\\Leftrightarrow & x = \frac{38}{255} & & \\ & V = \left\{ \frac{38}{255} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{7})& = & -3x+\frac{9}{4} \\\Leftrightarrow & -20x-\frac{10}{7}& = & -3x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-560}{ \color{blue}{28} }x- \frac{40}{ \color{blue}{28} })& = & (\frac{-84}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -560x \color{red}{-40} & = & \color{red}{-84x} +63 \\\Leftrightarrow & -560x \color{red}{-40} \color{blue}{+40} \color{blue}{+84x} & = & \color{red}{-84x} +63 \color{blue}{+84x} \color{blue}{+40} \\\Leftrightarrow & -560x+84x& = & 63+40 \\\Leftrightarrow & \color{red}{-476} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-476} & & \\\Leftrightarrow & x = \frac{-103}{476} & & \\ & V = \left\{ \frac{-103}{476} \right\} & \\\end{align}\)
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