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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{7})& = & -5x+\frac{8}{9} \\\Leftrightarrow & -12x+\frac{30}{7}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{+270} & = & \color{red}{-315x} +56 \\\Leftrightarrow & -756x \color{red}{+270} \color{blue}{-270} \color{blue}{+315x} & = & \color{red}{-315x} +56 \color{blue}{+315x} \color{blue}{-270} \\\Leftrightarrow & -756x+315x& = & 56-270 \\\Leftrightarrow & \color{red}{-441} x& = & -214 \\\Leftrightarrow & x = \frac{-214}{-441} & & \\\Leftrightarrow & x = \frac{214}{441} & & \\ & V = \left\{ \frac{214}{441} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{5}{3})& = & -4x+\frac{10}{11} \\\Leftrightarrow & -25x+\frac{25}{3}& = & -4x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-825}{ \color{blue}{33} }x+ \frac{275}{ \color{blue}{33} })& = & (\frac{-132}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -825x \color{red}{+275} & = & \color{red}{-132x} +30 \\\Leftrightarrow & -825x \color{red}{+275} \color{blue}{-275} \color{blue}{+132x} & = & \color{red}{-132x} +30 \color{blue}{+132x} \color{blue}{-275} \\\Leftrightarrow & -825x+132x& = & 30-275 \\\Leftrightarrow & \color{red}{-693} x& = & -245 \\\Leftrightarrow & x = \frac{-245}{-693} & & \\\Leftrightarrow & x = \frac{35}{99} & & \\ & V = \left\{ \frac{35}{99} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{3})& = & 8x+\frac{9}{4} \\\Leftrightarrow & -21x-\frac{14}{3}& = & 8x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-252}{ \color{blue}{12} }x- \frac{56}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -252x \color{red}{-56} & = & \color{red}{96x} +27 \\\Leftrightarrow & -252x \color{red}{-56} \color{blue}{+56} \color{blue}{-96x} & = & \color{red}{96x} +27 \color{blue}{-96x} \color{blue}{+56} \\\Leftrightarrow & -252x-96x& = & 27+56 \\\Leftrightarrow & \color{red}{-348} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-348} & & \\\Leftrightarrow & x = \frac{-83}{348} & & \\ & V = \left\{ \frac{-83}{348} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{2}{7})& = & 4x+\frac{10}{3} \\\Leftrightarrow & -15x-\frac{10}{7}& = & 4x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{84}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{-30} & = & \color{red}{84x} +70 \\\Leftrightarrow & -315x \color{red}{-30} \color{blue}{+30} \color{blue}{-84x} & = & \color{red}{84x} +70 \color{blue}{-84x} \color{blue}{+30} \\\Leftrightarrow & -315x-84x& = & 70+30 \\\Leftrightarrow & \color{red}{-399} x& = & 100 \\\Leftrightarrow & x = \frac{100}{-399} & & \\\Leftrightarrow & x = \frac{-100}{399} & & \\ & V = \left\{ \frac{-100}{399} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{4}{5})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -6x+\frac{12}{5}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+84} & = & \color{red}{245x} +45 \\\Leftrightarrow & -210x \color{red}{+84} \color{blue}{-84} \color{blue}{-245x} & = & \color{red}{245x} +45 \color{blue}{-245x} \color{blue}{-84} \\\Leftrightarrow & -210x-245x& = & 45-84 \\\Leftrightarrow & \color{red}{-455} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{-455} & & \\\Leftrightarrow & x = \frac{3}{35} & & \\ & V = \left\{ \frac{3}{35} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{11})& = & 7x+\frac{9}{10} \\\Leftrightarrow & 15x+\frac{6}{11}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1650}{ \color{blue}{110} }x+ \frac{60}{ \color{blue}{110} })& = & (\frac{770}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1650x \color{red}{+60} & = & \color{red}{770x} +99 \\\Leftrightarrow & 1650x \color{red}{+60} \color{blue}{-60} \color{blue}{-770x} & = & \color{red}{770x} +99 \color{blue}{-770x} \color{blue}{-60} \\\Leftrightarrow & 1650x-770x& = & 99-60 \\\Leftrightarrow & \color{red}{880} x& = & 39 \\\Leftrightarrow & x = \frac{39}{880} & & \\ & V = \left\{ \frac{39}{880} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{2}{11})& = & 3x+\frac{3}{11} \\\Leftrightarrow & 10x+\frac{10}{11}& = & 3x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{110}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 110x \color{red}{+10} & = & \color{red}{33x} +3 \\\Leftrightarrow & 110x \color{red}{+10} \color{blue}{-10} \color{blue}{-33x} & = & \color{red}{33x} +3 \color{blue}{-33x} \color{blue}{-10} \\\Leftrightarrow & 110x-33x& = & 3-10 \\\Leftrightarrow & \color{red}{77} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{77} & & \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{3}{5})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-84} & = & \color{red}{175x} +40 \\\Leftrightarrow & 420x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +40 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & 420x-175x& = & 40+84 \\\Leftrightarrow & \color{red}{245} x& = & 124 \\\Leftrightarrow & x = \frac{124}{245} & & \\ & V = \left\{ \frac{124}{245} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{4}{3})& = & -3x+\frac{10}{7} \\\Leftrightarrow & -25x+\frac{20}{3}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-525}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -525x \color{red}{+140} & = & \color{red}{-63x} +30 \\\Leftrightarrow & -525x \color{red}{+140} \color{blue}{-140} \color{blue}{+63x} & = & \color{red}{-63x} +30 \color{blue}{+63x} \color{blue}{-140} \\\Leftrightarrow & -525x+63x& = & 30-140 \\\Leftrightarrow & \color{red}{-462} x& = & -110 \\\Leftrightarrow & x = \frac{-110}{-462} & & \\\Leftrightarrow & x = \frac{5}{21} & & \\ & V = \left\{ \frac{5}{21} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{2}{3})& = & -7x+\frac{5}{6} \\\Leftrightarrow & 20x-\frac{10}{3}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x- \frac{20}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{-20} & = & \color{red}{-42x} +5 \\\Leftrightarrow & 120x \color{red}{-20} \color{blue}{+20} \color{blue}{+42x} & = & \color{red}{-42x} +5 \color{blue}{+42x} \color{blue}{+20} \\\Leftrightarrow & 120x+42x& = & 5+20 \\\Leftrightarrow & \color{red}{162} x& = & 25 \\\Leftrightarrow & x = \frac{25}{162} & & \\ & V = \left\{ \frac{25}{162} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{7})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 18x+\frac{30}{7}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{252}{ \color{blue}{14} }x+ \frac{60}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 252x \color{red}{+60} & = & \color{red}{-70x} +21 \\\Leftrightarrow & 252x \color{red}{+60} \color{blue}{-60} \color{blue}{+70x} & = & \color{red}{-70x} +21 \color{blue}{+70x} \color{blue}{-60} \\\Leftrightarrow & 252x+70x& = & 21-60 \\\Leftrightarrow & \color{red}{322} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{322} & & \\ & V = \left\{ \frac{-39}{322} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{4}{3})& = & 9x+\frac{9}{5} \\\Leftrightarrow & -8x-\frac{8}{3}& = & 9x+\frac{9}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{-40} & = & \color{red}{135x} +27 \\\Leftrightarrow & -120x \color{red}{-40} \color{blue}{+40} \color{blue}{-135x} & = & \color{red}{135x} +27 \color{blue}{-135x} \color{blue}{+40} \\\Leftrightarrow & -120x-135x& = & 27+40 \\\Leftrightarrow & \color{red}{-255} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-255} & & \\\Leftrightarrow & x = \frac{-67}{255} & & \\ & V = \left\{ \frac{-67}{255} \right\} & \\\end{align}\)
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