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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{5}{12})& = & -9x+\frac{6}{11} \\\Leftrightarrow & -28x-\frac{35}{12}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 12 en 11 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-3696}{ \color{blue}{132} }x- \frac{385}{ \color{blue}{132} })& = & (\frac{-1188}{ \color{blue}{132} }x+ \frac{72}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -3696x \color{red}{-385} & = & \color{red}{-1188x} +72 \\\Leftrightarrow & -3696x \color{red}{-385} \color{blue}{+385} \color{blue}{+1188x} & = & \color{red}{-1188x} +72 \color{blue}{+1188x} \color{blue}{+385} \\\Leftrightarrow & -3696x+1188x& = & 72+385 \\\Leftrightarrow & \color{red}{-2508} x& = & 457 \\\Leftrightarrow & x = \frac{457}{-2508} & & \\\Leftrightarrow & x = \frac{-457}{2508} & & \\ & V = \left\{ \frac{-457}{2508} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{3}{5})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -12x+\frac{18}{5}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{54}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+54} & = & \color{red}{-75x} +20 \\\Leftrightarrow & -180x \color{red}{+54} \color{blue}{-54} \color{blue}{+75x} & = & \color{red}{-75x} +20 \color{blue}{+75x} \color{blue}{-54} \\\Leftrightarrow & -180x+75x& = & 20-54 \\\Leftrightarrow & \color{red}{-105} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-105} & & \\\Leftrightarrow & x = \frac{34}{105} & & \\ & V = \left\{ \frac{34}{105} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{3}{7})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 24x-\frac{18}{7}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{168}{ \color{blue}{7} }x- \frac{18}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 168x \color{red}{-18} & = & \color{red}{-35x} +10 \\\Leftrightarrow & 168x \color{red}{-18} \color{blue}{+18} \color{blue}{+35x} & = & \color{red}{-35x} +10 \color{blue}{+35x} \color{blue}{+18} \\\Leftrightarrow & 168x+35x& = & 10+18 \\\Leftrightarrow & \color{red}{203} x& = & 28 \\\Leftrightarrow & x = \frac{28}{203} & & \\\Leftrightarrow & x = \frac{4}{29} & & \\ & V = \left\{ \frac{4}{29} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{3}{11})& = & -9x+\frac{4}{3} \\\Leftrightarrow & -8x+\frac{6}{11}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+18} & = & \color{red}{-297x} +44 \\\Leftrightarrow & -264x \color{red}{+18} \color{blue}{-18} \color{blue}{+297x} & = & \color{red}{-297x} +44 \color{blue}{+297x} \color{blue}{-18} \\\Leftrightarrow & -264x+297x& = & 44-18 \\\Leftrightarrow & \color{red}{33} x& = & 26 \\\Leftrightarrow & x = \frac{26}{33} & & \\ & V = \left\{ \frac{26}{33} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{1}{2})& = & 5x+\frac{9}{5} \\\Leftrightarrow & 14x+\frac{7}{2}& = & 5x+\frac{9}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{140}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{18}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 140x \color{red}{+35} & = & \color{red}{50x} +18 \\\Leftrightarrow & 140x \color{red}{+35} \color{blue}{-35} \color{blue}{-50x} & = & \color{red}{50x} +18 \color{blue}{-50x} \color{blue}{-35} \\\Leftrightarrow & 140x-50x& = & 18-35 \\\Leftrightarrow & \color{red}{90} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{90} & & \\ & V = \left\{ \frac{-17}{90} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{2}{9})& = & 2x+\frac{6}{11} \\\Leftrightarrow & 25x-\frac{10}{9}& = & 2x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2475}{ \color{blue}{99} }x- \frac{110}{ \color{blue}{99} })& = & (\frac{198}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2475x \color{red}{-110} & = & \color{red}{198x} +54 \\\Leftrightarrow & 2475x \color{red}{-110} \color{blue}{+110} \color{blue}{-198x} & = & \color{red}{198x} +54 \color{blue}{-198x} \color{blue}{+110} \\\Leftrightarrow & 2475x-198x& = & 54+110 \\\Leftrightarrow & \color{red}{2277} x& = & 164 \\\Leftrightarrow & x = \frac{164}{2277} & & \\ & V = \left\{ \frac{164}{2277} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{4}{11})& = & 5x+\frac{2}{7} \\\Leftrightarrow & -4x-\frac{8}{11}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-308}{ \color{blue}{77} }x- \frac{56}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -308x \color{red}{-56} & = & \color{red}{385x} +22 \\\Leftrightarrow & -308x \color{red}{-56} \color{blue}{+56} \color{blue}{-385x} & = & \color{red}{385x} +22 \color{blue}{-385x} \color{blue}{+56} \\\Leftrightarrow & -308x-385x& = & 22+56 \\\Leftrightarrow & \color{red}{-693} x& = & 78 \\\Leftrightarrow & x = \frac{78}{-693} & & \\\Leftrightarrow & x = \frac{-26}{231} & & \\ & V = \left\{ \frac{-26}{231} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{8})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 14x+\frac{21}{8}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{112}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{40}{ \color{blue}{8} }x+ \frac{12}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 112x \color{red}{+21} & = & \color{red}{40x} +12 \\\Leftrightarrow & 112x \color{red}{+21} \color{blue}{-21} \color{blue}{-40x} & = & \color{red}{40x} +12 \color{blue}{-40x} \color{blue}{-21} \\\Leftrightarrow & 112x-40x& = & 12-21 \\\Leftrightarrow & \color{red}{72} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{72} & & \\\Leftrightarrow & x = \frac{-1}{8} & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{2}{11})& = & 5x+\frac{3}{7} \\\Leftrightarrow & 12x-\frac{8}{11}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{56}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-56} & = & \color{red}{385x} +33 \\\Leftrightarrow & 924x \color{red}{-56} \color{blue}{+56} \color{blue}{-385x} & = & \color{red}{385x} +33 \color{blue}{-385x} \color{blue}{+56} \\\Leftrightarrow & 924x-385x& = & 33+56 \\\Leftrightarrow & \color{red}{539} x& = & 89 \\\Leftrightarrow & x = \frac{89}{539} & & \\ & V = \left\{ \frac{89}{539} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{2}{3})& = & 7x+\frac{10}{9} \\\Leftrightarrow & 10x+\frac{4}{3}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{+12} & = & \color{red}{63x} +10 \\\Leftrightarrow & 90x \color{red}{+12} \color{blue}{-12} \color{blue}{-63x} & = & \color{red}{63x} +10 \color{blue}{-63x} \color{blue}{-12} \\\Leftrightarrow & 90x-63x& = & 10-12 \\\Leftrightarrow & \color{red}{27} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{27} & & \\ & V = \left\{ \frac{-2}{27} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{4}{5})& = & 7x+\frac{3}{7} \\\Leftrightarrow & -30x+\frac{24}{5}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{+168} & = & \color{red}{245x} +15 \\\Leftrightarrow & -1050x \color{red}{+168} \color{blue}{-168} \color{blue}{-245x} & = & \color{red}{245x} +15 \color{blue}{-245x} \color{blue}{-168} \\\Leftrightarrow & -1050x-245x& = & 15-168 \\\Leftrightarrow & \color{red}{-1295} x& = & -153 \\\Leftrightarrow & x = \frac{-153}{-1295} & & \\\Leftrightarrow & x = \frac{153}{1295} & & \\ & V = \left\{ \frac{153}{1295} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{3}{11})& = & 2x+\frac{5}{8} \\\Leftrightarrow & 25x+\frac{15}{11}& = & 2x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2200}{ \color{blue}{88} }x+ \frac{120}{ \color{blue}{88} })& = & (\frac{176}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2200x \color{red}{+120} & = & \color{red}{176x} +55 \\\Leftrightarrow & 2200x \color{red}{+120} \color{blue}{-120} \color{blue}{-176x} & = & \color{red}{176x} +55 \color{blue}{-176x} \color{blue}{-120} \\\Leftrightarrow & 2200x-176x& = & 55-120 \\\Leftrightarrow & \color{red}{2024} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{2024} & & \\ & V = \left\{ \frac{-65}{2024} \right\} & \\\end{align}\)
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