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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{2}{11})& = & -3x+\frac{9}{10} \\\Leftrightarrow & -20x+\frac{10}{11}& = & -3x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-2200}{ \color{blue}{110} }x+ \frac{100}{ \color{blue}{110} })& = & (\frac{-330}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -2200x \color{red}{+100} & = & \color{red}{-330x} +99 \\\Leftrightarrow & -2200x \color{red}{+100} \color{blue}{-100} \color{blue}{+330x} & = & \color{red}{-330x} +99 \color{blue}{+330x} \color{blue}{-100} \\\Leftrightarrow & -2200x+330x& = & 99-100 \\\Leftrightarrow & \color{red}{-1870} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-1870} & & \\\Leftrightarrow & x = \frac{1}{1870} & & \\ & V = \left\{ \frac{1}{1870} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{5}{7})& = & -9x+\frac{2}{3} \\\Leftrightarrow & 20x+\frac{20}{7}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+60} & = & \color{red}{-189x} +14 \\\Leftrightarrow & 420x \color{red}{+60} \color{blue}{-60} \color{blue}{+189x} & = & \color{red}{-189x} +14 \color{blue}{+189x} \color{blue}{-60} \\\Leftrightarrow & 420x+189x& = & 14-60 \\\Leftrightarrow & \color{red}{609} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{609} & & \\ & V = \left\{ \frac{-46}{609} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{5}{7})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 8x-\frac{10}{7}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{-30} & = & \color{red}{105x} +56 \\\Leftrightarrow & 168x \color{red}{-30} \color{blue}{+30} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{+30} \\\Leftrightarrow & 168x-105x& = & 56+30 \\\Leftrightarrow & \color{red}{63} x& = & 86 \\\Leftrightarrow & x = \frac{86}{63} & & \\ & V = \left\{ \frac{86}{63} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{7})& = & 9x+\frac{7}{5} \\\Leftrightarrow & -8x+\frac{8}{7}& = & 9x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+40} & = & \color{red}{315x} +49 \\\Leftrightarrow & -280x \color{red}{+40} \color{blue}{-40} \color{blue}{-315x} & = & \color{red}{315x} +49 \color{blue}{-315x} \color{blue}{-40} \\\Leftrightarrow & -280x-315x& = & 49-40 \\\Leftrightarrow & \color{red}{-595} x& = & 9 \\\Leftrightarrow & x = \frac{9}{-595} & & \\\Leftrightarrow & x = \frac{-9}{595} & & \\ & V = \left\{ \frac{-9}{595} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{3}{11})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 18x+\frac{18}{11}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x+ \frac{90}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{+90} & = & \color{red}{385x} +66 \\\Leftrightarrow & 990x \color{red}{+90} \color{blue}{-90} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{-90} \\\Leftrightarrow & 990x-385x& = & 66-90 \\\Leftrightarrow & \color{red}{605} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{605} & & \\ & V = \left\{ \frac{-24}{605} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{4}{7})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -16x+\frac{16}{7}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-112}{ \color{blue}{7} }x+ \frac{16}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -112x \color{red}{+16} & = & \color{red}{49x} +9 \\\Leftrightarrow & -112x \color{red}{+16} \color{blue}{-16} \color{blue}{-49x} & = & \color{red}{49x} +9 \color{blue}{-49x} \color{blue}{-16} \\\Leftrightarrow & -112x-49x& = & 9-16 \\\Leftrightarrow & \color{red}{-161} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-161} & & \\\Leftrightarrow & x = \frac{1}{23} & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{7})& = & -5x+\frac{8}{11} \\\Leftrightarrow & 9x+\frac{15}{7}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{693}{ \color{blue}{77} }x+ \frac{165}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 693x \color{red}{+165} & = & \color{red}{-385x} +56 \\\Leftrightarrow & 693x \color{red}{+165} \color{blue}{-165} \color{blue}{+385x} & = & \color{red}{-385x} +56 \color{blue}{+385x} \color{blue}{-165} \\\Leftrightarrow & 693x+385x& = & 56-165 \\\Leftrightarrow & \color{red}{1078} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{1078} & & \\ & V = \left\{ \frac{-109}{1078} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{6})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 20x+\frac{25}{6}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{840}{ \color{blue}{42} }x+ \frac{175}{ \color{blue}{42} })& = & (\frac{-294}{ \color{blue}{42} }x+ \frac{60}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 840x \color{red}{+175} & = & \color{red}{-294x} +60 \\\Leftrightarrow & 840x \color{red}{+175} \color{blue}{-175} \color{blue}{+294x} & = & \color{red}{-294x} +60 \color{blue}{+294x} \color{blue}{-175} \\\Leftrightarrow & 840x+294x& = & 60-175 \\\Leftrightarrow & \color{red}{1134} x& = & -115 \\\Leftrightarrow & x = \frac{-115}{1134} & & \\ & V = \left\{ \frac{-115}{1134} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{3}{11})& = & 3x+\frac{5}{6} \\\Leftrightarrow & -18x+\frac{18}{11}& = & 3x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1188}{ \color{blue}{66} }x+ \frac{108}{ \color{blue}{66} })& = & (\frac{198}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1188x \color{red}{+108} & = & \color{red}{198x} +55 \\\Leftrightarrow & -1188x \color{red}{+108} \color{blue}{-108} \color{blue}{-198x} & = & \color{red}{198x} +55 \color{blue}{-198x} \color{blue}{-108} \\\Leftrightarrow & -1188x-198x& = & 55-108 \\\Leftrightarrow & \color{red}{-1386} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-1386} & & \\\Leftrightarrow & x = \frac{53}{1386} & & \\ & V = \left\{ \frac{53}{1386} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{4}{7})& = & -4x+\frac{3}{7} \\\Leftrightarrow & 15x+\frac{12}{7}& = & -4x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{105}{ \color{blue}{7} }x+ \frac{12}{ \color{blue}{7} })& = & (\frac{-28}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 105x \color{red}{+12} & = & \color{red}{-28x} +3 \\\Leftrightarrow & 105x \color{red}{+12} \color{blue}{-12} \color{blue}{+28x} & = & \color{red}{-28x} +3 \color{blue}{+28x} \color{blue}{-12} \\\Leftrightarrow & 105x+28x& = & 3-12 \\\Leftrightarrow & \color{red}{133} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{133} & & \\ & V = \left\{ \frac{-9}{133} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{3}{5})& = & -3x+\frac{5}{12} \\\Leftrightarrow & -20x-\frac{12}{5}& = & -3x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1200}{ \color{blue}{60} }x- \frac{144}{ \color{blue}{60} })& = & (\frac{-180}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1200x \color{red}{-144} & = & \color{red}{-180x} +25 \\\Leftrightarrow & -1200x \color{red}{-144} \color{blue}{+144} \color{blue}{+180x} & = & \color{red}{-180x} +25 \color{blue}{+180x} \color{blue}{+144} \\\Leftrightarrow & -1200x+180x& = & 25+144 \\\Leftrightarrow & \color{red}{-1020} x& = & 169 \\\Leftrightarrow & x = \frac{169}{-1020} & & \\\Leftrightarrow & x = \frac{-169}{1020} & & \\ & V = \left\{ \frac{-169}{1020} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{5}{2})& = & -9x+\frac{3}{2} \\\Leftrightarrow & -20x-\frac{25}{2}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-40}{ \color{blue}{2} }x- \frac{25}{ \color{blue}{2} })& = & (\frac{-18}{ \color{blue}{2} }x+ \frac{3}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -40x \color{red}{-25} & = & \color{red}{-18x} +3 \\\Leftrightarrow & -40x \color{red}{-25} \color{blue}{+25} \color{blue}{+18x} & = & \color{red}{-18x} +3 \color{blue}{+18x} \color{blue}{+25} \\\Leftrightarrow & -40x+18x& = & 3+25 \\\Leftrightarrow & \color{red}{-22} x& = & 28 \\\Leftrightarrow & x = \frac{28}{-22} & & \\\Leftrightarrow & x = \frac{-14}{11} & & \\ & V = \left\{ \frac{-14}{11} \right\} & \\\end{align}\)
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