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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{11})& = & -7x+\frac{9}{4} \\\Leftrightarrow & -30x-\frac{18}{11}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1320}{ \color{blue}{44} }x- \frac{72}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1320x \color{red}{-72} & = & \color{red}{-308x} +99 \\\Leftrightarrow & -1320x \color{red}{-72} \color{blue}{+72} \color{blue}{+308x} & = & \color{red}{-308x} +99 \color{blue}{+308x} \color{blue}{+72} \\\Leftrightarrow & -1320x+308x& = & 99+72 \\\Leftrightarrow & \color{red}{-1012} x& = & 171 \\\Leftrightarrow & x = \frac{171}{-1012} & & \\\Leftrightarrow & x = \frac{-171}{1012} & & \\ & V = \left\{ \frac{-171}{1012} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{5}{4})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 12x+\frac{15}{4}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{48}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{20}{ \color{blue}{4} }x+ \frac{6}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 48x \color{red}{+15} & = & \color{red}{20x} +6 \\\Leftrightarrow & 48x \color{red}{+15} \color{blue}{-15} \color{blue}{-20x} & = & \color{red}{20x} +6 \color{blue}{-20x} \color{blue}{-15} \\\Leftrightarrow & 48x-20x& = & 6-15 \\\Leftrightarrow & \color{red}{28} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{28} & & \\ & V = \left\{ \frac{-9}{28} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{3})& = & 2x+\frac{3}{11} \\\Leftrightarrow & 15x+\frac{20}{3}& = & 2x+\frac{3}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{66}{ \color{blue}{33} }x+ \frac{9}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{+220} & = & \color{red}{66x} +9 \\\Leftrightarrow & 495x \color{red}{+220} \color{blue}{-220} \color{blue}{-66x} & = & \color{red}{66x} +9 \color{blue}{-66x} \color{blue}{-220} \\\Leftrightarrow & 495x-66x& = & 9-220 \\\Leftrightarrow & \color{red}{429} x& = & -211 \\\Leftrightarrow & x = \frac{-211}{429} & & \\ & V = \left\{ \frac{-211}{429} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{3}{2})& = & 7x+\frac{9}{10} \\\Leftrightarrow & -6x+\frac{9}{2}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 2 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{+45} & = & \color{red}{70x} +9 \\\Leftrightarrow & -60x \color{red}{+45} \color{blue}{-45} \color{blue}{-70x} & = & \color{red}{70x} +9 \color{blue}{-70x} \color{blue}{-45} \\\Leftrightarrow & -60x-70x& = & 9-45 \\\Leftrightarrow & \color{red}{-130} x& = & -36 \\\Leftrightarrow & x = \frac{-36}{-130} & & \\\Leftrightarrow & x = \frac{18}{65} & & \\ & V = \left\{ \frac{18}{65} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{2}{7})& = & 7x+\frac{2}{5} \\\Leftrightarrow & 25x+\frac{10}{7}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{875}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 875x \color{red}{+50} & = & \color{red}{245x} +14 \\\Leftrightarrow & 875x \color{red}{+50} \color{blue}{-50} \color{blue}{-245x} & = & \color{red}{245x} +14 \color{blue}{-245x} \color{blue}{-50} \\\Leftrightarrow & 875x-245x& = & 14-50 \\\Leftrightarrow & \color{red}{630} x& = & -36 \\\Leftrightarrow & x = \frac{-36}{630} & & \\\Leftrightarrow & x = \frac{-2}{35} & & \\ & V = \left\{ \frac{-2}{35} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{-150} & = & \color{red}{-245x} +42 \\\Leftrightarrow & -1050x \color{red}{-150} \color{blue}{+150} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{+150} \\\Leftrightarrow & -1050x+245x& = & 42+150 \\\Leftrightarrow & \color{red}{-805} x& = & 192 \\\Leftrightarrow & x = \frac{192}{-805} & & \\\Leftrightarrow & x = \frac{-192}{805} & & \\ & V = \left\{ \frac{-192}{805} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{5}{8})& = & 8x+\frac{5}{12} \\\Leftrightarrow & 21x-\frac{35}{8}& = & 8x+\frac{5}{12} \\ & & & \text{kgv van noemers 8 en 12 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{504}{ \color{blue}{24} }x- \frac{105}{ \color{blue}{24} })& = & (\frac{192}{ \color{blue}{24} }x+ \frac{10}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 504x \color{red}{-105} & = & \color{red}{192x} +10 \\\Leftrightarrow & 504x \color{red}{-105} \color{blue}{+105} \color{blue}{-192x} & = & \color{red}{192x} +10 \color{blue}{-192x} \color{blue}{+105} \\\Leftrightarrow & 504x-192x& = & 10+105 \\\Leftrightarrow & \color{red}{312} x& = & 115 \\\Leftrightarrow & x = \frac{115}{312} & & \\ & V = \left\{ \frac{115}{312} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{2}{5})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{-75x} +20 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{+75x} & = & \color{red}{-75x} +20 \color{blue}{+75x} \color{blue}{+36} \\\Leftrightarrow & -180x+75x& = & 20+36 \\\Leftrightarrow & \color{red}{-105} x& = & 56 \\\Leftrightarrow & x = \frac{56}{-105} & & \\\Leftrightarrow & x = \frac{-8}{15} & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{3}{7})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{+6} & = & \color{red}{49x} +10 \\\Leftrightarrow & -42x \color{red}{+6} \color{blue}{-6} \color{blue}{-49x} & = & \color{red}{49x} +10 \color{blue}{-49x} \color{blue}{-6} \\\Leftrightarrow & -42x-49x& = & 10-6 \\\Leftrightarrow & \color{red}{-91} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-91} & & \\\Leftrightarrow & x = \frac{-4}{91} & & \\ & V = \left\{ \frac{-4}{91} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{5}{11})& = & 5x+\frac{9}{4} \\\Leftrightarrow & 4x+\frac{10}{11}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{176}{ \color{blue}{44} }x+ \frac{40}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 176x \color{red}{+40} & = & \color{red}{220x} +99 \\\Leftrightarrow & 176x \color{red}{+40} \color{blue}{-40} \color{blue}{-220x} & = & \color{red}{220x} +99 \color{blue}{-220x} \color{blue}{-40} \\\Leftrightarrow & 176x-220x& = & 99-40 \\\Leftrightarrow & \color{red}{-44} x& = & 59 \\\Leftrightarrow & x = \frac{59}{-44} & & \\\Leftrightarrow & x = \frac{-59}{44} & & \\ & V = \left\{ \frac{-59}{44} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{3}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 30x-\frac{18}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{150}{ \color{blue}{5} }x- \frac{18}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 150x \color{red}{-18} & = & \color{red}{35x} +6 \\\Leftrightarrow & 150x \color{red}{-18} \color{blue}{+18} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{+18} \\\Leftrightarrow & 150x-35x& = & 6+18 \\\Leftrightarrow & \color{red}{115} x& = & 24 \\\Leftrightarrow & x = \frac{24}{115} & & \\ & V = \left\{ \frac{24}{115} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{4}{3})& = & 7x+\frac{4}{9} \\\Leftrightarrow & -10x-\frac{20}{3}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x- \frac{60}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{-60} & = & \color{red}{63x} +4 \\\Leftrightarrow & -90x \color{red}{-60} \color{blue}{+60} \color{blue}{-63x} & = & \color{red}{63x} +4 \color{blue}{-63x} \color{blue}{+60} \\\Leftrightarrow & -90x-63x& = & 4+60 \\\Leftrightarrow & \color{red}{-153} x& = & 64 \\\Leftrightarrow & x = \frac{64}{-153} & & \\\Leftrightarrow & x = \frac{-64}{153} & & \\ & V = \left\{ \frac{-64}{153} \right\} & \\\end{align}\)
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