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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{4}{9})& = & 5x+\frac{7}{5} \\\Leftrightarrow & 4x+\frac{8}{9}& = & 5x+\frac{7}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{180}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{63}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 180x \color{red}{+40} & = & \color{red}{225x} +63 \\\Leftrightarrow & 180x \color{red}{+40} \color{blue}{-40} \color{blue}{-225x} & = & \color{red}{225x} +63 \color{blue}{-225x} \color{blue}{-40} \\\Leftrightarrow & 180x-225x& = & 63-40 \\\Leftrightarrow & \color{red}{-45} x& = & 23 \\\Leftrightarrow & x = \frac{23}{-45} & & \\\Leftrightarrow & x = \frac{-23}{45} & & \\ & V = \left\{ \frac{-23}{45} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{2}{5})& = & -5x+\frac{5}{12} \\\Leftrightarrow & -18x+\frac{12}{5}& = & -5x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1080}{ \color{blue}{60} }x+ \frac{144}{ \color{blue}{60} })& = & (\frac{-300}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1080x \color{red}{+144} & = & \color{red}{-300x} +25 \\\Leftrightarrow & -1080x \color{red}{+144} \color{blue}{-144} \color{blue}{+300x} & = & \color{red}{-300x} +25 \color{blue}{+300x} \color{blue}{-144} \\\Leftrightarrow & -1080x+300x& = & 25-144 \\\Leftrightarrow & \color{red}{-780} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{-780} & & \\\Leftrightarrow & x = \frac{119}{780} & & \\ & V = \left\{ \frac{119}{780} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{3}{5})& = & -7x+\frac{5}{6} \\\Leftrightarrow & 6x-\frac{9}{5}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{180}{ \color{blue}{30} }x- \frac{54}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 180x \color{red}{-54} & = & \color{red}{-210x} +25 \\\Leftrightarrow & 180x \color{red}{-54} \color{blue}{+54} \color{blue}{+210x} & = & \color{red}{-210x} +25 \color{blue}{+210x} \color{blue}{+54} \\\Leftrightarrow & 180x+210x& = & 25+54 \\\Leftrightarrow & \color{red}{390} x& = & 79 \\\Leftrightarrow & x = \frac{79}{390} & & \\ & V = \left\{ \frac{79}{390} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{3}{5})& = & 9x+\frac{8}{3} \\\Leftrightarrow & -20x-\frac{12}{5}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{-36} & = & \color{red}{135x} +40 \\\Leftrightarrow & -300x \color{red}{-36} \color{blue}{+36} \color{blue}{-135x} & = & \color{red}{135x} +40 \color{blue}{-135x} \color{blue}{+36} \\\Leftrightarrow & -300x-135x& = & 40+36 \\\Leftrightarrow & \color{red}{-435} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-435} & & \\\Leftrightarrow & x = \frac{-76}{435} & & \\ & V = \left\{ \frac{-76}{435} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{3})& = & -8x+\frac{2}{7} \\\Leftrightarrow & -21x-\frac{14}{3}& = & -8x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-441}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -441x \color{red}{-98} & = & \color{red}{-168x} +6 \\\Leftrightarrow & -441x \color{red}{-98} \color{blue}{+98} \color{blue}{+168x} & = & \color{red}{-168x} +6 \color{blue}{+168x} \color{blue}{+98} \\\Leftrightarrow & -441x+168x& = & 6+98 \\\Leftrightarrow & \color{red}{-273} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-273} & & \\\Leftrightarrow & x = \frac{-8}{21} & & \\ & V = \left\{ \frac{-8}{21} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{3}{8})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 25x+\frac{15}{8}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{600}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{72}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 600x \color{red}{+45} & = & \color{red}{72x} +32 \\\Leftrightarrow & 600x \color{red}{+45} \color{blue}{-45} \color{blue}{-72x} & = & \color{red}{72x} +32 \color{blue}{-72x} \color{blue}{-45} \\\Leftrightarrow & 600x-72x& = & 32-45 \\\Leftrightarrow & \color{red}{528} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{528} & & \\ & V = \left\{ \frac{-13}{528} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{7})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 18x-\frac{12}{7}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x- \frac{132}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{-132} & = & \color{red}{-385x} +70 \\\Leftrightarrow & 1386x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +70 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & 1386x+385x& = & 70+132 \\\Leftrightarrow & \color{red}{1771} x& = & 202 \\\Leftrightarrow & x = \frac{202}{1771} & & \\ & V = \left\{ \frac{202}{1771} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{7})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -16x+\frac{8}{7}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1008}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1008x \color{red}{+72} & = & \color{red}{-441x} +14 \\\Leftrightarrow & -1008x \color{red}{+72} \color{blue}{-72} \color{blue}{+441x} & = & \color{red}{-441x} +14 \color{blue}{+441x} \color{blue}{-72} \\\Leftrightarrow & -1008x+441x& = & 14-72 \\\Leftrightarrow & \color{red}{-567} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{-567} & & \\\Leftrightarrow & x = \frac{58}{567} & & \\ & V = \left\{ \frac{58}{567} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{9})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -6x+\frac{8}{9}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-378}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -378x \color{red}{+56} & = & \color{red}{441x} +90 \\\Leftrightarrow & -378x \color{red}{+56} \color{blue}{-56} \color{blue}{-441x} & = & \color{red}{441x} +90 \color{blue}{-441x} \color{blue}{-56} \\\Leftrightarrow & -378x-441x& = & 90-56 \\\Leftrightarrow & \color{red}{-819} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-819} & & \\\Leftrightarrow & x = \frac{-34}{819} & & \\ & V = \left\{ \frac{-34}{819} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{4}{5})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -9x+\frac{12}{5}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{+132} & = & \color{red}{385x} +30 \\\Leftrightarrow & -495x \color{red}{+132} \color{blue}{-132} \color{blue}{-385x} & = & \color{red}{385x} +30 \color{blue}{-385x} \color{blue}{-132} \\\Leftrightarrow & -495x-385x& = & 30-132 \\\Leftrightarrow & \color{red}{-880} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{-880} & & \\\Leftrightarrow & x = \frac{51}{440} & & \\ & V = \left\{ \frac{51}{440} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{4}{3})& = & -2x+\frac{10}{7} \\\Leftrightarrow & 15x+\frac{20}{3}& = & -2x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{-42}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{+140} & = & \color{red}{-42x} +30 \\\Leftrightarrow & 315x \color{red}{+140} \color{blue}{-140} \color{blue}{+42x} & = & \color{red}{-42x} +30 \color{blue}{+42x} \color{blue}{-140} \\\Leftrightarrow & 315x+42x& = & 30-140 \\\Leftrightarrow & \color{red}{357} x& = & -110 \\\Leftrightarrow & x = \frac{-110}{357} & & \\ & V = \left\{ \frac{-110}{357} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{4}{3})& = & -4x+\frac{10}{11} \\\Leftrightarrow & 21x-\frac{28}{3}& = & -4x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{693}{ \color{blue}{33} }x- \frac{308}{ \color{blue}{33} })& = & (\frac{-132}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 693x \color{red}{-308} & = & \color{red}{-132x} +30 \\\Leftrightarrow & 693x \color{red}{-308} \color{blue}{+308} \color{blue}{+132x} & = & \color{red}{-132x} +30 \color{blue}{+132x} \color{blue}{+308} \\\Leftrightarrow & 693x+132x& = & 30+308 \\\Leftrightarrow & \color{red}{825} x& = & 338 \\\Leftrightarrow & x = \frac{338}{825} & & \\ & V = \left\{ \frac{338}{825} \right\} & \\\end{align}\)
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