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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{3}{11})& = & 9x+\frac{5}{2} \\\Leftrightarrow & 28x+\frac{21}{11}& = & 9x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{616}{ \color{blue}{22} }x+ \frac{42}{ \color{blue}{22} })& = & (\frac{198}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 616x \color{red}{+42} & = & \color{red}{198x} +55 \\\Leftrightarrow & 616x \color{red}{+42} \color{blue}{-42} \color{blue}{-198x} & = & \color{red}{198x} +55 \color{blue}{-198x} \color{blue}{-42} \\\Leftrightarrow & 616x-198x& = & 55-42 \\\Leftrightarrow & \color{red}{418} x& = & 13 \\\Leftrightarrow & x = \frac{13}{418} & & \\ & V = \left\{ \frac{13}{418} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{5}{12})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -25x-\frac{25}{12}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 12 en 5 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1500}{ \color{blue}{60} }x- \frac{125}{ \color{blue}{60} })& = & (\frac{300}{ \color{blue}{60} }x+ \frac{72}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1500x \color{red}{-125} & = & \color{red}{300x} +72 \\\Leftrightarrow & -1500x \color{red}{-125} \color{blue}{+125} \color{blue}{-300x} & = & \color{red}{300x} +72 \color{blue}{-300x} \color{blue}{+125} \\\Leftrightarrow & -1500x-300x& = & 72+125 \\\Leftrightarrow & \color{red}{-1800} x& = & 197 \\\Leftrightarrow & x = \frac{197}{-1800} & & \\\Leftrightarrow & x = \frac{-197}{1800} & & \\ & V = \left\{ \frac{-197}{1800} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{7})& = & 3x+\frac{9}{2} \\\Leftrightarrow & 16x+\frac{20}{7}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{224}{ \color{blue}{14} }x+ \frac{40}{ \color{blue}{14} })& = & (\frac{42}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 224x \color{red}{+40} & = & \color{red}{42x} +63 \\\Leftrightarrow & 224x \color{red}{+40} \color{blue}{-40} \color{blue}{-42x} & = & \color{red}{42x} +63 \color{blue}{-42x} \color{blue}{-40} \\\Leftrightarrow & 224x-42x& = & 63-40 \\\Leftrightarrow & \color{red}{182} x& = & 23 \\\Leftrightarrow & x = \frac{23}{182} & & \\ & V = \left\{ \frac{23}{182} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{4}{11})& = & 4x+\frac{10}{3} \\\Leftrightarrow & -15x-\frac{12}{11}& = & 4x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-495}{ \color{blue}{33} }x- \frac{36}{ \color{blue}{33} })& = & (\frac{132}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -495x \color{red}{-36} & = & \color{red}{132x} +110 \\\Leftrightarrow & -495x \color{red}{-36} \color{blue}{+36} \color{blue}{-132x} & = & \color{red}{132x} +110 \color{blue}{-132x} \color{blue}{+36} \\\Leftrightarrow & -495x-132x& = & 110+36 \\\Leftrightarrow & \color{red}{-627} x& = & 146 \\\Leftrightarrow & x = \frac{146}{-627} & & \\\Leftrightarrow & x = \frac{-146}{627} & & \\ & V = \left\{ \frac{-146}{627} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{1}{2})& = & -2x+\frac{10}{3} \\\Leftrightarrow & 15x-\frac{5}{2}& = & -2x+\frac{10}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{90}{ \color{blue}{6} }x- \frac{15}{ \color{blue}{6} })& = & (\frac{-12}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 90x \color{red}{-15} & = & \color{red}{-12x} +20 \\\Leftrightarrow & 90x \color{red}{-15} \color{blue}{+15} \color{blue}{+12x} & = & \color{red}{-12x} +20 \color{blue}{+12x} \color{blue}{+15} \\\Leftrightarrow & 90x+12x& = & 20+15 \\\Leftrightarrow & \color{red}{102} x& = & 35 \\\Leftrightarrow & x = \frac{35}{102} & & \\ & V = \left\{ \frac{35}{102} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{5}{9})& = & -9x+\frac{8}{9} \\\Leftrightarrow & -8x+\frac{10}{9}& = & -9x+\frac{8}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{+10} & = & \color{red}{-81x} +8 \\\Leftrightarrow & -72x \color{red}{+10} \color{blue}{-10} \color{blue}{+81x} & = & \color{red}{-81x} +8 \color{blue}{+81x} \color{blue}{-10} \\\Leftrightarrow & -72x+81x& = & 8-10 \\\Leftrightarrow & \color{red}{9} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{9} & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{4}{11})& = & 9x+\frac{6}{11} \\\Leftrightarrow & -8x+\frac{16}{11}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-88}{ \color{blue}{11} }x+ \frac{16}{ \color{blue}{11} })& = & (\frac{99}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -88x \color{red}{+16} & = & \color{red}{99x} +6 \\\Leftrightarrow & -88x \color{red}{+16} \color{blue}{-16} \color{blue}{-99x} & = & \color{red}{99x} +6 \color{blue}{-99x} \color{blue}{-16} \\\Leftrightarrow & -88x-99x& = & 6-16 \\\Leftrightarrow & \color{red}{-187} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-187} & & \\\Leftrightarrow & x = \frac{10}{187} & & \\ & V = \left\{ \frac{10}{187} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{11})& = & -7x+\frac{7}{10} \\\Leftrightarrow & -24x-\frac{18}{11}& = & -7x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-2640}{ \color{blue}{110} }x- \frac{180}{ \color{blue}{110} })& = & (\frac{-770}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -2640x \color{red}{-180} & = & \color{red}{-770x} +77 \\\Leftrightarrow & -2640x \color{red}{-180} \color{blue}{+180} \color{blue}{+770x} & = & \color{red}{-770x} +77 \color{blue}{+770x} \color{blue}{+180} \\\Leftrightarrow & -2640x+770x& = & 77+180 \\\Leftrightarrow & \color{red}{-1870} x& = & 257 \\\Leftrightarrow & x = \frac{257}{-1870} & & \\\Leftrightarrow & x = \frac{-257}{1870} & & \\ & V = \left\{ \frac{-257}{1870} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{4}{11})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -9x-\frac{12}{11}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-99}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -99x \color{red}{-12} & = & \color{red}{55x} +5 \\\Leftrightarrow & -99x \color{red}{-12} \color{blue}{+12} \color{blue}{-55x} & = & \color{red}{55x} +5 \color{blue}{-55x} \color{blue}{+12} \\\Leftrightarrow & -99x-55x& = & 5+12 \\\Leftrightarrow & \color{red}{-154} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-154} & & \\\Leftrightarrow & x = \frac{-17}{154} & & \\ & V = \left\{ \frac{-17}{154} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{4}{9})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 8x-\frac{8}{9}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-56} & = & \color{red}{315x} +90 \\\Leftrightarrow & 504x \color{red}{-56} \color{blue}{+56} \color{blue}{-315x} & = & \color{red}{315x} +90 \color{blue}{-315x} \color{blue}{+56} \\\Leftrightarrow & 504x-315x& = & 90+56 \\\Leftrightarrow & \color{red}{189} x& = & 146 \\\Leftrightarrow & x = \frac{146}{189} & & \\ & V = \left\{ \frac{146}{189} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{2}{7})& = & -4x+\frac{4}{3} \\\Leftrightarrow & -15x+\frac{6}{7}& = & -4x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-84}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{+18} & = & \color{red}{-84x} +28 \\\Leftrightarrow & -315x \color{red}{+18} \color{blue}{-18} \color{blue}{+84x} & = & \color{red}{-84x} +28 \color{blue}{+84x} \color{blue}{-18} \\\Leftrightarrow & -315x+84x& = & 28-18 \\\Leftrightarrow & \color{red}{-231} x& = & 10 \\\Leftrightarrow & x = \frac{10}{-231} & & \\\Leftrightarrow & x = \frac{-10}{231} & & \\ & V = \left\{ \frac{-10}{231} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{5}{7})& = & 5x+\frac{3}{11} \\\Leftrightarrow & 8x+\frac{20}{7}& = & 5x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{+220} & = & \color{red}{385x} +21 \\\Leftrightarrow & 616x \color{red}{+220} \color{blue}{-220} \color{blue}{-385x} & = & \color{red}{385x} +21 \color{blue}{-385x} \color{blue}{-220} \\\Leftrightarrow & 616x-385x& = & 21-220 \\\Leftrightarrow & \color{red}{231} x& = & -199 \\\Leftrightarrow & x = \frac{-199}{231} & & \\ & V = \left\{ \frac{-199}{231} \right\} & \\\end{align}\)
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