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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{5}{7})& = & -3x+\frac{10}{3} \\\Leftrightarrow & -25x-\frac{25}{7}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-525}{ \color{blue}{21} }x- \frac{75}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -525x \color{red}{-75} & = & \color{red}{-63x} +70 \\\Leftrightarrow & -525x \color{red}{-75} \color{blue}{+75} \color{blue}{+63x} & = & \color{red}{-63x} +70 \color{blue}{+63x} \color{blue}{+75} \\\Leftrightarrow & -525x+63x& = & 70+75 \\\Leftrightarrow & \color{red}{-462} x& = & 145 \\\Leftrightarrow & x = \frac{145}{-462} & & \\\Leftrightarrow & x = \frac{-145}{462} & & \\ & V = \left\{ \frac{-145}{462} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{7})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 12x+\frac{12}{7}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{36}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+36} & = & \color{red}{105x} +14 \\\Leftrightarrow & 252x \color{red}{+36} \color{blue}{-36} \color{blue}{-105x} & = & \color{red}{105x} +14 \color{blue}{-105x} \color{blue}{-36} \\\Leftrightarrow & 252x-105x& = & 14-36 \\\Leftrightarrow & \color{red}{147} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{147} & & \\ & V = \left\{ \frac{-22}{147} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{2}{11})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -6x-\frac{6}{11}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-198}{ \color{blue}{33} }x- \frac{18}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -198x \color{red}{-18} & = & \color{red}{-231x} +44 \\\Leftrightarrow & -198x \color{red}{-18} \color{blue}{+18} \color{blue}{+231x} & = & \color{red}{-231x} +44 \color{blue}{+231x} \color{blue}{+18} \\\Leftrightarrow & -198x+231x& = & 44+18 \\\Leftrightarrow & \color{red}{33} x& = & 62 \\\Leftrightarrow & x = \frac{62}{33} & & \\ & V = \left\{ \frac{62}{33} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{4}{3})& = & -9x+\frac{9}{2} \\\Leftrightarrow & 35x-\frac{28}{3}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{210}{ \color{blue}{6} }x- \frac{56}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 210x \color{red}{-56} & = & \color{red}{-54x} +27 \\\Leftrightarrow & 210x \color{red}{-56} \color{blue}{+56} \color{blue}{+54x} & = & \color{red}{-54x} +27 \color{blue}{+54x} \color{blue}{+56} \\\Leftrightarrow & 210x+54x& = & 27+56 \\\Leftrightarrow & \color{red}{264} x& = & 83 \\\Leftrightarrow & x = \frac{83}{264} & & \\ & V = \left\{ \frac{83}{264} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{3}{7})& = & -9x+\frac{3}{8} \\\Leftrightarrow & -8x+\frac{12}{7}& = & -9x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-448}{ \color{blue}{56} }x+ \frac{96}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -448x \color{red}{+96} & = & \color{red}{-504x} +21 \\\Leftrightarrow & -448x \color{red}{+96} \color{blue}{-96} \color{blue}{+504x} & = & \color{red}{-504x} +21 \color{blue}{+504x} \color{blue}{-96} \\\Leftrightarrow & -448x+504x& = & 21-96 \\\Leftrightarrow & \color{red}{56} x& = & -75 \\\Leftrightarrow & x = \frac{-75}{56} & & \\ & V = \left\{ \frac{-75}{56} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{4}{11})& = & -4x+\frac{7}{11} \\\Leftrightarrow & -15x+\frac{12}{11}& = & -4x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-165}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{-44}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -165x \color{red}{+12} & = & \color{red}{-44x} +7 \\\Leftrightarrow & -165x \color{red}{+12} \color{blue}{-12} \color{blue}{+44x} & = & \color{red}{-44x} +7 \color{blue}{+44x} \color{blue}{-12} \\\Leftrightarrow & -165x+44x& = & 7-12 \\\Leftrightarrow & \color{red}{-121} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-121} & & \\\Leftrightarrow & x = \frac{5}{121} & & \\ & V = \left\{ \frac{5}{121} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{5}{7})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 24x+\frac{30}{7}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{504}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 504x \color{red}{+90} & = & \color{red}{-105x} +14 \\\Leftrightarrow & 504x \color{red}{+90} \color{blue}{-90} \color{blue}{+105x} & = & \color{red}{-105x} +14 \color{blue}{+105x} \color{blue}{-90} \\\Leftrightarrow & 504x+105x& = & 14-90 \\\Leftrightarrow & \color{red}{609} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{609} & & \\ & V = \left\{ \frac{-76}{609} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{4}{7})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -16x+\frac{16}{7}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-112}{ \color{blue}{7} }x+ \frac{16}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -112x \color{red}{+16} & = & \color{red}{-49x} +9 \\\Leftrightarrow & -112x \color{red}{+16} \color{blue}{-16} \color{blue}{+49x} & = & \color{red}{-49x} +9 \color{blue}{+49x} \color{blue}{-16} \\\Leftrightarrow & -112x+49x& = & 9-16 \\\Leftrightarrow & \color{red}{-63} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-63} & & \\\Leftrightarrow & x = \frac{1}{9} & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{3}{7})& = & -5x+\frac{4}{9} \\\Leftrightarrow & 6x-\frac{6}{7}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{-54} & = & \color{red}{-315x} +28 \\\Leftrightarrow & 378x \color{red}{-54} \color{blue}{+54} \color{blue}{+315x} & = & \color{red}{-315x} +28 \color{blue}{+315x} \color{blue}{+54} \\\Leftrightarrow & 378x+315x& = & 28+54 \\\Leftrightarrow & \color{red}{693} x& = & 82 \\\Leftrightarrow & x = \frac{82}{693} & & \\ & V = \left\{ \frac{82}{693} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{4}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 16x+\frac{16}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x+ \frac{48}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{+48} & = & \color{red}{-147x} +14 \\\Leftrightarrow & 336x \color{red}{+48} \color{blue}{-48} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{-48} \\\Leftrightarrow & 336x+147x& = & 14-48 \\\Leftrightarrow & \color{red}{483} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{483} & & \\ & V = \left\{ \frac{-34}{483} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{4}{7})& = & 7x+\frac{7}{2} \\\Leftrightarrow & 20x-\frac{16}{7}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{280}{ \color{blue}{14} }x- \frac{32}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 280x \color{red}{-32} & = & \color{red}{98x} +49 \\\Leftrightarrow & 280x \color{red}{-32} \color{blue}{+32} \color{blue}{-98x} & = & \color{red}{98x} +49 \color{blue}{-98x} \color{blue}{+32} \\\Leftrightarrow & 280x-98x& = & 49+32 \\\Leftrightarrow & \color{red}{182} x& = & 81 \\\Leftrightarrow & x = \frac{81}{182} & & \\ & V = \left\{ \frac{81}{182} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{5}{11})& = & -4x+\frac{3}{10} \\\Leftrightarrow & -15x-\frac{25}{11}& = & -4x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1650}{ \color{blue}{110} }x- \frac{250}{ \color{blue}{110} })& = & (\frac{-440}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1650x \color{red}{-250} & = & \color{red}{-440x} +33 \\\Leftrightarrow & -1650x \color{red}{-250} \color{blue}{+250} \color{blue}{+440x} & = & \color{red}{-440x} +33 \color{blue}{+440x} \color{blue}{+250} \\\Leftrightarrow & -1650x+440x& = & 33+250 \\\Leftrightarrow & \color{red}{-1210} x& = & 283 \\\Leftrightarrow & x = \frac{283}{-1210} & & \\\Leftrightarrow & x = \frac{-283}{1210} & & \\ & V = \left\{ \frac{-283}{1210} \right\} & \\\end{align}\)
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