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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{2}{5})& = & -3x+\frac{7}{11} \\\Leftrightarrow & -20x-\frac{8}{5}& = & -3x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1100}{ \color{blue}{55} }x- \frac{88}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1100x \color{red}{-88} & = & \color{red}{-165x} +35 \\\Leftrightarrow & -1100x \color{red}{-88} \color{blue}{+88} \color{blue}{+165x} & = & \color{red}{-165x} +35 \color{blue}{+165x} \color{blue}{+88} \\\Leftrightarrow & -1100x+165x& = & 35+88 \\\Leftrightarrow & \color{red}{-935} x& = & 123 \\\Leftrightarrow & x = \frac{123}{-935} & & \\\Leftrightarrow & x = \frac{-123}{935} & & \\ & V = \left\{ \frac{-123}{935} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{2}{9})& = & -5x+\frac{3}{10} \\\Leftrightarrow & 8x+\frac{8}{9}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{720}{ \color{blue}{90} }x+ \frac{80}{ \color{blue}{90} })& = & (\frac{-450}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 720x \color{red}{+80} & = & \color{red}{-450x} +27 \\\Leftrightarrow & 720x \color{red}{+80} \color{blue}{-80} \color{blue}{+450x} & = & \color{red}{-450x} +27 \color{blue}{+450x} \color{blue}{-80} \\\Leftrightarrow & 720x+450x& = & 27-80 \\\Leftrightarrow & \color{red}{1170} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{1170} & & \\ & V = \left\{ \frac{-53}{1170} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{9})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 21x-\frac{35}{9}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1323}{ \color{blue}{63} }x- \frac{245}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1323x \color{red}{-245} & = & \color{red}{-315x} +54 \\\Leftrightarrow & 1323x \color{red}{-245} \color{blue}{+245} \color{blue}{+315x} & = & \color{red}{-315x} +54 \color{blue}{+315x} \color{blue}{+245} \\\Leftrightarrow & 1323x+315x& = & 54+245 \\\Leftrightarrow & \color{red}{1638} x& = & 299 \\\Leftrightarrow & x = \frac{299}{1638} & & \\\Leftrightarrow & x = \frac{23}{126} & & \\ & V = \left\{ \frac{23}{126} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{2}{3})& = & 8x+\frac{10}{9} \\\Leftrightarrow & -21x+\frac{14}{3}& = & 8x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-189}{ \color{blue}{9} }x+ \frac{42}{ \color{blue}{9} })& = & (\frac{72}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -189x \color{red}{+42} & = & \color{red}{72x} +10 \\\Leftrightarrow & -189x \color{red}{+42} \color{blue}{-42} \color{blue}{-72x} & = & \color{red}{72x} +10 \color{blue}{-72x} \color{blue}{-42} \\\Leftrightarrow & -189x-72x& = & 10-42 \\\Leftrightarrow & \color{red}{-261} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-261} & & \\\Leftrightarrow & x = \frac{32}{261} & & \\ & V = \left\{ \frac{32}{261} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{4}{5})& = & 7x+\frac{10}{11} \\\Leftrightarrow & 12x+\frac{24}{5}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+264} & = & \color{red}{385x} +50 \\\Leftrightarrow & 660x \color{red}{+264} \color{blue}{-264} \color{blue}{-385x} & = & \color{red}{385x} +50 \color{blue}{-385x} \color{blue}{-264} \\\Leftrightarrow & 660x-385x& = & 50-264 \\\Leftrightarrow & \color{red}{275} x& = & -214 \\\Leftrightarrow & x = \frac{-214}{275} & & \\ & V = \left\{ \frac{-214}{275} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{3}{7})& = & 7x+\frac{9}{10} \\\Leftrightarrow & -10x-\frac{6}{7}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-700}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -700x \color{red}{-60} & = & \color{red}{490x} +63 \\\Leftrightarrow & -700x \color{red}{-60} \color{blue}{+60} \color{blue}{-490x} & = & \color{red}{490x} +63 \color{blue}{-490x} \color{blue}{+60} \\\Leftrightarrow & -700x-490x& = & 63+60 \\\Leftrightarrow & \color{red}{-1190} x& = & 123 \\\Leftrightarrow & x = \frac{123}{-1190} & & \\\Leftrightarrow & x = \frac{-123}{1190} & & \\ & V = \left\{ \frac{-123}{1190} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{3}{4})& = & -6x+\frac{6}{7} \\\Leftrightarrow & 25x-\frac{15}{4}& = & -6x+\frac{6}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{700}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-168}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 700x \color{red}{-105} & = & \color{red}{-168x} +24 \\\Leftrightarrow & 700x \color{red}{-105} \color{blue}{+105} \color{blue}{+168x} & = & \color{red}{-168x} +24 \color{blue}{+168x} \color{blue}{+105} \\\Leftrightarrow & 700x+168x& = & 24+105 \\\Leftrightarrow & \color{red}{868} x& = & 129 \\\Leftrightarrow & x = \frac{129}{868} & & \\ & V = \left\{ \frac{129}{868} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{5})& = & 7x+\frac{7}{8} \\\Leftrightarrow & -30x+\frac{24}{5}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1200}{ \color{blue}{40} }x+ \frac{192}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1200x \color{red}{+192} & = & \color{red}{280x} +35 \\\Leftrightarrow & -1200x \color{red}{+192} \color{blue}{-192} \color{blue}{-280x} & = & \color{red}{280x} +35 \color{blue}{-280x} \color{blue}{-192} \\\Leftrightarrow & -1200x-280x& = & 35-192 \\\Leftrightarrow & \color{red}{-1480} x& = & -157 \\\Leftrightarrow & x = \frac{-157}{-1480} & & \\\Leftrightarrow & x = \frac{157}{1480} & & \\ & V = \left\{ \frac{157}{1480} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{5}{11})& = & -7x+\frac{9}{11} \\\Leftrightarrow & 20x+\frac{25}{11}& = & -7x+\frac{9}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{220}{ \color{blue}{11} }x+ \frac{25}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 220x \color{red}{+25} & = & \color{red}{-77x} +9 \\\Leftrightarrow & 220x \color{red}{+25} \color{blue}{-25} \color{blue}{+77x} & = & \color{red}{-77x} +9 \color{blue}{+77x} \color{blue}{-25} \\\Leftrightarrow & 220x+77x& = & 9-25 \\\Leftrightarrow & \color{red}{297} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{297} & & \\ & V = \left\{ \frac{-16}{297} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{5}{3})& = & 7x+\frac{5}{2} \\\Leftrightarrow & 20x-\frac{25}{3}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x- \frac{50}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{-50} & = & \color{red}{42x} +15 \\\Leftrightarrow & 120x \color{red}{-50} \color{blue}{+50} \color{blue}{-42x} & = & \color{red}{42x} +15 \color{blue}{-42x} \color{blue}{+50} \\\Leftrightarrow & 120x-42x& = & 15+50 \\\Leftrightarrow & \color{red}{78} x& = & 65 \\\Leftrightarrow & x = \frac{65}{78} & & \\\Leftrightarrow & x = \frac{5}{6} & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{5}{7})& = & 3x+\frac{6}{5} \\\Leftrightarrow & -20x+\frac{20}{7}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{+100} & = & \color{red}{105x} +42 \\\Leftrightarrow & -700x \color{red}{+100} \color{blue}{-100} \color{blue}{-105x} & = & \color{red}{105x} +42 \color{blue}{-105x} \color{blue}{-100} \\\Leftrightarrow & -700x-105x& = & 42-100 \\\Leftrightarrow & \color{red}{-805} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{-805} & & \\\Leftrightarrow & x = \frac{58}{805} & & \\ & V = \left\{ \frac{58}{805} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 15x-\frac{6}{7}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{-18} & = & \color{red}{147x} +70 \\\Leftrightarrow & 315x \color{red}{-18} \color{blue}{+18} \color{blue}{-147x} & = & \color{red}{147x} +70 \color{blue}{-147x} \color{blue}{+18} \\\Leftrightarrow & 315x-147x& = & 70+18 \\\Leftrightarrow & \color{red}{168} x& = & 88 \\\Leftrightarrow & x = \frac{88}{168} & & \\\Leftrightarrow & x = \frac{11}{21} & & \\ & V = \left\{ \frac{11}{21} \right\} & \\\end{align}\)
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