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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{2}{11})& = & -7x+\frac{5}{8} \\\Leftrightarrow & 4x-\frac{4}{11}& = & -7x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{352}{ \color{blue}{88} }x- \frac{32}{ \color{blue}{88} })& = & (\frac{-616}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 352x \color{red}{-32} & = & \color{red}{-616x} +55 \\\Leftrightarrow & 352x \color{red}{-32} \color{blue}{+32} \color{blue}{+616x} & = & \color{red}{-616x} +55 \color{blue}{+616x} \color{blue}{+32} \\\Leftrightarrow & 352x+616x& = & 55+32 \\\Leftrightarrow & \color{red}{968} x& = & 87 \\\Leftrightarrow & x = \frac{87}{968} & & \\ & V = \left\{ \frac{87}{968} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{11})& = & 5x+\frac{5}{3} \\\Leftrightarrow & 24x+\frac{24}{11}& = & 5x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{792}{ \color{blue}{33} }x+ \frac{72}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{+72} & = & \color{red}{165x} +55 \\\Leftrightarrow & 792x \color{red}{+72} \color{blue}{-72} \color{blue}{-165x} & = & \color{red}{165x} +55 \color{blue}{-165x} \color{blue}{-72} \\\Leftrightarrow & 792x-165x& = & 55-72 \\\Leftrightarrow & \color{red}{627} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{627} & & \\ & V = \left\{ \frac{-17}{627} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{2}{9})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -16x-\frac{8}{9}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-144}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -144x \color{red}{-8} & = & \color{red}{-63x} +30 \\\Leftrightarrow & -144x \color{red}{-8} \color{blue}{+8} \color{blue}{+63x} & = & \color{red}{-63x} +30 \color{blue}{+63x} \color{blue}{+8} \\\Leftrightarrow & -144x+63x& = & 30+8 \\\Leftrightarrow & \color{red}{-81} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-81} & & \\\Leftrightarrow & x = \frac{-38}{81} & & \\ & V = \left\{ \frac{-38}{81} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{2}{9})& = & 5x+\frac{2}{5} \\\Leftrightarrow & -12x+\frac{8}{9}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-540}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{18}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -540x \color{red}{+40} & = & \color{red}{225x} +18 \\\Leftrightarrow & -540x \color{red}{+40} \color{blue}{-40} \color{blue}{-225x} & = & \color{red}{225x} +18 \color{blue}{-225x} \color{blue}{-40} \\\Leftrightarrow & -540x-225x& = & 18-40 \\\Leftrightarrow & \color{red}{-765} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-765} & & \\\Leftrightarrow & x = \frac{22}{765} & & \\ & V = \left\{ \frac{22}{765} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{9})& = & 4x+\frac{2}{11} \\\Leftrightarrow & 21x-\frac{35}{9}& = & 4x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2079}{ \color{blue}{99} }x- \frac{385}{ \color{blue}{99} })& = & (\frac{396}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2079x \color{red}{-385} & = & \color{red}{396x} +18 \\\Leftrightarrow & 2079x \color{red}{-385} \color{blue}{+385} \color{blue}{-396x} & = & \color{red}{396x} +18 \color{blue}{-396x} \color{blue}{+385} \\\Leftrightarrow & 2079x-396x& = & 18+385 \\\Leftrightarrow & \color{red}{1683} x& = & 403 \\\Leftrightarrow & x = \frac{403}{1683} & & \\ & V = \left\{ \frac{403}{1683} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{3}{11})& = & 4x+\frac{3}{10} \\\Leftrightarrow & -35x-\frac{21}{11}& = & 4x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-3850}{ \color{blue}{110} }x- \frac{210}{ \color{blue}{110} })& = & (\frac{440}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -3850x \color{red}{-210} & = & \color{red}{440x} +33 \\\Leftrightarrow & -3850x \color{red}{-210} \color{blue}{+210} \color{blue}{-440x} & = & \color{red}{440x} +33 \color{blue}{-440x} \color{blue}{+210} \\\Leftrightarrow & -3850x-440x& = & 33+210 \\\Leftrightarrow & \color{red}{-4290} x& = & 243 \\\Leftrightarrow & x = \frac{243}{-4290} & & \\\Leftrightarrow & x = \frac{-81}{1430} & & \\ & V = \left\{ \frac{-81}{1430} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{3}{2})& = & 7x+\frac{5}{7} \\\Leftrightarrow & -6x-\frac{9}{2}& = & 7x+\frac{5}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-84}{ \color{blue}{14} }x- \frac{63}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{10}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -84x \color{red}{-63} & = & \color{red}{98x} +10 \\\Leftrightarrow & -84x \color{red}{-63} \color{blue}{+63} \color{blue}{-98x} & = & \color{red}{98x} +10 \color{blue}{-98x} \color{blue}{+63} \\\Leftrightarrow & -84x-98x& = & 10+63 \\\Leftrightarrow & \color{red}{-182} x& = & 73 \\\Leftrightarrow & x = \frac{73}{-182} & & \\\Leftrightarrow & x = \frac{-73}{182} & & \\ & V = \left\{ \frac{-73}{182} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{6})& = & -7x+\frac{9}{7} \\\Leftrightarrow & 20x+\frac{25}{6}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{840}{ \color{blue}{42} }x+ \frac{175}{ \color{blue}{42} })& = & (\frac{-294}{ \color{blue}{42} }x+ \frac{54}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 840x \color{red}{+175} & = & \color{red}{-294x} +54 \\\Leftrightarrow & 840x \color{red}{+175} \color{blue}{-175} \color{blue}{+294x} & = & \color{red}{-294x} +54 \color{blue}{+294x} \color{blue}{-175} \\\Leftrightarrow & 840x+294x& = & 54-175 \\\Leftrightarrow & \color{red}{1134} x& = & -121 \\\Leftrightarrow & x = \frac{-121}{1134} & & \\ & V = \left\{ \frac{-121}{1134} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{4}{5})& = & -5x+\frac{5}{9} \\\Leftrightarrow & 18x-\frac{24}{5}& = & -5x+\frac{5}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{810}{ \color{blue}{45} }x- \frac{216}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{25}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 810x \color{red}{-216} & = & \color{red}{-225x} +25 \\\Leftrightarrow & 810x \color{red}{-216} \color{blue}{+216} \color{blue}{+225x} & = & \color{red}{-225x} +25 \color{blue}{+225x} \color{blue}{+216} \\\Leftrightarrow & 810x+225x& = & 25+216 \\\Leftrightarrow & \color{red}{1035} x& = & 241 \\\Leftrightarrow & x = \frac{241}{1035} & & \\ & V = \left\{ \frac{241}{1035} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{7})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 16x+\frac{20}{7}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1232}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1232x \color{red}{+220} & = & \color{red}{-385x} +42 \\\Leftrightarrow & 1232x \color{red}{+220} \color{blue}{-220} \color{blue}{+385x} & = & \color{red}{-385x} +42 \color{blue}{+385x} \color{blue}{-220} \\\Leftrightarrow & 1232x+385x& = & 42-220 \\\Leftrightarrow & \color{red}{1617} x& = & -178 \\\Leftrightarrow & x = \frac{-178}{1617} & & \\ & V = \left\{ \frac{-178}{1617} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{2}{7})& = & 4x+\frac{2}{7} \\\Leftrightarrow & 9x+\frac{6}{7}& = & 4x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{63}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{28}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 63x \color{red}{+6} & = & \color{red}{28x} +2 \\\Leftrightarrow & 63x \color{red}{+6} \color{blue}{-6} \color{blue}{-28x} & = & \color{red}{28x} +2 \color{blue}{-28x} \color{blue}{-6} \\\Leftrightarrow & 63x-28x& = & 2-6 \\\Leftrightarrow & \color{red}{35} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{35} & & \\ & V = \left\{ \frac{-4}{35} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{3})& = & 9x+\frac{5}{8} \\\Leftrightarrow & -20x+\frac{16}{3}& = & 9x+\frac{5}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-480}{ \color{blue}{24} }x+ \frac{128}{ \color{blue}{24} })& = & (\frac{216}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -480x \color{red}{+128} & = & \color{red}{216x} +15 \\\Leftrightarrow & -480x \color{red}{+128} \color{blue}{-128} \color{blue}{-216x} & = & \color{red}{216x} +15 \color{blue}{-216x} \color{blue}{-128} \\\Leftrightarrow & -480x-216x& = & 15-128 \\\Leftrightarrow & \color{red}{-696} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{-696} & & \\\Leftrightarrow & x = \frac{113}{696} & & \\ & V = \left\{ \frac{113}{696} \right\} & \\\end{align}\)
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