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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{3}{7})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -4x-\frac{6}{7}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-56}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -56x \color{red}{-12} & = & \color{red}{70x} +63 \\\Leftrightarrow & -56x \color{red}{-12} \color{blue}{+12} \color{blue}{-70x} & = & \color{red}{70x} +63 \color{blue}{-70x} \color{blue}{+12} \\\Leftrightarrow & -56x-70x& = & 63+12 \\\Leftrightarrow & \color{red}{-126} x& = & 75 \\\Leftrightarrow & x = \frac{75}{-126} & & \\\Leftrightarrow & x = \frac{-25}{42} & & \\ & V = \left\{ \frac{-25}{42} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{2}{9})& = & 9x+\frac{4}{11} \\\Leftrightarrow & -8x-\frac{4}{9}& = & 9x+\frac{4}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-792}{ \color{blue}{99} }x- \frac{44}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{36}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -792x \color{red}{-44} & = & \color{red}{891x} +36 \\\Leftrightarrow & -792x \color{red}{-44} \color{blue}{+44} \color{blue}{-891x} & = & \color{red}{891x} +36 \color{blue}{-891x} \color{blue}{+44} \\\Leftrightarrow & -792x-891x& = & 36+44 \\\Leftrightarrow & \color{red}{-1683} x& = & 80 \\\Leftrightarrow & x = \frac{80}{-1683} & & \\\Leftrightarrow & x = \frac{-80}{1683} & & \\ & V = \left\{ \frac{-80}{1683} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{2}{11})& = & -2x+\frac{2}{11} \\\Leftrightarrow & 15x+\frac{10}{11}& = & -2x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{165}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{-22}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 165x \color{red}{+10} & = & \color{red}{-22x} +2 \\\Leftrightarrow & 165x \color{red}{+10} \color{blue}{-10} \color{blue}{+22x} & = & \color{red}{-22x} +2 \color{blue}{+22x} \color{blue}{-10} \\\Leftrightarrow & 165x+22x& = & 2-10 \\\Leftrightarrow & \color{red}{187} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{187} & & \\ & V = \left\{ \frac{-8}{187} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{2}{9})& = & -3x+\frac{2}{11} \\\Leftrightarrow & 10x-\frac{4}{9}& = & -3x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{990}{ \color{blue}{99} }x- \frac{44}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{-44} & = & \color{red}{-297x} +18 \\\Leftrightarrow & 990x \color{red}{-44} \color{blue}{+44} \color{blue}{+297x} & = & \color{red}{-297x} +18 \color{blue}{+297x} \color{blue}{+44} \\\Leftrightarrow & 990x+297x& = & 18+44 \\\Leftrightarrow & \color{red}{1287} x& = & 62 \\\Leftrightarrow & x = \frac{62}{1287} & & \\ & V = \left\{ \frac{62}{1287} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{2}{9})& = & 8x+\frac{6}{11} \\\Leftrightarrow & -15x-\frac{10}{9}& = & 8x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1485}{ \color{blue}{99} }x- \frac{110}{ \color{blue}{99} })& = & (\frac{792}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1485x \color{red}{-110} & = & \color{red}{792x} +54 \\\Leftrightarrow & -1485x \color{red}{-110} \color{blue}{+110} \color{blue}{-792x} & = & \color{red}{792x} +54 \color{blue}{-792x} \color{blue}{+110} \\\Leftrightarrow & -1485x-792x& = & 54+110 \\\Leftrightarrow & \color{red}{-2277} x& = & 164 \\\Leftrightarrow & x = \frac{164}{-2277} & & \\\Leftrightarrow & x = \frac{-164}{2277} & & \\ & V = \left\{ \frac{-164}{2277} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{7})& = & 3x+\frac{8}{3} \\\Leftrightarrow & 20x+\frac{10}{7}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+30} & = & \color{red}{63x} +56 \\\Leftrightarrow & 420x \color{red}{+30} \color{blue}{-30} \color{blue}{-63x} & = & \color{red}{63x} +56 \color{blue}{-63x} \color{blue}{-30} \\\Leftrightarrow & 420x-63x& = & 56-30 \\\Leftrightarrow & \color{red}{357} x& = & 26 \\\Leftrightarrow & x = \frac{26}{357} & & \\ & V = \left\{ \frac{26}{357} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{2}{3})& = & -2x+\frac{5}{11} \\\Leftrightarrow & -25x-\frac{10}{3}& = & -2x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-825}{ \color{blue}{33} }x- \frac{110}{ \color{blue}{33} })& = & (\frac{-66}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -825x \color{red}{-110} & = & \color{red}{-66x} +15 \\\Leftrightarrow & -825x \color{red}{-110} \color{blue}{+110} \color{blue}{+66x} & = & \color{red}{-66x} +15 \color{blue}{+66x} \color{blue}{+110} \\\Leftrightarrow & -825x+66x& = & 15+110 \\\Leftrightarrow & \color{red}{-759} x& = & 125 \\\Leftrightarrow & x = \frac{125}{-759} & & \\\Leftrightarrow & x = \frac{-125}{759} & & \\ & V = \left\{ \frac{-125}{759} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{2}{9})& = & -9x+\frac{4}{3} \\\Leftrightarrow & 14x-\frac{14}{9}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{126}{ \color{blue}{9} }x- \frac{14}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 126x \color{red}{-14} & = & \color{red}{-81x} +12 \\\Leftrightarrow & 126x \color{red}{-14} \color{blue}{+14} \color{blue}{+81x} & = & \color{red}{-81x} +12 \color{blue}{+81x} \color{blue}{+14} \\\Leftrightarrow & 126x+81x& = & 12+14 \\\Leftrightarrow & \color{red}{207} x& = & 26 \\\Leftrightarrow & x = \frac{26}{207} & & \\ & V = \left\{ \frac{26}{207} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{4}{3})& = & -9x+\frac{10}{7} \\\Leftrightarrow & -25x-\frac{20}{3}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-525}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -525x \color{red}{-140} & = & \color{red}{-189x} +30 \\\Leftrightarrow & -525x \color{red}{-140} \color{blue}{+140} \color{blue}{+189x} & = & \color{red}{-189x} +30 \color{blue}{+189x} \color{blue}{+140} \\\Leftrightarrow & -525x+189x& = & 30+140 \\\Leftrightarrow & \color{red}{-336} x& = & 170 \\\Leftrightarrow & x = \frac{170}{-336} & & \\\Leftrightarrow & x = \frac{-85}{168} & & \\ & V = \left\{ \frac{-85}{168} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & -5x+\frac{3}{5} \\\Leftrightarrow & -24x-\frac{18}{11}& = & -5x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{-90} & = & \color{red}{-275x} +33 \\\Leftrightarrow & -1320x \color{red}{-90} \color{blue}{+90} \color{blue}{+275x} & = & \color{red}{-275x} +33 \color{blue}{+275x} \color{blue}{+90} \\\Leftrightarrow & -1320x+275x& = & 33+90 \\\Leftrightarrow & \color{red}{-1045} x& = & 123 \\\Leftrightarrow & x = \frac{123}{-1045} & & \\\Leftrightarrow & x = \frac{-123}{1045} & & \\ & V = \left\{ \frac{-123}{1045} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{4}{11})& = & 5x+\frac{3}{4} \\\Leftrightarrow & -24x-\frac{24}{11}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1056}{ \color{blue}{44} }x- \frac{96}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1056x \color{red}{-96} & = & \color{red}{220x} +33 \\\Leftrightarrow & -1056x \color{red}{-96} \color{blue}{+96} \color{blue}{-220x} & = & \color{red}{220x} +33 \color{blue}{-220x} \color{blue}{+96} \\\Leftrightarrow & -1056x-220x& = & 33+96 \\\Leftrightarrow & \color{red}{-1276} x& = & 129 \\\Leftrightarrow & x = \frac{129}{-1276} & & \\\Leftrightarrow & x = \frac{-129}{1276} & & \\ & V = \left\{ \frac{-129}{1276} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{4}{5})& = & -5x+\frac{5}{6} \\\Leftrightarrow & -9x-\frac{12}{5}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-270}{ \color{blue}{30} }x- \frac{72}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -270x \color{red}{-72} & = & \color{red}{-150x} +25 \\\Leftrightarrow & -270x \color{red}{-72} \color{blue}{+72} \color{blue}{+150x} & = & \color{red}{-150x} +25 \color{blue}{+150x} \color{blue}{+72} \\\Leftrightarrow & -270x+150x& = & 25+72 \\\Leftrightarrow & \color{red}{-120} x& = & 97 \\\Leftrightarrow & x = \frac{97}{-120} & & \\\Leftrightarrow & x = \frac{-97}{120} & & \\ & V = \left\{ \frac{-97}{120} \right\} & \\\end{align}\)
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