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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{2}{9})& = & 9x+\frac{10}{7} \\\Leftrightarrow & -8x+\frac{8}{9}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-504}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{+56} & = & \color{red}{567x} +90 \\\Leftrightarrow & -504x \color{red}{+56} \color{blue}{-56} \color{blue}{-567x} & = & \color{red}{567x} +90 \color{blue}{-567x} \color{blue}{-56} \\\Leftrightarrow & -504x-567x& = & 90-56 \\\Leftrightarrow & \color{red}{-1071} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-1071} & & \\\Leftrightarrow & x = \frac{-2}{63} & & \\ & V = \left\{ \frac{-2}{63} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{5}{3})& = & 3x+\frac{6}{11} \\\Leftrightarrow & -14x-\frac{35}{3}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-462}{ \color{blue}{33} }x- \frac{385}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -462x \color{red}{-385} & = & \color{red}{99x} +18 \\\Leftrightarrow & -462x \color{red}{-385} \color{blue}{+385} \color{blue}{-99x} & = & \color{red}{99x} +18 \color{blue}{-99x} \color{blue}{+385} \\\Leftrightarrow & -462x-99x& = & 18+385 \\\Leftrightarrow & \color{red}{-561} x& = & 403 \\\Leftrightarrow & x = \frac{403}{-561} & & \\\Leftrightarrow & x = \frac{-403}{561} & & \\ & V = \left\{ \frac{-403}{561} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{5}{7})& = & -3x+\frac{4}{11} \\\Leftrightarrow & 10x+\frac{10}{7}& = & -3x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+110} & = & \color{red}{-231x} +28 \\\Leftrightarrow & 770x \color{red}{+110} \color{blue}{-110} \color{blue}{+231x} & = & \color{red}{-231x} +28 \color{blue}{+231x} \color{blue}{-110} \\\Leftrightarrow & 770x+231x& = & 28-110 \\\Leftrightarrow & \color{red}{1001} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{1001} & & \\ & V = \left\{ \frac{-82}{1001} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{2}{9})& = & -9x+\frac{8}{7} \\\Leftrightarrow & 16x-\frac{8}{9}& = & -9x+\frac{8}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1008}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1008x \color{red}{-56} & = & \color{red}{-567x} +72 \\\Leftrightarrow & 1008x \color{red}{-56} \color{blue}{+56} \color{blue}{+567x} & = & \color{red}{-567x} +72 \color{blue}{+567x} \color{blue}{+56} \\\Leftrightarrow & 1008x+567x& = & 72+56 \\\Leftrightarrow & \color{red}{1575} x& = & 128 \\\Leftrightarrow & x = \frac{128}{1575} & & \\ & V = \left\{ \frac{128}{1575} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{3}{10})& = & 4x+\frac{7}{2} \\\Leftrightarrow & -15x-\frac{9}{10}& = & 4x+\frac{7}{2} \\ & & & \text{kgv van noemers 10 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-150}{ \color{blue}{10} }x- \frac{9}{ \color{blue}{10} })& = & (\frac{40}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -150x \color{red}{-9} & = & \color{red}{40x} +35 \\\Leftrightarrow & -150x \color{red}{-9} \color{blue}{+9} \color{blue}{-40x} & = & \color{red}{40x} +35 \color{blue}{-40x} \color{blue}{+9} \\\Leftrightarrow & -150x-40x& = & 35+9 \\\Leftrightarrow & \color{red}{-190} x& = & 44 \\\Leftrightarrow & x = \frac{44}{-190} & & \\\Leftrightarrow & x = \frac{-22}{95} & & \\ & V = \left\{ \frac{-22}{95} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{2}{3})& = & 7x+\frac{7}{9} \\\Leftrightarrow & 20x+\frac{8}{3}& = & 7x+\frac{7}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+24} & = & \color{red}{63x} +7 \\\Leftrightarrow & 180x \color{red}{+24} \color{blue}{-24} \color{blue}{-63x} & = & \color{red}{63x} +7 \color{blue}{-63x} \color{blue}{-24} \\\Leftrightarrow & 180x-63x& = & 7-24 \\\Leftrightarrow & \color{red}{117} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{117} & & \\ & V = \left\{ \frac{-17}{117} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{2}{11})& = & -7x+\frac{8}{11} \\\Leftrightarrow & 12x-\frac{8}{11}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x- \frac{8}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{-8} & = & \color{red}{-77x} +8 \\\Leftrightarrow & 132x \color{red}{-8} \color{blue}{+8} \color{blue}{+77x} & = & \color{red}{-77x} +8 \color{blue}{+77x} \color{blue}{+8} \\\Leftrightarrow & 132x+77x& = & 8+8 \\\Leftrightarrow & \color{red}{209} x& = & 16 \\\Leftrightarrow & x = \frac{16}{209} & & \\ & V = \left\{ \frac{16}{209} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{3}{4})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 20x+\frac{15}{4}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{400}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{60}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 400x \color{red}{+75} & = & \color{red}{60x} +24 \\\Leftrightarrow & 400x \color{red}{+75} \color{blue}{-75} \color{blue}{-60x} & = & \color{red}{60x} +24 \color{blue}{-60x} \color{blue}{-75} \\\Leftrightarrow & 400x-60x& = & 24-75 \\\Leftrightarrow & \color{red}{340} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{340} & & \\\Leftrightarrow & x = \frac{-3}{20} & & \\ & V = \left\{ \frac{-3}{20} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{5}{8})& = & -8x+\frac{8}{5} \\\Leftrightarrow & -15x-\frac{25}{8}& = & -8x+\frac{8}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-600}{ \color{blue}{40} }x- \frac{125}{ \color{blue}{40} })& = & (\frac{-320}{ \color{blue}{40} }x+ \frac{64}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -600x \color{red}{-125} & = & \color{red}{-320x} +64 \\\Leftrightarrow & -600x \color{red}{-125} \color{blue}{+125} \color{blue}{+320x} & = & \color{red}{-320x} +64 \color{blue}{+320x} \color{blue}{+125} \\\Leftrightarrow & -600x+320x& = & 64+125 \\\Leftrightarrow & \color{red}{-280} x& = & 189 \\\Leftrightarrow & x = \frac{189}{-280} & & \\\Leftrightarrow & x = \frac{-27}{40} & & \\ & V = \left\{ \frac{-27}{40} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{7})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 18x+\frac{30}{7}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{126}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 126x \color{red}{+30} & = & \color{red}{35x} +10 \\\Leftrightarrow & 126x \color{red}{+30} \color{blue}{-30} \color{blue}{-35x} & = & \color{red}{35x} +10 \color{blue}{-35x} \color{blue}{-30} \\\Leftrightarrow & 126x-35x& = & 10-30 \\\Leftrightarrow & \color{red}{91} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{91} & & \\ & V = \left\{ \frac{-20}{91} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{5}{4})& = & 5x+\frac{3}{7} \\\Leftrightarrow & 12x+\frac{15}{4}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{336}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{12}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 336x \color{red}{+105} & = & \color{red}{140x} +12 \\\Leftrightarrow & 336x \color{red}{+105} \color{blue}{-105} \color{blue}{-140x} & = & \color{red}{140x} +12 \color{blue}{-140x} \color{blue}{-105} \\\Leftrightarrow & 336x-140x& = & 12-105 \\\Leftrightarrow & \color{red}{196} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{196} & & \\ & V = \left\{ \frac{-93}{196} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{4}{7})& = & 5x+\frac{6}{7} \\\Leftrightarrow & -12x-\frac{16}{7}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{-16} & = & \color{red}{35x} +6 \\\Leftrightarrow & -84x \color{red}{-16} \color{blue}{+16} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{+16} \\\Leftrightarrow & -84x-35x& = & 6+16 \\\Leftrightarrow & \color{red}{-119} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-119} & & \\\Leftrightarrow & x = \frac{-22}{119} & & \\ & V = \left\{ \frac{-22}{119} \right\} & \\\end{align}\)
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