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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{11})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -16x+\frac{8}{11}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-176}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -176x \color{red}{+8} & = & \color{red}{-77x} +2 \\\Leftrightarrow & -176x \color{red}{+8} \color{blue}{-8} \color{blue}{+77x} & = & \color{red}{-77x} +2 \color{blue}{+77x} \color{blue}{-8} \\\Leftrightarrow & -176x+77x& = & 2-8 \\\Leftrightarrow & \color{red}{-99} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-99} & & \\\Leftrightarrow & x = \frac{2}{33} & & \\ & V = \left\{ \frac{2}{33} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{2}{3})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 14x-\frac{14}{3}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{294}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 294x \color{red}{-98} & = & \color{red}{-105x} +18 \\\Leftrightarrow & 294x \color{red}{-98} \color{blue}{+98} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{+98} \\\Leftrightarrow & 294x+105x& = & 18+98 \\\Leftrightarrow & \color{red}{399} x& = & 116 \\\Leftrightarrow & x = \frac{116}{399} & & \\ & V = \left\{ \frac{116}{399} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{3}{7})& = & 5x+\frac{8}{9} \\\Leftrightarrow & -12x-\frac{9}{7}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x- \frac{81}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{-81} & = & \color{red}{315x} +56 \\\Leftrightarrow & -756x \color{red}{-81} \color{blue}{+81} \color{blue}{-315x} & = & \color{red}{315x} +56 \color{blue}{-315x} \color{blue}{+81} \\\Leftrightarrow & -756x-315x& = & 56+81 \\\Leftrightarrow & \color{red}{-1071} x& = & 137 \\\Leftrightarrow & x = \frac{137}{-1071} & & \\\Leftrightarrow & x = \frac{-137}{1071} & & \\ & V = \left\{ \frac{-137}{1071} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{5})& = & 7x+\frac{9}{5} \\\Leftrightarrow & 8x+\frac{4}{5}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{40}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 40x \color{red}{+4} & = & \color{red}{35x} +9 \\\Leftrightarrow & 40x \color{red}{+4} \color{blue}{-4} \color{blue}{-35x} & = & \color{red}{35x} +9 \color{blue}{-35x} \color{blue}{-4} \\\Leftrightarrow & 40x-35x& = & 9-4 \\\Leftrightarrow & \color{red}{5} x& = & 5 \\\Leftrightarrow & x = \frac{5}{5} & & \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{10})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -9x-\frac{9}{10}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-270}{ \color{blue}{30} }x- \frac{27}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{40}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -270x \color{red}{-27} & = & \color{red}{-150x} +40 \\\Leftrightarrow & -270x \color{red}{-27} \color{blue}{+27} \color{blue}{+150x} & = & \color{red}{-150x} +40 \color{blue}{+150x} \color{blue}{+27} \\\Leftrightarrow & -270x+150x& = & 40+27 \\\Leftrightarrow & \color{red}{-120} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-120} & & \\\Leftrightarrow & x = \frac{-67}{120} & & \\ & V = \left\{ \frac{-67}{120} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{3}{8})& = & 3x+\frac{6}{11} \\\Leftrightarrow & -14x+\frac{21}{8}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1232}{ \color{blue}{88} }x+ \frac{231}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1232x \color{red}{+231} & = & \color{red}{264x} +48 \\\Leftrightarrow & -1232x \color{red}{+231} \color{blue}{-231} \color{blue}{-264x} & = & \color{red}{264x} +48 \color{blue}{-264x} \color{blue}{-231} \\\Leftrightarrow & -1232x-264x& = & 48-231 \\\Leftrightarrow & \color{red}{-1496} x& = & -183 \\\Leftrightarrow & x = \frac{-183}{-1496} & & \\\Leftrightarrow & x = \frac{183}{1496} & & \\ & V = \left\{ \frac{183}{1496} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{4}{7})& = & 5x+\frac{5}{4} \\\Leftrightarrow & 6x-\frac{12}{7}& = & 5x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{168}{ \color{blue}{28} }x- \frac{48}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 168x \color{red}{-48} & = & \color{red}{140x} +35 \\\Leftrightarrow & 168x \color{red}{-48} \color{blue}{+48} \color{blue}{-140x} & = & \color{red}{140x} +35 \color{blue}{-140x} \color{blue}{+48} \\\Leftrightarrow & 168x-140x& = & 35+48 \\\Leftrightarrow & \color{red}{28} x& = & 83 \\\Leftrightarrow & x = \frac{83}{28} & & \\ & V = \left\{ \frac{83}{28} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{4}{5})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+36} & = & \color{red}{-105x} +20 \\\Leftrightarrow & 180x \color{red}{+36} \color{blue}{-36} \color{blue}{+105x} & = & \color{red}{-105x} +20 \color{blue}{+105x} \color{blue}{-36} \\\Leftrightarrow & 180x+105x& = & 20-36 \\\Leftrightarrow & \color{red}{285} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{285} & & \\ & V = \left\{ \frac{-16}{285} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{4}{7})& = & 8x+\frac{8}{9} \\\Leftrightarrow & -25x-\frac{20}{7}& = & 8x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1575}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{504}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1575x \color{red}{-180} & = & \color{red}{504x} +56 \\\Leftrightarrow & -1575x \color{red}{-180} \color{blue}{+180} \color{blue}{-504x} & = & \color{red}{504x} +56 \color{blue}{-504x} \color{blue}{+180} \\\Leftrightarrow & -1575x-504x& = & 56+180 \\\Leftrightarrow & \color{red}{-2079} x& = & 236 \\\Leftrightarrow & x = \frac{236}{-2079} & & \\\Leftrightarrow & x = \frac{-236}{2079} & & \\ & V = \left\{ \frac{-236}{2079} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{4}{3})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -10x-\frac{20}{3}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-120}{ \color{blue}{12} }x- \frac{80}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -120x \color{red}{-80} & = & \color{red}{84x} +9 \\\Leftrightarrow & -120x \color{red}{-80} \color{blue}{+80} \color{blue}{-84x} & = & \color{red}{84x} +9 \color{blue}{-84x} \color{blue}{+80} \\\Leftrightarrow & -120x-84x& = & 9+80 \\\Leftrightarrow & \color{red}{-204} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-204} & & \\\Leftrightarrow & x = \frac{-89}{204} & & \\ & V = \left\{ \frac{-89}{204} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{5}{4})& = & -5x+\frac{2}{9} \\\Leftrightarrow & 12x-\frac{15}{4}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{432}{ \color{blue}{36} }x- \frac{135}{ \color{blue}{36} })& = & (\frac{-180}{ \color{blue}{36} }x+ \frac{8}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 432x \color{red}{-135} & = & \color{red}{-180x} +8 \\\Leftrightarrow & 432x \color{red}{-135} \color{blue}{+135} \color{blue}{+180x} & = & \color{red}{-180x} +8 \color{blue}{+180x} \color{blue}{+135} \\\Leftrightarrow & 432x+180x& = & 8+135 \\\Leftrightarrow & \color{red}{612} x& = & 143 \\\Leftrightarrow & x = \frac{143}{612} & & \\ & V = \left\{ \frac{143}{612} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{5}{9})& = & 9x+\frac{8}{3} \\\Leftrightarrow & 14x+\frac{35}{9}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{126}{ \color{blue}{9} }x+ \frac{35}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 126x \color{red}{+35} & = & \color{red}{81x} +24 \\\Leftrightarrow & 126x \color{red}{+35} \color{blue}{-35} \color{blue}{-81x} & = & \color{red}{81x} +24 \color{blue}{-81x} \color{blue}{-35} \\\Leftrightarrow & 126x-81x& = & 24-35 \\\Leftrightarrow & \color{red}{45} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{45} & & \\ & V = \left\{ \frac{-11}{45} \right\} & \\\end{align}\)
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