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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{5}{11})& = & -9x+\frac{4}{3} \\\Leftrightarrow & -18x-\frac{30}{11}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-594}{ \color{blue}{33} }x- \frac{90}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -594x \color{red}{-90} & = & \color{red}{-297x} +44 \\\Leftrightarrow & -594x \color{red}{-90} \color{blue}{+90} \color{blue}{+297x} & = & \color{red}{-297x} +44 \color{blue}{+297x} \color{blue}{+90} \\\Leftrightarrow & -594x+297x& = & 44+90 \\\Leftrightarrow & \color{red}{-297} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-297} & & \\\Leftrightarrow & x = \frac{-134}{297} & & \\ & V = \left\{ \frac{-134}{297} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{4}{3})& = & -4x+\frac{8}{3} \\\Leftrightarrow & -15x-\frac{20}{3}& = & -4x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-45}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{-12}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -45x \color{red}{-20} & = & \color{red}{-12x} +8 \\\Leftrightarrow & -45x \color{red}{-20} \color{blue}{+20} \color{blue}{+12x} & = & \color{red}{-12x} +8 \color{blue}{+12x} \color{blue}{+20} \\\Leftrightarrow & -45x+12x& = & 8+20 \\\Leftrightarrow & \color{red}{-33} x& = & 28 \\\Leftrightarrow & x = \frac{28}{-33} & & \\\Leftrightarrow & x = \frac{-28}{33} & & \\ & V = \left\{ \frac{-28}{33} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{5}{12})& = & 6x+\frac{10}{3} \\\Leftrightarrow & -25x+\frac{25}{12}& = & 6x+\frac{10}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-300}{ \color{blue}{12} }x+ \frac{25}{ \color{blue}{12} })& = & (\frac{72}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -300x \color{red}{+25} & = & \color{red}{72x} +40 \\\Leftrightarrow & -300x \color{red}{+25} \color{blue}{-25} \color{blue}{-72x} & = & \color{red}{72x} +40 \color{blue}{-72x} \color{blue}{-25} \\\Leftrightarrow & -300x-72x& = & 40-25 \\\Leftrightarrow & \color{red}{-372} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-372} & & \\\Leftrightarrow & x = \frac{-5}{124} & & \\ & V = \left\{ \frac{-5}{124} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{4}{5})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -9x-\frac{12}{5}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-135}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -135x \color{red}{-36} & = & \color{red}{-105x} +50 \\\Leftrightarrow & -135x \color{red}{-36} \color{blue}{+36} \color{blue}{+105x} & = & \color{red}{-105x} +50 \color{blue}{+105x} \color{blue}{+36} \\\Leftrightarrow & -135x+105x& = & 50+36 \\\Leftrightarrow & \color{red}{-30} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-30} & & \\\Leftrightarrow & x = \frac{-43}{15} & & \\ & V = \left\{ \frac{-43}{15} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{3}{5})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 8x+\frac{12}{5}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+36} & = & \color{red}{75x} +20 \\\Leftrightarrow & 120x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +20 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & 120x-75x& = & 20-36 \\\Leftrightarrow & \color{red}{45} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{45} & & \\ & V = \left\{ \frac{-16}{45} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{5}{6})& = & -2x+\frac{5}{7} \\\Leftrightarrow & 21x+\frac{35}{6}& = & -2x+\frac{5}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{882}{ \color{blue}{42} }x+ \frac{245}{ \color{blue}{42} })& = & (\frac{-84}{ \color{blue}{42} }x+ \frac{30}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 882x \color{red}{+245} & = & \color{red}{-84x} +30 \\\Leftrightarrow & 882x \color{red}{+245} \color{blue}{-245} \color{blue}{+84x} & = & \color{red}{-84x} +30 \color{blue}{+84x} \color{blue}{-245} \\\Leftrightarrow & 882x+84x& = & 30-245 \\\Leftrightarrow & \color{red}{966} x& = & -215 \\\Leftrightarrow & x = \frac{-215}{966} & & \\ & V = \left\{ \frac{-215}{966} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{4}{11})& = & 5x+\frac{7}{5} \\\Leftrightarrow & 24x+\frac{24}{11}& = & 5x+\frac{7}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x+ \frac{120}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{77}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{+120} & = & \color{red}{275x} +77 \\\Leftrightarrow & 1320x \color{red}{+120} \color{blue}{-120} \color{blue}{-275x} & = & \color{red}{275x} +77 \color{blue}{-275x} \color{blue}{-120} \\\Leftrightarrow & 1320x-275x& = & 77-120 \\\Leftrightarrow & \color{red}{1045} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{1045} & & \\ & V = \left\{ \frac{-43}{1045} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{2}{5})& = & -7x+\frac{8}{7} \\\Leftrightarrow & -30x+\frac{12}{5}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{+84} & = & \color{red}{-245x} +40 \\\Leftrightarrow & -1050x \color{red}{+84} \color{blue}{-84} \color{blue}{+245x} & = & \color{red}{-245x} +40 \color{blue}{+245x} \color{blue}{-84} \\\Leftrightarrow & -1050x+245x& = & 40-84 \\\Leftrightarrow & \color{red}{-805} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{-805} & & \\\Leftrightarrow & x = \frac{44}{805} & & \\ & V = \left\{ \frac{44}{805} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{4}{7})& = & 7x+\frac{5}{11} \\\Leftrightarrow & -10x+\frac{20}{7}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{+220} & = & \color{red}{539x} +35 \\\Leftrightarrow & -770x \color{red}{+220} \color{blue}{-220} \color{blue}{-539x} & = & \color{red}{539x} +35 \color{blue}{-539x} \color{blue}{-220} \\\Leftrightarrow & -770x-539x& = & 35-220 \\\Leftrightarrow & \color{red}{-1309} x& = & -185 \\\Leftrightarrow & x = \frac{-185}{-1309} & & \\\Leftrightarrow & x = \frac{185}{1309} & & \\ & V = \left\{ \frac{185}{1309} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{5}{7})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 18x-\frac{30}{7}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1134}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1134x \color{red}{-270} & = & \color{red}{-315x} +56 \\\Leftrightarrow & 1134x \color{red}{-270} \color{blue}{+270} \color{blue}{+315x} & = & \color{red}{-315x} +56 \color{blue}{+315x} \color{blue}{+270} \\\Leftrightarrow & 1134x+315x& = & 56+270 \\\Leftrightarrow & \color{red}{1449} x& = & 326 \\\Leftrightarrow & x = \frac{326}{1449} & & \\ & V = \left\{ \frac{326}{1449} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{4}{3})& = & 3x+\frac{2}{11} \\\Leftrightarrow & 4x+\frac{8}{3}& = & 3x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{132}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 132x \color{red}{+88} & = & \color{red}{99x} +6 \\\Leftrightarrow & 132x \color{red}{+88} \color{blue}{-88} \color{blue}{-99x} & = & \color{red}{99x} +6 \color{blue}{-99x} \color{blue}{-88} \\\Leftrightarrow & 132x-99x& = & 6-88 \\\Leftrightarrow & \color{red}{33} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{33} & & \\ & V = \left\{ \frac{-82}{33} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{4}{3})& = & -3x+\frac{5}{3} \\\Leftrightarrow & 20x-\frac{20}{3}& = & -3x+\frac{5}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{60}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{5}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 60x \color{red}{-20} & = & \color{red}{-9x} +5 \\\Leftrightarrow & 60x \color{red}{-20} \color{blue}{+20} \color{blue}{+9x} & = & \color{red}{-9x} +5 \color{blue}{+9x} \color{blue}{+20} \\\Leftrightarrow & 60x+9x& = & 5+20 \\\Leftrightarrow & \color{red}{69} x& = & 25 \\\Leftrightarrow & x = \frac{25}{69} & & \\ & V = \left\{ \frac{25}{69} \right\} & \\\end{align}\)
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