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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{2}{11})& = & 7x+\frac{9}{7} \\\Leftrightarrow & 9x-\frac{6}{11}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{693}{ \color{blue}{77} }x- \frac{42}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 693x \color{red}{-42} & = & \color{red}{539x} +99 \\\Leftrightarrow & 693x \color{red}{-42} \color{blue}{+42} \color{blue}{-539x} & = & \color{red}{539x} +99 \color{blue}{-539x} \color{blue}{+42} \\\Leftrightarrow & 693x-539x& = & 99+42 \\\Leftrightarrow & \color{red}{154} x& = & 141 \\\Leftrightarrow & x = \frac{141}{154} & & \\ & V = \left\{ \frac{141}{154} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{3}{5})& = & -9x+\frac{3}{4} \\\Leftrightarrow & 8x+\frac{12}{5}& = & -9x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{160}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{-180}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 160x \color{red}{+48} & = & \color{red}{-180x} +15 \\\Leftrightarrow & 160x \color{red}{+48} \color{blue}{-48} \color{blue}{+180x} & = & \color{red}{-180x} +15 \color{blue}{+180x} \color{blue}{-48} \\\Leftrightarrow & 160x+180x& = & 15-48 \\\Leftrightarrow & \color{red}{340} x& = & -33 \\\Leftrightarrow & x = \frac{-33}{340} & & \\ & V = \left\{ \frac{-33}{340} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{5})& = & -4x+\frac{4}{3} \\\Leftrightarrow & -15x+\frac{6}{5}& = & -4x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} })& = & (\frac{-60}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{+18} & = & \color{red}{-60x} +20 \\\Leftrightarrow & -225x \color{red}{+18} \color{blue}{-18} \color{blue}{+60x} & = & \color{red}{-60x} +20 \color{blue}{+60x} \color{blue}{-18} \\\Leftrightarrow & -225x+60x& = & 20-18 \\\Leftrightarrow & \color{red}{-165} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-165} & & \\\Leftrightarrow & x = \frac{-2}{165} & & \\ & V = \left\{ \frac{-2}{165} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{5})& = & 9x+\frac{3}{8} \\\Leftrightarrow & -8x+\frac{8}{5}& = & 9x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-320}{ \color{blue}{40} }x+ \frac{64}{ \color{blue}{40} })& = & (\frac{360}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -320x \color{red}{+64} & = & \color{red}{360x} +15 \\\Leftrightarrow & -320x \color{red}{+64} \color{blue}{-64} \color{blue}{-360x} & = & \color{red}{360x} +15 \color{blue}{-360x} \color{blue}{-64} \\\Leftrightarrow & -320x-360x& = & 15-64 \\\Leftrightarrow & \color{red}{-680} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{-680} & & \\\Leftrightarrow & x = \frac{49}{680} & & \\ & V = \left\{ \frac{49}{680} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{5}{7})& = & 7x+\frac{5}{12} \\\Leftrightarrow & 30x-\frac{30}{7}& = & 7x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{2520}{ \color{blue}{84} }x- \frac{360}{ \color{blue}{84} })& = & (\frac{588}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 2520x \color{red}{-360} & = & \color{red}{588x} +35 \\\Leftrightarrow & 2520x \color{red}{-360} \color{blue}{+360} \color{blue}{-588x} & = & \color{red}{588x} +35 \color{blue}{-588x} \color{blue}{+360} \\\Leftrightarrow & 2520x-588x& = & 35+360 \\\Leftrightarrow & \color{red}{1932} x& = & 395 \\\Leftrightarrow & x = \frac{395}{1932} & & \\ & V = \left\{ \frac{395}{1932} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{7})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 12x-\frac{15}{7}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x- \frac{45}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{-45} & = & \color{red}{147x} +70 \\\Leftrightarrow & 252x \color{red}{-45} \color{blue}{+45} \color{blue}{-147x} & = & \color{red}{147x} +70 \color{blue}{-147x} \color{blue}{+45} \\\Leftrightarrow & 252x-147x& = & 70+45 \\\Leftrightarrow & \color{red}{105} x& = & 115 \\\Leftrightarrow & x = \frac{115}{105} & & \\\Leftrightarrow & x = \frac{23}{21} & & \\ & V = \left\{ \frac{23}{21} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{1}{3})& = & -4x+\frac{2}{5} \\\Leftrightarrow & 21x+\frac{7}{3}& = & -4x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x+ \frac{35}{ \color{blue}{15} })& = & (\frac{-60}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{+35} & = & \color{red}{-60x} +6 \\\Leftrightarrow & 315x \color{red}{+35} \color{blue}{-35} \color{blue}{+60x} & = & \color{red}{-60x} +6 \color{blue}{+60x} \color{blue}{-35} \\\Leftrightarrow & 315x+60x& = & 6-35 \\\Leftrightarrow & \color{red}{375} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{375} & & \\ & V = \left\{ \frac{-29}{375} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{4}{3})& = & -3x+\frac{3}{11} \\\Leftrightarrow & -8x-\frac{16}{3}& = & -3x+\frac{3}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x- \frac{176}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{9}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{-176} & = & \color{red}{-99x} +9 \\\Leftrightarrow & -264x \color{red}{-176} \color{blue}{+176} \color{blue}{+99x} & = & \color{red}{-99x} +9 \color{blue}{+99x} \color{blue}{+176} \\\Leftrightarrow & -264x+99x& = & 9+176 \\\Leftrightarrow & \color{red}{-165} x& = & 185 \\\Leftrightarrow & x = \frac{185}{-165} & & \\\Leftrightarrow & x = \frac{-37}{33} & & \\ & V = \left\{ \frac{-37}{33} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{2}{9})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 10x+\frac{10}{9}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{180}{ \color{blue}{18} }x+ \frac{20}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 180x \color{red}{+20} & = & \color{red}{126x} +81 \\\Leftrightarrow & 180x \color{red}{+20} \color{blue}{-20} \color{blue}{-126x} & = & \color{red}{126x} +81 \color{blue}{-126x} \color{blue}{-20} \\\Leftrightarrow & 180x-126x& = & 81-20 \\\Leftrightarrow & \color{red}{54} x& = & 61 \\\Leftrightarrow & x = \frac{61}{54} & & \\ & V = \left\{ \frac{61}{54} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{5})& = & -9x+\frac{7}{2} \\\Leftrightarrow & 4x-\frac{4}{5}& = & -9x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{40}{ \color{blue}{10} }x- \frac{8}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 40x \color{red}{-8} & = & \color{red}{-90x} +35 \\\Leftrightarrow & 40x \color{red}{-8} \color{blue}{+8} \color{blue}{+90x} & = & \color{red}{-90x} +35 \color{blue}{+90x} \color{blue}{+8} \\\Leftrightarrow & 40x+90x& = & 35+8 \\\Leftrightarrow & \color{red}{130} x& = & 43 \\\Leftrightarrow & x = \frac{43}{130} & & \\ & V = \left\{ \frac{43}{130} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{8})& = & -9x+\frac{8}{5} \\\Leftrightarrow & -35x-\frac{35}{8}& = & -9x+\frac{8}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1400}{ \color{blue}{40} }x- \frac{175}{ \color{blue}{40} })& = & (\frac{-360}{ \color{blue}{40} }x+ \frac{64}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1400x \color{red}{-175} & = & \color{red}{-360x} +64 \\\Leftrightarrow & -1400x \color{red}{-175} \color{blue}{+175} \color{blue}{+360x} & = & \color{red}{-360x} +64 \color{blue}{+360x} \color{blue}{+175} \\\Leftrightarrow & -1400x+360x& = & 64+175 \\\Leftrightarrow & \color{red}{-1040} x& = & 239 \\\Leftrightarrow & x = \frac{239}{-1040} & & \\\Leftrightarrow & x = \frac{-239}{1040} & & \\ & V = \left\{ \frac{-239}{1040} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{4}{7})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -20x+\frac{16}{7}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x+ \frac{80}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{+80} & = & \color{red}{-315x} +42 \\\Leftrightarrow & -700x \color{red}{+80} \color{blue}{-80} \color{blue}{+315x} & = & \color{red}{-315x} +42 \color{blue}{+315x} \color{blue}{-80} \\\Leftrightarrow & -700x+315x& = & 42-80 \\\Leftrightarrow & \color{red}{-385} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-385} & & \\\Leftrightarrow & x = \frac{38}{385} & & \\ & V = \left\{ \frac{38}{385} \right\} & \\\end{align}\)
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