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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{2}{9})& = & -3x+\frac{8}{5} \\\Leftrightarrow & -14x-\frac{14}{9}& = & -3x+\frac{8}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-630}{ \color{blue}{45} }x- \frac{70}{ \color{blue}{45} })& = & (\frac{-135}{ \color{blue}{45} }x+ \frac{72}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -630x \color{red}{-70} & = & \color{red}{-135x} +72 \\\Leftrightarrow & -630x \color{red}{-70} \color{blue}{+70} \color{blue}{+135x} & = & \color{red}{-135x} +72 \color{blue}{+135x} \color{blue}{+70} \\\Leftrightarrow & -630x+135x& = & 72+70 \\\Leftrightarrow & \color{red}{-495} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-495} & & \\\Leftrightarrow & x = \frac{-142}{495} & & \\ & V = \left\{ \frac{-142}{495} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{2}{11})& = & -7x+\frac{6}{7} \\\Leftrightarrow & 6x-\frac{4}{11}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x- \frac{28}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{-28} & = & \color{red}{-539x} +66 \\\Leftrightarrow & 462x \color{red}{-28} \color{blue}{+28} \color{blue}{+539x} & = & \color{red}{-539x} +66 \color{blue}{+539x} \color{blue}{+28} \\\Leftrightarrow & 462x+539x& = & 66+28 \\\Leftrightarrow & \color{red}{1001} x& = & 94 \\\Leftrightarrow & x = \frac{94}{1001} & & \\ & V = \left\{ \frac{94}{1001} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{4}{7})& = & -5x+\frac{2}{3} \\\Leftrightarrow & -25x-\frac{20}{7}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-525}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -525x \color{red}{-60} & = & \color{red}{-105x} +14 \\\Leftrightarrow & -525x \color{red}{-60} \color{blue}{+60} \color{blue}{+105x} & = & \color{red}{-105x} +14 \color{blue}{+105x} \color{blue}{+60} \\\Leftrightarrow & -525x+105x& = & 14+60 \\\Leftrightarrow & \color{red}{-420} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-420} & & \\\Leftrightarrow & x = \frac{-37}{210} & & \\ & V = \left\{ \frac{-37}{210} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{4}{3})& = & -5x+\frac{3}{4} \\\Leftrightarrow & -4x-\frac{8}{3}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-48}{ \color{blue}{12} }x- \frac{32}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -48x \color{red}{-32} & = & \color{red}{-60x} +9 \\\Leftrightarrow & -48x \color{red}{-32} \color{blue}{+32} \color{blue}{+60x} & = & \color{red}{-60x} +9 \color{blue}{+60x} \color{blue}{+32} \\\Leftrightarrow & -48x+60x& = & 9+32 \\\Leftrightarrow & \color{red}{12} x& = & 41 \\\Leftrightarrow & x = \frac{41}{12} & & \\ & V = \left\{ \frac{41}{12} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{4}{7})& = & -9x+\frac{5}{11} \\\Leftrightarrow & -8x+\frac{16}{7}& = & -9x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x+ \frac{176}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{+176} & = & \color{red}{-693x} +35 \\\Leftrightarrow & -616x \color{red}{+176} \color{blue}{-176} \color{blue}{+693x} & = & \color{red}{-693x} +35 \color{blue}{+693x} \color{blue}{-176} \\\Leftrightarrow & -616x+693x& = & 35-176 \\\Leftrightarrow & \color{red}{77} x& = & -141 \\\Leftrightarrow & x = \frac{-141}{77} & & \\ & V = \left\{ \frac{-141}{77} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{3})& = & 2x+\frac{2}{3} \\\Leftrightarrow & -28x-\frac{14}{3}& = & 2x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-84}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{6}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -84x \color{red}{-14} & = & \color{red}{6x} +2 \\\Leftrightarrow & -84x \color{red}{-14} \color{blue}{+14} \color{blue}{-6x} & = & \color{red}{6x} +2 \color{blue}{-6x} \color{blue}{+14} \\\Leftrightarrow & -84x-6x& = & 2+14 \\\Leftrightarrow & \color{red}{-90} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-90} & & \\\Leftrightarrow & x = \frac{-8}{45} & & \\ & V = \left\{ \frac{-8}{45} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{5}{7})& = & 4x+\frac{2}{3} \\\Leftrightarrow & -15x-\frac{15}{7}& = & 4x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x- \frac{45}{ \color{blue}{21} })& = & (\frac{84}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{-45} & = & \color{red}{84x} +14 \\\Leftrightarrow & -315x \color{red}{-45} \color{blue}{+45} \color{blue}{-84x} & = & \color{red}{84x} +14 \color{blue}{-84x} \color{blue}{+45} \\\Leftrightarrow & -315x-84x& = & 14+45 \\\Leftrightarrow & \color{red}{-399} x& = & 59 \\\Leftrightarrow & x = \frac{59}{-399} & & \\\Leftrightarrow & x = \frac{-59}{399} & & \\ & V = \left\{ \frac{-59}{399} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{3}{8})& = & 9x+\frac{7}{11} \\\Leftrightarrow & -25x+\frac{15}{8}& = & 9x+\frac{7}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2200}{ \color{blue}{88} }x+ \frac{165}{ \color{blue}{88} })& = & (\frac{792}{ \color{blue}{88} }x+ \frac{56}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2200x \color{red}{+165} & = & \color{red}{792x} +56 \\\Leftrightarrow & -2200x \color{red}{+165} \color{blue}{-165} \color{blue}{-792x} & = & \color{red}{792x} +56 \color{blue}{-792x} \color{blue}{-165} \\\Leftrightarrow & -2200x-792x& = & 56-165 \\\Leftrightarrow & \color{red}{-2992} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{-2992} & & \\\Leftrightarrow & x = \frac{109}{2992} & & \\ & V = \left\{ \frac{109}{2992} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{2}{3})& = & -9x+\frac{5}{2} \\\Leftrightarrow & 14x+\frac{14}{3}& = & -9x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{84}{ \color{blue}{6} }x+ \frac{28}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 84x \color{red}{+28} & = & \color{red}{-54x} +15 \\\Leftrightarrow & 84x \color{red}{+28} \color{blue}{-28} \color{blue}{+54x} & = & \color{red}{-54x} +15 \color{blue}{+54x} \color{blue}{-28} \\\Leftrightarrow & 84x+54x& = & 15-28 \\\Leftrightarrow & \color{red}{138} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{138} & & \\ & V = \left\{ \frac{-13}{138} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{6})& = & 9x+\frac{2}{9} \\\Leftrightarrow & 20x+\frac{25}{6}& = & 9x+\frac{2}{9} \\ & & & \text{kgv van noemers 6 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{360}{ \color{blue}{18} }x+ \frac{75}{ \color{blue}{18} })& = & (\frac{162}{ \color{blue}{18} }x+ \frac{4}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 360x \color{red}{+75} & = & \color{red}{162x} +4 \\\Leftrightarrow & 360x \color{red}{+75} \color{blue}{-75} \color{blue}{-162x} & = & \color{red}{162x} +4 \color{blue}{-162x} \color{blue}{-75} \\\Leftrightarrow & 360x-162x& = & 4-75 \\\Leftrightarrow & \color{red}{198} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{198} & & \\ & V = \left\{ \frac{-71}{198} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{2}{3})& = & -2x+\frac{8}{11} \\\Leftrightarrow & 21x+\frac{14}{3}& = & -2x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{693}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{-66}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 693x \color{red}{+154} & = & \color{red}{-66x} +24 \\\Leftrightarrow & 693x \color{red}{+154} \color{blue}{-154} \color{blue}{+66x} & = & \color{red}{-66x} +24 \color{blue}{+66x} \color{blue}{-154} \\\Leftrightarrow & 693x+66x& = & 24-154 \\\Leftrightarrow & \color{red}{759} x& = & -130 \\\Leftrightarrow & x = \frac{-130}{759} & & \\ & V = \left\{ \frac{-130}{759} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{2}{5})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -24x-\frac{12}{5}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-360}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -360x \color{red}{-36} & = & \color{red}{75x} +40 \\\Leftrightarrow & -360x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +40 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & -360x-75x& = & 40+36 \\\Leftrightarrow & \color{red}{-435} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-435} & & \\\Leftrightarrow & x = \frac{-76}{435} & & \\ & V = \left\{ \frac{-76}{435} \right\} & \\\end{align}\)
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