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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{3}{7})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 6x+\frac{6}{7}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{42}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 42x \color{red}{+6} & = & \color{red}{-35x} +3 \\\Leftrightarrow & 42x \color{red}{+6} \color{blue}{-6} \color{blue}{+35x} & = & \color{red}{-35x} +3 \color{blue}{+35x} \color{blue}{-6} \\\Leftrightarrow & 42x+35x& = & 3-6 \\\Leftrightarrow & \color{red}{77} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{77} & & \\ & V = \left\{ \frac{-3}{77} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{5}{7})& = & 7x+\frac{6}{11} \\\Leftrightarrow & 30x+\frac{30}{7}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2310}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2310x \color{red}{+330} & = & \color{red}{539x} +42 \\\Leftrightarrow & 2310x \color{red}{+330} \color{blue}{-330} \color{blue}{-539x} & = & \color{red}{539x} +42 \color{blue}{-539x} \color{blue}{-330} \\\Leftrightarrow & 2310x-539x& = & 42-330 \\\Leftrightarrow & \color{red}{1771} x& = & -288 \\\Leftrightarrow & x = \frac{-288}{1771} & & \\ & V = \left\{ \frac{-288}{1771} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{7})& = & -9x+\frac{4}{3} \\\Leftrightarrow & -4x+\frac{6}{7}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-84}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -84x \color{red}{+18} & = & \color{red}{-189x} +28 \\\Leftrightarrow & -84x \color{red}{+18} \color{blue}{-18} \color{blue}{+189x} & = & \color{red}{-189x} +28 \color{blue}{+189x} \color{blue}{-18} \\\Leftrightarrow & -84x+189x& = & 28-18 \\\Leftrightarrow & \color{red}{105} x& = & 10 \\\Leftrightarrow & x = \frac{10}{105} & & \\\Leftrightarrow & x = \frac{2}{21} & & \\ & V = \left\{ \frac{2}{21} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{4}{3})& = & -3x+\frac{3}{10} \\\Leftrightarrow & -25x-\frac{20}{3}& = & -3x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-750}{ \color{blue}{30} }x- \frac{200}{ \color{blue}{30} })& = & (\frac{-90}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -750x \color{red}{-200} & = & \color{red}{-90x} +9 \\\Leftrightarrow & -750x \color{red}{-200} \color{blue}{+200} \color{blue}{+90x} & = & \color{red}{-90x} +9 \color{blue}{+90x} \color{blue}{+200} \\\Leftrightarrow & -750x+90x& = & 9+200 \\\Leftrightarrow & \color{red}{-660} x& = & 209 \\\Leftrightarrow & x = \frac{209}{-660} & & \\\Leftrightarrow & x = \frac{-19}{60} & & \\ & V = \left\{ \frac{-19}{60} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{4}{3})& = & -5x+\frac{7}{8} \\\Leftrightarrow & 12x+\frac{16}{3}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{288}{ \color{blue}{24} }x+ \frac{128}{ \color{blue}{24} })& = & (\frac{-120}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 288x \color{red}{+128} & = & \color{red}{-120x} +21 \\\Leftrightarrow & 288x \color{red}{+128} \color{blue}{-128} \color{blue}{+120x} & = & \color{red}{-120x} +21 \color{blue}{+120x} \color{blue}{-128} \\\Leftrightarrow & 288x+120x& = & 21-128 \\\Leftrightarrow & \color{red}{408} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{408} & & \\ & V = \left\{ \frac{-107}{408} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{5}{3})& = & 5x+\frac{8}{9} \\\Leftrightarrow & -12x+\frac{20}{3}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-108}{ \color{blue}{9} }x+ \frac{60}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -108x \color{red}{+60} & = & \color{red}{45x} +8 \\\Leftrightarrow & -108x \color{red}{+60} \color{blue}{-60} \color{blue}{-45x} & = & \color{red}{45x} +8 \color{blue}{-45x} \color{blue}{-60} \\\Leftrightarrow & -108x-45x& = & 8-60 \\\Leftrightarrow & \color{red}{-153} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-153} & & \\\Leftrightarrow & x = \frac{52}{153} & & \\ & V = \left\{ \frac{52}{153} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{5}{12})& = & -9x+\frac{2}{3} \\\Leftrightarrow & 14x+\frac{35}{12}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{168}{ \color{blue}{12} }x+ \frac{35}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 168x \color{red}{+35} & = & \color{red}{-108x} +8 \\\Leftrightarrow & 168x \color{red}{+35} \color{blue}{-35} \color{blue}{+108x} & = & \color{red}{-108x} +8 \color{blue}{+108x} \color{blue}{-35} \\\Leftrightarrow & 168x+108x& = & 8-35 \\\Leftrightarrow & \color{red}{276} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{276} & & \\\Leftrightarrow & x = \frac{-9}{92} & & \\ & V = \left\{ \frac{-9}{92} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{4}{5})& = & -7x+\frac{3}{11} \\\Leftrightarrow & 30x+\frac{24}{5}& = & -7x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{+264} & = & \color{red}{-385x} +15 \\\Leftrightarrow & 1650x \color{red}{+264} \color{blue}{-264} \color{blue}{+385x} & = & \color{red}{-385x} +15 \color{blue}{+385x} \color{blue}{-264} \\\Leftrightarrow & 1650x+385x& = & 15-264 \\\Leftrightarrow & \color{red}{2035} x& = & -249 \\\Leftrightarrow & x = \frac{-249}{2035} & & \\ & V = \left\{ \frac{-249}{2035} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{7})& = & 9x+\frac{5}{6} \\\Leftrightarrow & 20x+\frac{20}{7}& = & 9x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{840}{ \color{blue}{42} }x+ \frac{120}{ \color{blue}{42} })& = & (\frac{378}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 840x \color{red}{+120} & = & \color{red}{378x} +35 \\\Leftrightarrow & 840x \color{red}{+120} \color{blue}{-120} \color{blue}{-378x} & = & \color{red}{378x} +35 \color{blue}{-378x} \color{blue}{-120} \\\Leftrightarrow & 840x-378x& = & 35-120 \\\Leftrightarrow & \color{red}{462} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{462} & & \\ & V = \left\{ \frac{-85}{462} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{2}{3})& = & -9x+\frac{6}{5} \\\Leftrightarrow & 28x-\frac{14}{3}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{420}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 420x \color{red}{-70} & = & \color{red}{-135x} +18 \\\Leftrightarrow & 420x \color{red}{-70} \color{blue}{+70} \color{blue}{+135x} & = & \color{red}{-135x} +18 \color{blue}{+135x} \color{blue}{+70} \\\Leftrightarrow & 420x+135x& = & 18+70 \\\Leftrightarrow & \color{red}{555} x& = & 88 \\\Leftrightarrow & x = \frac{88}{555} & & \\ & V = \left\{ \frac{88}{555} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{11})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -30x+\frac{18}{11}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-330}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -330x \color{red}{+18} & = & \color{red}{77x} +8 \\\Leftrightarrow & -330x \color{red}{+18} \color{blue}{-18} \color{blue}{-77x} & = & \color{red}{77x} +8 \color{blue}{-77x} \color{blue}{-18} \\\Leftrightarrow & -330x-77x& = & 8-18 \\\Leftrightarrow & \color{red}{-407} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-407} & & \\\Leftrightarrow & x = \frac{10}{407} & & \\ & V = \left\{ \frac{10}{407} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{5}{11})& = & -3x+\frac{4}{9} \\\Leftrightarrow & -14x+\frac{35}{11}& = & -3x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1386}{ \color{blue}{99} }x+ \frac{315}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1386x \color{red}{+315} & = & \color{red}{-297x} +44 \\\Leftrightarrow & -1386x \color{red}{+315} \color{blue}{-315} \color{blue}{+297x} & = & \color{red}{-297x} +44 \color{blue}{+297x} \color{blue}{-315} \\\Leftrightarrow & -1386x+297x& = & 44-315 \\\Leftrightarrow & \color{red}{-1089} x& = & -271 \\\Leftrightarrow & x = \frac{-271}{-1089} & & \\\Leftrightarrow & x = \frac{271}{1089} & & \\ & V = \left\{ \frac{271}{1089} \right\} & \\\end{align}\)
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