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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{3}{7})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 6x+\frac{6}{7}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{+66} & = & \color{red}{385x} +35 \\\Leftrightarrow & 462x \color{red}{+66} \color{blue}{-66} \color{blue}{-385x} & = & \color{red}{385x} +35 \color{blue}{-385x} \color{blue}{-66} \\\Leftrightarrow & 462x-385x& = & 35-66 \\\Leftrightarrow & \color{red}{77} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{77} & & \\ & V = \left\{ \frac{-31}{77} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{11})& = & 4x+\frac{8}{7} \\\Leftrightarrow & 9x+\frac{15}{11}& = & 4x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{693}{ \color{blue}{77} }x+ \frac{105}{ \color{blue}{77} })& = & (\frac{308}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 693x \color{red}{+105} & = & \color{red}{308x} +88 \\\Leftrightarrow & 693x \color{red}{+105} \color{blue}{-105} \color{blue}{-308x} & = & \color{red}{308x} +88 \color{blue}{-308x} \color{blue}{-105} \\\Leftrightarrow & 693x-308x& = & 88-105 \\\Leftrightarrow & \color{red}{385} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{385} & & \\ & V = \left\{ \frac{-17}{385} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{5}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -24x+\frac{30}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-168}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -168x \color{red}{+30} & = & \color{red}{-49x} +10 \\\Leftrightarrow & -168x \color{red}{+30} \color{blue}{-30} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{-30} \\\Leftrightarrow & -168x+49x& = & 10-30 \\\Leftrightarrow & \color{red}{-119} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-119} & & \\\Leftrightarrow & x = \frac{20}{119} & & \\ & V = \left\{ \frac{20}{119} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{5})& = & -7x+\frac{7}{6} \\\Leftrightarrow & 6x-\frac{6}{5}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{180}{ \color{blue}{30} }x- \frac{36}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 180x \color{red}{-36} & = & \color{red}{-210x} +35 \\\Leftrightarrow & 180x \color{red}{-36} \color{blue}{+36} \color{blue}{+210x} & = & \color{red}{-210x} +35 \color{blue}{+210x} \color{blue}{+36} \\\Leftrightarrow & 180x+210x& = & 35+36 \\\Leftrightarrow & \color{red}{390} x& = & 71 \\\Leftrightarrow & x = \frac{71}{390} & & \\ & V = \left\{ \frac{71}{390} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{2})& = & 3x+\frac{8}{9} \\\Leftrightarrow & 14x-\frac{35}{2}& = & 3x+\frac{8}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{252}{ \color{blue}{18} }x- \frac{315}{ \color{blue}{18} })& = & (\frac{54}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 252x \color{red}{-315} & = & \color{red}{54x} +16 \\\Leftrightarrow & 252x \color{red}{-315} \color{blue}{+315} \color{blue}{-54x} & = & \color{red}{54x} +16 \color{blue}{-54x} \color{blue}{+315} \\\Leftrightarrow & 252x-54x& = & 16+315 \\\Leftrightarrow & \color{red}{198} x& = & 331 \\\Leftrightarrow & x = \frac{331}{198} & & \\ & V = \left\{ \frac{331}{198} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{5}{7})& = & -3x+\frac{10}{11} \\\Leftrightarrow & 4x+\frac{10}{7}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{308}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 308x \color{red}{+110} & = & \color{red}{-231x} +70 \\\Leftrightarrow & 308x \color{red}{+110} \color{blue}{-110} \color{blue}{+231x} & = & \color{red}{-231x} +70 \color{blue}{+231x} \color{blue}{-110} \\\Leftrightarrow & 308x+231x& = & 70-110 \\\Leftrightarrow & \color{red}{539} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{539} & & \\ & V = \left\{ \frac{-40}{539} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{11})& = & -5x+\frac{7}{8} \\\Leftrightarrow & 18x+\frac{24}{11}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1584}{ \color{blue}{88} }x+ \frac{192}{ \color{blue}{88} })& = & (\frac{-440}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1584x \color{red}{+192} & = & \color{red}{-440x} +77 \\\Leftrightarrow & 1584x \color{red}{+192} \color{blue}{-192} \color{blue}{+440x} & = & \color{red}{-440x} +77 \color{blue}{+440x} \color{blue}{-192} \\\Leftrightarrow & 1584x+440x& = & 77-192 \\\Leftrightarrow & \color{red}{2024} x& = & -115 \\\Leftrightarrow & x = \frac{-115}{2024} & & \\\Leftrightarrow & x = \frac{-5}{88} & & \\ & V = \left\{ \frac{-5}{88} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{5}{4})& = & -8x+\frac{4}{9} \\\Leftrightarrow & -28x+\frac{35}{4}& = & -8x+\frac{4}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-1008}{ \color{blue}{36} }x+ \frac{315}{ \color{blue}{36} })& = & (\frac{-288}{ \color{blue}{36} }x+ \frac{16}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -1008x \color{red}{+315} & = & \color{red}{-288x} +16 \\\Leftrightarrow & -1008x \color{red}{+315} \color{blue}{-315} \color{blue}{+288x} & = & \color{red}{-288x} +16 \color{blue}{+288x} \color{blue}{-315} \\\Leftrightarrow & -1008x+288x& = & 16-315 \\\Leftrightarrow & \color{red}{-720} x& = & -299 \\\Leftrightarrow & x = \frac{-299}{-720} & & \\\Leftrightarrow & x = \frac{299}{720} & & \\ & V = \left\{ \frac{299}{720} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{3}{5})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -16x+\frac{12}{5}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-160}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -160x \color{red}{+24} & = & \color{red}{70x} +15 \\\Leftrightarrow & -160x \color{red}{+24} \color{blue}{-24} \color{blue}{-70x} & = & \color{red}{70x} +15 \color{blue}{-70x} \color{blue}{-24} \\\Leftrightarrow & -160x-70x& = & 15-24 \\\Leftrightarrow & \color{red}{-230} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-230} & & \\\Leftrightarrow & x = \frac{9}{230} & & \\ & V = \left\{ \frac{9}{230} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{4}{9})& = & 7x+\frac{5}{11} \\\Leftrightarrow & -10x-\frac{20}{9}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-990}{ \color{blue}{99} }x- \frac{220}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -990x \color{red}{-220} & = & \color{red}{693x} +45 \\\Leftrightarrow & -990x \color{red}{-220} \color{blue}{+220} \color{blue}{-693x} & = & \color{red}{693x} +45 \color{blue}{-693x} \color{blue}{+220} \\\Leftrightarrow & -990x-693x& = & 45+220 \\\Leftrightarrow & \color{red}{-1683} x& = & 265 \\\Leftrightarrow & x = \frac{265}{-1683} & & \\\Leftrightarrow & x = \frac{-265}{1683} & & \\ & V = \left\{ \frac{-265}{1683} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{4}{7})& = & 9x+\frac{9}{10} \\\Leftrightarrow & 28x+4& = & 9x+\frac{9}{10} \\ & & & \text{kgv van noemers 1 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{280}{ \color{blue}{10} }x+ \frac{40}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 280x \color{red}{+40} & = & \color{red}{90x} +9 \\\Leftrightarrow & 280x \color{red}{+40} \color{blue}{-40} \color{blue}{-90x} & = & \color{red}{90x} +9 \color{blue}{-90x} \color{blue}{-40} \\\Leftrightarrow & 280x-90x& = & 9-40 \\\Leftrightarrow & \color{red}{190} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{190} & & \\ & V = \left\{ \frac{-31}{190} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{2}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 18x+\frac{12}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{90}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 90x \color{red}{+12} & = & \color{red}{-25x} +6 \\\Leftrightarrow & 90x \color{red}{+12} \color{blue}{-12} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{-12} \\\Leftrightarrow & 90x+25x& = & 6-12 \\\Leftrightarrow & \color{red}{115} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{115} & & \\ & V = \left\{ \frac{-6}{115} \right\} & \\\end{align}\)
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