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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{4}{11})& = & 7x+\frac{4}{5} \\\Leftrightarrow & 20x-\frac{16}{11}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1100}{ \color{blue}{55} }x- \frac{80}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1100x \color{red}{-80} & = & \color{red}{385x} +44 \\\Leftrightarrow & 1100x \color{red}{-80} \color{blue}{+80} \color{blue}{-385x} & = & \color{red}{385x} +44 \color{blue}{-385x} \color{blue}{+80} \\\Leftrightarrow & 1100x-385x& = & 44+80 \\\Leftrightarrow & \color{red}{715} x& = & 124 \\\Leftrightarrow & x = \frac{124}{715} & & \\ & V = \left\{ \frac{124}{715} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{4}{7})& = & 7x+\frac{5}{6} \\\Leftrightarrow & -9x+\frac{12}{7}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-378}{ \color{blue}{42} }x+ \frac{72}{ \color{blue}{42} })& = & (\frac{294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -378x \color{red}{+72} & = & \color{red}{294x} +35 \\\Leftrightarrow & -378x \color{red}{+72} \color{blue}{-72} \color{blue}{-294x} & = & \color{red}{294x} +35 \color{blue}{-294x} \color{blue}{-72} \\\Leftrightarrow & -378x-294x& = & 35-72 \\\Leftrightarrow & \color{red}{-672} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-672} & & \\\Leftrightarrow & x = \frac{37}{672} & & \\ & V = \left\{ \frac{37}{672} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{5}{7})& = & 3x+\frac{4}{11} \\\Leftrightarrow & -8x-\frac{20}{7}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{-220} & = & \color{red}{231x} +28 \\\Leftrightarrow & -616x \color{red}{-220} \color{blue}{+220} \color{blue}{-231x} & = & \color{red}{231x} +28 \color{blue}{-231x} \color{blue}{+220} \\\Leftrightarrow & -616x-231x& = & 28+220 \\\Leftrightarrow & \color{red}{-847} x& = & 248 \\\Leftrightarrow & x = \frac{248}{-847} & & \\\Leftrightarrow & x = \frac{-248}{847} & & \\ & V = \left\{ \frac{-248}{847} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{4}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 4x-\frac{8}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{220}{ \color{blue}{55} }x- \frac{40}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 220x \color{red}{-40} & = & \color{red}{-275x} +66 \\\Leftrightarrow & 220x \color{red}{-40} \color{blue}{+40} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{+40} \\\Leftrightarrow & 220x+275x& = & 66+40 \\\Leftrightarrow & \color{red}{495} x& = & 106 \\\Leftrightarrow & x = \frac{106}{495} & & \\ & V = \left\{ \frac{106}{495} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{3}{5})& = & 3x+\frac{8}{3} \\\Leftrightarrow & -8x+\frac{6}{5}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{+18} & = & \color{red}{45x} +40 \\\Leftrightarrow & -120x \color{red}{+18} \color{blue}{-18} \color{blue}{-45x} & = & \color{red}{45x} +40 \color{blue}{-45x} \color{blue}{-18} \\\Leftrightarrow & -120x-45x& = & 40-18 \\\Leftrightarrow & \color{red}{-165} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-165} & & \\\Leftrightarrow & x = \frac{-2}{15} & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{4}{7})& = & -5x+\frac{6}{7} \\\Leftrightarrow & -12x-\frac{16}{7}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{-16} & = & \color{red}{-35x} +6 \\\Leftrightarrow & -84x \color{red}{-16} \color{blue}{+16} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{+16} \\\Leftrightarrow & -84x+35x& = & 6+16 \\\Leftrightarrow & \color{red}{-49} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-49} & & \\\Leftrightarrow & x = \frac{-22}{49} & & \\ & V = \left\{ \frac{-22}{49} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{5})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -30x+\frac{24}{5}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-600}{ \color{blue}{20} }x+ \frac{96}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -600x \color{red}{+96} & = & \color{red}{140x} +15 \\\Leftrightarrow & -600x \color{red}{+96} \color{blue}{-96} \color{blue}{-140x} & = & \color{red}{140x} +15 \color{blue}{-140x} \color{blue}{-96} \\\Leftrightarrow & -600x-140x& = & 15-96 \\\Leftrightarrow & \color{red}{-740} x& = & -81 \\\Leftrightarrow & x = \frac{-81}{-740} & & \\\Leftrightarrow & x = \frac{81}{740} & & \\ & V = \left\{ \frac{81}{740} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{3}{7})& = & 3x+\frac{4}{7} \\\Leftrightarrow & 16x-\frac{12}{7}& = & 3x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{112}{ \color{blue}{7} }x- \frac{12}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 112x \color{red}{-12} & = & \color{red}{21x} +4 \\\Leftrightarrow & 112x \color{red}{-12} \color{blue}{+12} \color{blue}{-21x} & = & \color{red}{21x} +4 \color{blue}{-21x} \color{blue}{+12} \\\Leftrightarrow & 112x-21x& = & 4+12 \\\Leftrightarrow & \color{red}{91} x& = & 16 \\\Leftrightarrow & x = \frac{16}{91} & & \\ & V = \left\{ \frac{16}{91} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{4}{11})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 8x+\frac{16}{11}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x+ \frac{112}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{+112} & = & \color{red}{-385x} +110 \\\Leftrightarrow & 616x \color{red}{+112} \color{blue}{-112} \color{blue}{+385x} & = & \color{red}{-385x} +110 \color{blue}{+385x} \color{blue}{-112} \\\Leftrightarrow & 616x+385x& = & 110-112 \\\Leftrightarrow & \color{red}{1001} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{1001} & & \\ & V = \left\{ \frac{-2}{1001} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{5}{4})& = & -5x+\frac{9}{4} \\\Leftrightarrow & -9x+\frac{15}{4}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-36}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{-20}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -36x \color{red}{+15} & = & \color{red}{-20x} +9 \\\Leftrightarrow & -36x \color{red}{+15} \color{blue}{-15} \color{blue}{+20x} & = & \color{red}{-20x} +9 \color{blue}{+20x} \color{blue}{-15} \\\Leftrightarrow & -36x+20x& = & 9-15 \\\Leftrightarrow & \color{red}{-16} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-16} & & \\\Leftrightarrow & x = \frac{3}{8} & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{3}{10})& = & 7x+\frac{7}{9} \\\Leftrightarrow & -6x-\frac{9}{10}& = & 7x+\frac{7}{9} \\ & & & \text{kgv van noemers 10 en 9 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-540}{ \color{blue}{90} }x- \frac{81}{ \color{blue}{90} })& = & (\frac{630}{ \color{blue}{90} }x+ \frac{70}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -540x \color{red}{-81} & = & \color{red}{630x} +70 \\\Leftrightarrow & -540x \color{red}{-81} \color{blue}{+81} \color{blue}{-630x} & = & \color{red}{630x} +70 \color{blue}{-630x} \color{blue}{+81} \\\Leftrightarrow & -540x-630x& = & 70+81 \\\Leftrightarrow & \color{red}{-1170} x& = & 151 \\\Leftrightarrow & x = \frac{151}{-1170} & & \\\Leftrightarrow & x = \frac{-151}{1170} & & \\ & V = \left\{ \frac{-151}{1170} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{3}{11})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 14x-\frac{21}{11}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x- \frac{63}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{-63} & = & \color{red}{-165x} +110 \\\Leftrightarrow & 462x \color{red}{-63} \color{blue}{+63} \color{blue}{+165x} & = & \color{red}{-165x} +110 \color{blue}{+165x} \color{blue}{+63} \\\Leftrightarrow & 462x+165x& = & 110+63 \\\Leftrightarrow & \color{red}{627} x& = & 173 \\\Leftrightarrow & x = \frac{173}{627} & & \\ & V = \left\{ \frac{173}{627} \right\} & \\\end{align}\)
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