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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{2})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 14x-\frac{35}{2}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{28}{ \color{blue}{2} }x- \frac{35}{ \color{blue}{2} })& = & (\frac{-10}{ \color{blue}{2} }x+ \frac{3}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 28x \color{red}{-35} & = & \color{red}{-10x} +3 \\\Leftrightarrow & 28x \color{red}{-35} \color{blue}{+35} \color{blue}{+10x} & = & \color{red}{-10x} +3 \color{blue}{+10x} \color{blue}{+35} \\\Leftrightarrow & 28x+10x& = & 3+35 \\\Leftrightarrow & \color{red}{38} x& = & 38 \\\Leftrightarrow & x = \frac{38}{38} & & \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{2}{3})& = & 9x+\frac{3}{2} \\\Leftrightarrow & 28x+\frac{14}{3}& = & 9x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{168}{ \color{blue}{6} }x+ \frac{28}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 168x \color{red}{+28} & = & \color{red}{54x} +9 \\\Leftrightarrow & 168x \color{red}{+28} \color{blue}{-28} \color{blue}{-54x} & = & \color{red}{54x} +9 \color{blue}{-54x} \color{blue}{-28} \\\Leftrightarrow & 168x-54x& = & 9-28 \\\Leftrightarrow & \color{red}{114} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{114} & & \\\Leftrightarrow & x = \frac{-1}{6} & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{5})& = & -9x+\frac{3}{5} \\\Leftrightarrow & -20x-\frac{12}{5}& = & -9x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-100}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -100x \color{red}{-12} & = & \color{red}{-45x} +3 \\\Leftrightarrow & -100x \color{red}{-12} \color{blue}{+12} \color{blue}{+45x} & = & \color{red}{-45x} +3 \color{blue}{+45x} \color{blue}{+12} \\\Leftrightarrow & -100x+45x& = & 3+12 \\\Leftrightarrow & \color{red}{-55} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-55} & & \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{2}{9})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -20x+\frac{10}{9}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-360}{ \color{blue}{18} }x+ \frac{20}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -360x \color{red}{+20} & = & \color{red}{-126x} +81 \\\Leftrightarrow & -360x \color{red}{+20} \color{blue}{-20} \color{blue}{+126x} & = & \color{red}{-126x} +81 \color{blue}{+126x} \color{blue}{-20} \\\Leftrightarrow & -360x+126x& = & 81-20 \\\Leftrightarrow & \color{red}{-234} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-234} & & \\\Leftrightarrow & x = \frac{-61}{234} & & \\ & V = \left\{ \frac{-61}{234} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{5}{7})& = & -5x+\frac{7}{12} \\\Leftrightarrow & 24x+\frac{30}{7}& = & -5x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{2016}{ \color{blue}{84} }x+ \frac{360}{ \color{blue}{84} })& = & (\frac{-420}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 2016x \color{red}{+360} & = & \color{red}{-420x} +49 \\\Leftrightarrow & 2016x \color{red}{+360} \color{blue}{-360} \color{blue}{+420x} & = & \color{red}{-420x} +49 \color{blue}{+420x} \color{blue}{-360} \\\Leftrightarrow & 2016x+420x& = & 49-360 \\\Leftrightarrow & \color{red}{2436} x& = & -311 \\\Leftrightarrow & x = \frac{-311}{2436} & & \\ & V = \left\{ \frac{-311}{2436} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{3}{7})& = & 5x+\frac{9}{5} \\\Leftrightarrow & 6x+\frac{9}{7}& = & 5x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{+45} & = & \color{red}{175x} +63 \\\Leftrightarrow & 210x \color{red}{+45} \color{blue}{-45} \color{blue}{-175x} & = & \color{red}{175x} +63 \color{blue}{-175x} \color{blue}{-45} \\\Leftrightarrow & 210x-175x& = & 63-45 \\\Leftrightarrow & \color{red}{35} x& = & 18 \\\Leftrightarrow & x = \frac{18}{35} & & \\ & V = \left\{ \frac{18}{35} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{3})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -6x+\frac{10}{3}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{+30} & = & \color{red}{-63x} +2 \\\Leftrightarrow & -54x \color{red}{+30} \color{blue}{-30} \color{blue}{+63x} & = & \color{red}{-63x} +2 \color{blue}{+63x} \color{blue}{-30} \\\Leftrightarrow & -54x+63x& = & 2-30 \\\Leftrightarrow & \color{red}{9} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{9} & & \\ & V = \left\{ \frac{-28}{9} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{3}{4})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -10x+\frac{15}{4}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-120}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -120x \color{red}{+45} & = & \color{red}{84x} +16 \\\Leftrightarrow & -120x \color{red}{+45} \color{blue}{-45} \color{blue}{-84x} & = & \color{red}{84x} +16 \color{blue}{-84x} \color{blue}{-45} \\\Leftrightarrow & -120x-84x& = & 16-45 \\\Leftrightarrow & \color{red}{-204} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-204} & & \\\Leftrightarrow & x = \frac{29}{204} & & \\ & V = \left\{ \frac{29}{204} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{5})& = & 7x+\frac{4}{5} \\\Leftrightarrow & 30x+\frac{24}{5}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{150}{ \color{blue}{5} }x+ \frac{24}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 150x \color{red}{+24} & = & \color{red}{35x} +4 \\\Leftrightarrow & 150x \color{red}{+24} \color{blue}{-24} \color{blue}{-35x} & = & \color{red}{35x} +4 \color{blue}{-35x} \color{blue}{-24} \\\Leftrightarrow & 150x-35x& = & 4-24 \\\Leftrightarrow & \color{red}{115} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{115} & & \\\Leftrightarrow & x = \frac{-4}{23} & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{2}{11})& = & 7x+\frac{9}{8} \\\Leftrightarrow & -16x-\frac{8}{11}& = & 7x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1408}{ \color{blue}{88} }x- \frac{64}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1408x \color{red}{-64} & = & \color{red}{616x} +99 \\\Leftrightarrow & -1408x \color{red}{-64} \color{blue}{+64} \color{blue}{-616x} & = & \color{red}{616x} +99 \color{blue}{-616x} \color{blue}{+64} \\\Leftrightarrow & -1408x-616x& = & 99+64 \\\Leftrightarrow & \color{red}{-2024} x& = & 163 \\\Leftrightarrow & x = \frac{163}{-2024} & & \\\Leftrightarrow & x = \frac{-163}{2024} & & \\ & V = \left\{ \frac{-163}{2024} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{5}{7})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 18x-\frac{30}{7}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{126}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 126x \color{red}{-30} & = & \color{red}{-35x} +6 \\\Leftrightarrow & 126x \color{red}{-30} \color{blue}{+30} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{+30} \\\Leftrightarrow & 126x+35x& = & 6+30 \\\Leftrightarrow & \color{red}{161} x& = & 36 \\\Leftrightarrow & x = \frac{36}{161} & & \\ & V = \left\{ \frac{36}{161} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{3}{11})& = & 7x+\frac{7}{8} \\\Leftrightarrow & 30x-\frac{18}{11}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2640}{ \color{blue}{88} }x- \frac{144}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2640x \color{red}{-144} & = & \color{red}{616x} +77 \\\Leftrightarrow & 2640x \color{red}{-144} \color{blue}{+144} \color{blue}{-616x} & = & \color{red}{616x} +77 \color{blue}{-616x} \color{blue}{+144} \\\Leftrightarrow & 2640x-616x& = & 77+144 \\\Leftrightarrow & \color{red}{2024} x& = & 221 \\\Leftrightarrow & x = \frac{221}{2024} & & \\ & V = \left\{ \frac{221}{2024} \right\} & \\\end{align}\)
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