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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{4}{9})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -6x+\frac{8}{9}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{+8} & = & \color{red}{-63x} +24 \\\Leftrightarrow & -54x \color{red}{+8} \color{blue}{-8} \color{blue}{+63x} & = & \color{red}{-63x} +24 \color{blue}{+63x} \color{blue}{-8} \\\Leftrightarrow & -54x+63x& = & 24-8 \\\Leftrightarrow & \color{red}{9} x& = & 16 \\\Leftrightarrow & x = \frac{16}{9} & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{5}{11})& = & 7x+\frac{2}{11} \\\Leftrightarrow & 30x+\frac{30}{11}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{330}{ \color{blue}{11} }x+ \frac{30}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 330x \color{red}{+30} & = & \color{red}{77x} +2 \\\Leftrightarrow & 330x \color{red}{+30} \color{blue}{-30} \color{blue}{-77x} & = & \color{red}{77x} +2 \color{blue}{-77x} \color{blue}{-30} \\\Leftrightarrow & 330x-77x& = & 2-30 \\\Leftrightarrow & \color{red}{253} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{253} & & \\ & V = \left\{ \frac{-28}{253} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{4}{11})& = & -7x+\frac{2}{11} \\\Leftrightarrow & 18x-\frac{24}{11}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{198}{ \color{blue}{11} }x- \frac{24}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 198x \color{red}{-24} & = & \color{red}{-77x} +2 \\\Leftrightarrow & 198x \color{red}{-24} \color{blue}{+24} \color{blue}{+77x} & = & \color{red}{-77x} +2 \color{blue}{+77x} \color{blue}{+24} \\\Leftrightarrow & 198x+77x& = & 2+24 \\\Leftrightarrow & \color{red}{275} x& = & 26 \\\Leftrightarrow & x = \frac{26}{275} & & \\ & V = \left\{ \frac{26}{275} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{3}{5})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 8x-\frac{6}{5}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{-18} & = & \color{red}{-105x} +20 \\\Leftrightarrow & 120x \color{red}{-18} \color{blue}{+18} \color{blue}{+105x} & = & \color{red}{-105x} +20 \color{blue}{+105x} \color{blue}{+18} \\\Leftrightarrow & 120x+105x& = & 20+18 \\\Leftrightarrow & \color{red}{225} x& = & 38 \\\Leftrightarrow & x = \frac{38}{225} & & \\ & V = \left\{ \frac{38}{225} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{5}{7})& = & -8x+\frac{8}{7} \\\Leftrightarrow & -15x+\frac{15}{7}& = & -8x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-105}{ \color{blue}{7} }x+ \frac{15}{ \color{blue}{7} })& = & (\frac{-56}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -105x \color{red}{+15} & = & \color{red}{-56x} +8 \\\Leftrightarrow & -105x \color{red}{+15} \color{blue}{-15} \color{blue}{+56x} & = & \color{red}{-56x} +8 \color{blue}{+56x} \color{blue}{-15} \\\Leftrightarrow & -105x+56x& = & 8-15 \\\Leftrightarrow & \color{red}{-49} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-49} & & \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{5}{11})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -6x-\frac{15}{11}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-198}{ \color{blue}{33} }x- \frac{45}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -198x \color{red}{-45} & = & \color{red}{-231x} +22 \\\Leftrightarrow & -198x \color{red}{-45} \color{blue}{+45} \color{blue}{+231x} & = & \color{red}{-231x} +22 \color{blue}{+231x} \color{blue}{+45} \\\Leftrightarrow & -198x+231x& = & 22+45 \\\Leftrightarrow & \color{red}{33} x& = & 67 \\\Leftrightarrow & x = \frac{67}{33} & & \\ & V = \left\{ \frac{67}{33} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{3})& = & -7x+\frac{7}{2} \\\Leftrightarrow & -16x+\frac{8}{3}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-96}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -96x \color{red}{+16} & = & \color{red}{-42x} +21 \\\Leftrightarrow & -96x \color{red}{+16} \color{blue}{-16} \color{blue}{+42x} & = & \color{red}{-42x} +21 \color{blue}{+42x} \color{blue}{-16} \\\Leftrightarrow & -96x+42x& = & 21-16 \\\Leftrightarrow & \color{red}{-54} x& = & 5 \\\Leftrightarrow & x = \frac{5}{-54} & & \\\Leftrightarrow & x = \frac{-5}{54} & & \\ & V = \left\{ \frac{-5}{54} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{5}{3})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 6x-\frac{10}{3}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{36}{ \color{blue}{6} }x- \frac{20}{ \color{blue}{6} })& = & (\frac{30}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 36x \color{red}{-20} & = & \color{red}{30x} +9 \\\Leftrightarrow & 36x \color{red}{-20} \color{blue}{+20} \color{blue}{-30x} & = & \color{red}{30x} +9 \color{blue}{-30x} \color{blue}{+20} \\\Leftrightarrow & 36x-30x& = & 9+20 \\\Leftrightarrow & \color{red}{6} x& = & 29 \\\Leftrightarrow & x = \frac{29}{6} & & \\ & V = \left\{ \frac{29}{6} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{5})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 6x-\frac{6}{5}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-42} & = & \color{red}{175x} +20 \\\Leftrightarrow & 210x \color{red}{-42} \color{blue}{+42} \color{blue}{-175x} & = & \color{red}{175x} +20 \color{blue}{-175x} \color{blue}{+42} \\\Leftrightarrow & 210x-175x& = & 20+42 \\\Leftrightarrow & \color{red}{35} x& = & 62 \\\Leftrightarrow & x = \frac{62}{35} & & \\ & V = \left\{ \frac{62}{35} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{5}{6})& = & 3x+\frac{4}{7} \\\Leftrightarrow & 10x+\frac{25}{6}& = & 3x+\frac{4}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{420}{ \color{blue}{42} }x+ \frac{175}{ \color{blue}{42} })& = & (\frac{126}{ \color{blue}{42} }x+ \frac{24}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 420x \color{red}{+175} & = & \color{red}{126x} +24 \\\Leftrightarrow & 420x \color{red}{+175} \color{blue}{-175} \color{blue}{-126x} & = & \color{red}{126x} +24 \color{blue}{-126x} \color{blue}{-175} \\\Leftrightarrow & 420x-126x& = & 24-175 \\\Leftrightarrow & \color{red}{294} x& = & -151 \\\Leftrightarrow & x = \frac{-151}{294} & & \\ & V = \left\{ \frac{-151}{294} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & 7x+\frac{7}{6} \\\Leftrightarrow & 30x+\frac{12}{5}& = & 7x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{900}{ \color{blue}{30} }x+ \frac{72}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 900x \color{red}{+72} & = & \color{red}{210x} +35 \\\Leftrightarrow & 900x \color{red}{+72} \color{blue}{-72} \color{blue}{-210x} & = & \color{red}{210x} +35 \color{blue}{-210x} \color{blue}{-72} \\\Leftrightarrow & 900x-210x& = & 35-72 \\\Leftrightarrow & \color{red}{690} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{690} & & \\ & V = \left\{ \frac{-37}{690} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{2}{11})& = & 9x+\frac{8}{3} \\\Leftrightarrow & 20x-\frac{10}{11}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{-30} & = & \color{red}{297x} +88 \\\Leftrightarrow & 660x \color{red}{-30} \color{blue}{+30} \color{blue}{-297x} & = & \color{red}{297x} +88 \color{blue}{-297x} \color{blue}{+30} \\\Leftrightarrow & 660x-297x& = & 88+30 \\\Leftrightarrow & \color{red}{363} x& = & 118 \\\Leftrightarrow & x = \frac{118}{363} & & \\ & V = \left\{ \frac{118}{363} \right\} & \\\end{align}\)
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