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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{2}{7})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{+6} & = & \color{red}{-49x} +9 \\\Leftrightarrow & -42x \color{red}{+6} \color{blue}{-6} \color{blue}{+49x} & = & \color{red}{-49x} +9 \color{blue}{+49x} \color{blue}{-6} \\\Leftrightarrow & -42x+49x& = & 9-6 \\\Leftrightarrow & \color{red}{7} x& = & 3 \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{7})& = & 4x+\frac{9}{7} \\\Leftrightarrow & -15x-\frac{15}{7}& = & 4x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-105}{ \color{blue}{7} }x- \frac{15}{ \color{blue}{7} })& = & (\frac{28}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -105x \color{red}{-15} & = & \color{red}{28x} +9 \\\Leftrightarrow & -105x \color{red}{-15} \color{blue}{+15} \color{blue}{-28x} & = & \color{red}{28x} +9 \color{blue}{-28x} \color{blue}{+15} \\\Leftrightarrow & -105x-28x& = & 9+15 \\\Leftrightarrow & \color{red}{-133} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-133} & & \\\Leftrightarrow & x = \frac{-24}{133} & & \\ & V = \left\{ \frac{-24}{133} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{4}{3})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 10x+\frac{20}{3}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{150}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 150x \color{red}{+100} & = & \color{red}{45x} +18 \\\Leftrightarrow & 150x \color{red}{+100} \color{blue}{-100} \color{blue}{-45x} & = & \color{red}{45x} +18 \color{blue}{-45x} \color{blue}{-100} \\\Leftrightarrow & 150x-45x& = & 18-100 \\\Leftrightarrow & \color{red}{105} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{105} & & \\ & V = \left\{ \frac{-82}{105} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{2}{11})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 20x-\frac{10}{11}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x- \frac{70}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{-70} & = & \color{red}{-539x} +110 \\\Leftrightarrow & 1540x \color{red}{-70} \color{blue}{+70} \color{blue}{+539x} & = & \color{red}{-539x} +110 \color{blue}{+539x} \color{blue}{+70} \\\Leftrightarrow & 1540x+539x& = & 110+70 \\\Leftrightarrow & \color{red}{2079} x& = & 180 \\\Leftrightarrow & x = \frac{180}{2079} & & \\\Leftrightarrow & x = \frac{20}{231} & & \\ & V = \left\{ \frac{20}{231} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{5}{3})& = & -9x+\frac{7}{6} \\\Leftrightarrow & -20x-\frac{20}{3}& = & -9x+\frac{7}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{-40} & = & \color{red}{-54x} +7 \\\Leftrightarrow & -120x \color{red}{-40} \color{blue}{+40} \color{blue}{+54x} & = & \color{red}{-54x} +7 \color{blue}{+54x} \color{blue}{+40} \\\Leftrightarrow & -120x+54x& = & 7+40 \\\Leftrightarrow & \color{red}{-66} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-66} & & \\\Leftrightarrow & x = \frac{-47}{66} & & \\ & V = \left\{ \frac{-47}{66} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{4}{7})& = & -7x+\frac{9}{10} \\\Leftrightarrow & 20x-\frac{20}{7}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1400}{ \color{blue}{70} }x- \frac{200}{ \color{blue}{70} })& = & (\frac{-490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1400x \color{red}{-200} & = & \color{red}{-490x} +63 \\\Leftrightarrow & 1400x \color{red}{-200} \color{blue}{+200} \color{blue}{+490x} & = & \color{red}{-490x} +63 \color{blue}{+490x} \color{blue}{+200} \\\Leftrightarrow & 1400x+490x& = & 63+200 \\\Leftrightarrow & \color{red}{1890} x& = & 263 \\\Leftrightarrow & x = \frac{263}{1890} & & \\ & V = \left\{ \frac{263}{1890} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{5}{2})& = & 4x+\frac{10}{9} \\\Leftrightarrow & 25x-\frac{25}{2}& = & 4x+\frac{10}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{450}{ \color{blue}{18} }x- \frac{225}{ \color{blue}{18} })& = & (\frac{72}{ \color{blue}{18} }x+ \frac{20}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 450x \color{red}{-225} & = & \color{red}{72x} +20 \\\Leftrightarrow & 450x \color{red}{-225} \color{blue}{+225} \color{blue}{-72x} & = & \color{red}{72x} +20 \color{blue}{-72x} \color{blue}{+225} \\\Leftrightarrow & 450x-72x& = & 20+225 \\\Leftrightarrow & \color{red}{378} x& = & 245 \\\Leftrightarrow & x = \frac{245}{378} & & \\\Leftrightarrow & x = \frac{35}{54} & & \\ & V = \left\{ \frac{35}{54} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{9})& = & -9x+\frac{8}{3} \\\Leftrightarrow & 14x+\frac{28}{9}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{126}{ \color{blue}{9} }x+ \frac{28}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 126x \color{red}{+28} & = & \color{red}{-81x} +24 \\\Leftrightarrow & 126x \color{red}{+28} \color{blue}{-28} \color{blue}{+81x} & = & \color{red}{-81x} +24 \color{blue}{+81x} \color{blue}{-28} \\\Leftrightarrow & 126x+81x& = & 24-28 \\\Leftrightarrow & \color{red}{207} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{207} & & \\ & V = \left\{ \frac{-4}{207} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{5}{7})& = & -3x+\frac{6}{7} \\\Leftrightarrow & 16x+\frac{20}{7}& = & -3x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{112}{ \color{blue}{7} }x+ \frac{20}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 112x \color{red}{+20} & = & \color{red}{-21x} +6 \\\Leftrightarrow & 112x \color{red}{+20} \color{blue}{-20} \color{blue}{+21x} & = & \color{red}{-21x} +6 \color{blue}{+21x} \color{blue}{-20} \\\Leftrightarrow & 112x+21x& = & 6-20 \\\Leftrightarrow & \color{red}{133} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{133} & & \\\Leftrightarrow & x = \frac{-2}{19} & & \\ & V = \left\{ \frac{-2}{19} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{5}{7})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -30x+\frac{30}{7}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1890}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1890x \color{red}{+270} & = & \color{red}{-441x} +56 \\\Leftrightarrow & -1890x \color{red}{+270} \color{blue}{-270} \color{blue}{+441x} & = & \color{red}{-441x} +56 \color{blue}{+441x} \color{blue}{-270} \\\Leftrightarrow & -1890x+441x& = & 56-270 \\\Leftrightarrow & \color{red}{-1449} x& = & -214 \\\Leftrightarrow & x = \frac{-214}{-1449} & & \\\Leftrightarrow & x = \frac{214}{1449} & & \\ & V = \left\{ \frac{214}{1449} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{3}{5})& = & 7x+\frac{3}{8} \\\Leftrightarrow & -16x+\frac{12}{5}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-640}{ \color{blue}{40} }x+ \frac{96}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -640x \color{red}{+96} & = & \color{red}{280x} +15 \\\Leftrightarrow & -640x \color{red}{+96} \color{blue}{-96} \color{blue}{-280x} & = & \color{red}{280x} +15 \color{blue}{-280x} \color{blue}{-96} \\\Leftrightarrow & -640x-280x& = & 15-96 \\\Leftrightarrow & \color{red}{-920} x& = & -81 \\\Leftrightarrow & x = \frac{-81}{-920} & & \\\Leftrightarrow & x = \frac{81}{920} & & \\ & V = \left\{ \frac{81}{920} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{5})& = & -9x+\frac{9}{4} \\\Leftrightarrow & 8x+\frac{4}{5}& = & -9x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{160}{ \color{blue}{20} }x+ \frac{16}{ \color{blue}{20} })& = & (\frac{-180}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 160x \color{red}{+16} & = & \color{red}{-180x} +45 \\\Leftrightarrow & 160x \color{red}{+16} \color{blue}{-16} \color{blue}{+180x} & = & \color{red}{-180x} +45 \color{blue}{+180x} \color{blue}{-16} \\\Leftrightarrow & 160x+180x& = & 45-16 \\\Leftrightarrow & \color{red}{340} x& = & 29 \\\Leftrightarrow & x = \frac{29}{340} & & \\ & V = \left\{ \frac{29}{340} \right\} & \\\end{align}\)
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