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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{4}{9})& = & -9x+\frac{4}{9} \\\Leftrightarrow & -25x+\frac{20}{9}& = & -9x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-225}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -225x \color{red}{+20} & = & \color{red}{-81x} +4 \\\Leftrightarrow & -225x \color{red}{+20} \color{blue}{-20} \color{blue}{+81x} & = & \color{red}{-81x} +4 \color{blue}{+81x} \color{blue}{-20} \\\Leftrightarrow & -225x+81x& = & 4-20 \\\Leftrightarrow & \color{red}{-144} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-144} & & \\\Leftrightarrow & x = \frac{1}{9} & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{3}{10})& = & -3x+\frac{8}{9} \\\Leftrightarrow & 14x-\frac{21}{10}& = & -3x+\frac{8}{9} \\ & & & \text{kgv van noemers 10 en 9 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{1260}{ \color{blue}{90} }x- \frac{189}{ \color{blue}{90} })& = & (\frac{-270}{ \color{blue}{90} }x+ \frac{80}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 1260x \color{red}{-189} & = & \color{red}{-270x} +80 \\\Leftrightarrow & 1260x \color{red}{-189} \color{blue}{+189} \color{blue}{+270x} & = & \color{red}{-270x} +80 \color{blue}{+270x} \color{blue}{+189} \\\Leftrightarrow & 1260x+270x& = & 80+189 \\\Leftrightarrow & \color{red}{1530} x& = & 269 \\\Leftrightarrow & x = \frac{269}{1530} & & \\ & V = \left\{ \frac{269}{1530} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{5}{7})& = & -3x+\frac{9}{2} \\\Leftrightarrow & -20x-\frac{20}{7}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-280}{ \color{blue}{14} }x- \frac{40}{ \color{blue}{14} })& = & (\frac{-42}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -280x \color{red}{-40} & = & \color{red}{-42x} +63 \\\Leftrightarrow & -280x \color{red}{-40} \color{blue}{+40} \color{blue}{+42x} & = & \color{red}{-42x} +63 \color{blue}{+42x} \color{blue}{+40} \\\Leftrightarrow & -280x+42x& = & 63+40 \\\Leftrightarrow & \color{red}{-238} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-238} & & \\\Leftrightarrow & x = \frac{-103}{238} & & \\ & V = \left\{ \frac{-103}{238} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{3})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 16x+\frac{20}{3}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{48}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 48x \color{red}{+20} & = & \color{red}{-21x} +2 \\\Leftrightarrow & 48x \color{red}{+20} \color{blue}{-20} \color{blue}{+21x} & = & \color{red}{-21x} +2 \color{blue}{+21x} \color{blue}{-20} \\\Leftrightarrow & 48x+21x& = & 2-20 \\\Leftrightarrow & \color{red}{69} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{69} & & \\\Leftrightarrow & x = \frac{-6}{23} & & \\ & V = \left\{ \frac{-6}{23} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{3}{7})& = & -8x+\frac{5}{2} \\\Leftrightarrow & 15x-\frac{9}{7}& = & -8x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{210}{ \color{blue}{14} }x- \frac{18}{ \color{blue}{14} })& = & (\frac{-112}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 210x \color{red}{-18} & = & \color{red}{-112x} +35 \\\Leftrightarrow & 210x \color{red}{-18} \color{blue}{+18} \color{blue}{+112x} & = & \color{red}{-112x} +35 \color{blue}{+112x} \color{blue}{+18} \\\Leftrightarrow & 210x+112x& = & 35+18 \\\Leftrightarrow & \color{red}{322} x& = & 53 \\\Leftrightarrow & x = \frac{53}{322} & & \\ & V = \left\{ \frac{53}{322} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{4}{5})& = & -6x+\frac{4}{11} \\\Leftrightarrow & -18x+\frac{24}{5}& = & -6x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{-330}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{+264} & = & \color{red}{-330x} +20 \\\Leftrightarrow & -990x \color{red}{+264} \color{blue}{-264} \color{blue}{+330x} & = & \color{red}{-330x} +20 \color{blue}{+330x} \color{blue}{-264} \\\Leftrightarrow & -990x+330x& = & 20-264 \\\Leftrightarrow & \color{red}{-660} x& = & -244 \\\Leftrightarrow & x = \frac{-244}{-660} & & \\\Leftrightarrow & x = \frac{61}{165} & & \\ & V = \left\{ \frac{61}{165} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{3}{5})& = & -3x+\frac{3}{10} \\\Leftrightarrow & 4x+\frac{6}{5}& = & -3x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{40}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 40x \color{red}{+12} & = & \color{red}{-30x} +3 \\\Leftrightarrow & 40x \color{red}{+12} \color{blue}{-12} \color{blue}{+30x} & = & \color{red}{-30x} +3 \color{blue}{+30x} \color{blue}{-12} \\\Leftrightarrow & 40x+30x& = & 3-12 \\\Leftrightarrow & \color{red}{70} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{70} & & \\ & V = \left\{ \frac{-9}{70} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{11})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -16x+\frac{8}{11}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-528}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -528x \color{red}{+24} & = & \color{red}{-231x} +110 \\\Leftrightarrow & -528x \color{red}{+24} \color{blue}{-24} \color{blue}{+231x} & = & \color{red}{-231x} +110 \color{blue}{+231x} \color{blue}{-24} \\\Leftrightarrow & -528x+231x& = & 110-24 \\\Leftrightarrow & \color{red}{-297} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-297} & & \\\Leftrightarrow & x = \frac{-86}{297} & & \\ & V = \left\{ \frac{-86}{297} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{5}{4})& = & 7x+\frac{5}{12} \\\Leftrightarrow & -9x-\frac{15}{4}& = & 7x+\frac{5}{12} \\ & & & \text{kgv van noemers 4 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-108}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -108x \color{red}{-45} & = & \color{red}{84x} +5 \\\Leftrightarrow & -108x \color{red}{-45} \color{blue}{+45} \color{blue}{-84x} & = & \color{red}{84x} +5 \color{blue}{-84x} \color{blue}{+45} \\\Leftrightarrow & -108x-84x& = & 5+45 \\\Leftrightarrow & \color{red}{-192} x& = & 50 \\\Leftrightarrow & x = \frac{50}{-192} & & \\\Leftrightarrow & x = \frac{-25}{96} & & \\ & V = \left\{ \frac{-25}{96} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{3}{5})& = & 5x+\frac{3}{10} \\\Leftrightarrow & -9x+\frac{9}{5}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-90}{ \color{blue}{10} }x+ \frac{18}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -90x \color{red}{+18} & = & \color{red}{50x} +3 \\\Leftrightarrow & -90x \color{red}{+18} \color{blue}{-18} \color{blue}{-50x} & = & \color{red}{50x} +3 \color{blue}{-50x} \color{blue}{-18} \\\Leftrightarrow & -90x-50x& = & 3-18 \\\Leftrightarrow & \color{red}{-140} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-140} & & \\\Leftrightarrow & x = \frac{3}{28} & & \\ & V = \left\{ \frac{3}{28} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{1}{3})& = & -2x+\frac{6}{7} \\\Leftrightarrow & 21x-\frac{7}{3}& = & -2x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{441}{ \color{blue}{21} }x- \frac{49}{ \color{blue}{21} })& = & (\frac{-42}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 441x \color{red}{-49} & = & \color{red}{-42x} +18 \\\Leftrightarrow & 441x \color{red}{-49} \color{blue}{+49} \color{blue}{+42x} & = & \color{red}{-42x} +18 \color{blue}{+42x} \color{blue}{+49} \\\Leftrightarrow & 441x+42x& = & 18+49 \\\Leftrightarrow & \color{red}{483} x& = & 67 \\\Leftrightarrow & x = \frac{67}{483} & & \\ & V = \left\{ \frac{67}{483} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{2}{7})& = & 9x+\frac{5}{2} \\\Leftrightarrow & 25x+\frac{10}{7}& = & 9x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{350}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{126}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 350x \color{red}{+20} & = & \color{red}{126x} +35 \\\Leftrightarrow & 350x \color{red}{+20} \color{blue}{-20} \color{blue}{-126x} & = & \color{red}{126x} +35 \color{blue}{-126x} \color{blue}{-20} \\\Leftrightarrow & 350x-126x& = & 35-20 \\\Leftrightarrow & \color{red}{224} x& = & 15 \\\Leftrightarrow & x = \frac{15}{224} & & \\ & V = \left\{ \frac{15}{224} \right\} & \\\end{align}\)
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