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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{3}{7})& = & -9x+\frac{9}{4} \\\Leftrightarrow & -4x+\frac{6}{7}& = & -9x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-112}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{-252}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -112x \color{red}{+24} & = & \color{red}{-252x} +63 \\\Leftrightarrow & -112x \color{red}{+24} \color{blue}{-24} \color{blue}{+252x} & = & \color{red}{-252x} +63 \color{blue}{+252x} \color{blue}{-24} \\\Leftrightarrow & -112x+252x& = & 63-24 \\\Leftrightarrow & \color{red}{140} x& = & 39 \\\Leftrightarrow & x = \frac{39}{140} & & \\ & V = \left\{ \frac{39}{140} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{3}{10})& = & 9x+\frac{6}{11} \\\Leftrightarrow & -35x+\frac{21}{10}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-3850}{ \color{blue}{110} }x+ \frac{231}{ \color{blue}{110} })& = & (\frac{990}{ \color{blue}{110} }x+ \frac{60}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -3850x \color{red}{+231} & = & \color{red}{990x} +60 \\\Leftrightarrow & -3850x \color{red}{+231} \color{blue}{-231} \color{blue}{-990x} & = & \color{red}{990x} +60 \color{blue}{-990x} \color{blue}{-231} \\\Leftrightarrow & -3850x-990x& = & 60-231 \\\Leftrightarrow & \color{red}{-4840} x& = & -171 \\\Leftrightarrow & x = \frac{-171}{-4840} & & \\\Leftrightarrow & x = \frac{171}{4840} & & \\ & V = \left\{ \frac{171}{4840} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{2}{11})& = & 4x+\frac{10}{11} \\\Leftrightarrow & 15x+\frac{10}{11}& = & 4x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{165}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{44}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 165x \color{red}{+10} & = & \color{red}{44x} +10 \\\Leftrightarrow & 165x \color{red}{+10} \color{blue}{-10} \color{blue}{-44x} & = & \color{red}{44x} +10 \color{blue}{-44x} \color{blue}{-10} \\\Leftrightarrow & 165x-44x& = & 10-10 \\\Leftrightarrow & \color{red}{121} x& = & 0 \\\Leftrightarrow & x = \frac{0}{121} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{4})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -20x-\frac{15}{4}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-240}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -240x \color{red}{-45} & = & \color{red}{-108x} +8 \\\Leftrightarrow & -240x \color{red}{-45} \color{blue}{+45} \color{blue}{+108x} & = & \color{red}{-108x} +8 \color{blue}{+108x} \color{blue}{+45} \\\Leftrightarrow & -240x+108x& = & 8+45 \\\Leftrightarrow & \color{red}{-132} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-132} & & \\\Leftrightarrow & x = \frac{-53}{132} & & \\ & V = \left\{ \frac{-53}{132} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{3}{5})& = & -3x+\frac{2}{3} \\\Leftrightarrow & -20x+\frac{12}{5}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{+36} & = & \color{red}{-45x} +10 \\\Leftrightarrow & -300x \color{red}{+36} \color{blue}{-36} \color{blue}{+45x} & = & \color{red}{-45x} +10 \color{blue}{+45x} \color{blue}{-36} \\\Leftrightarrow & -300x+45x& = & 10-36 \\\Leftrightarrow & \color{red}{-255} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-255} & & \\\Leftrightarrow & x = \frac{26}{255} & & \\ & V = \left\{ \frac{26}{255} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{2}{9})& = & -3x+\frac{2}{3} \\\Leftrightarrow & 4x-\frac{4}{9}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{36}{ \color{blue}{9} }x- \frac{4}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 36x \color{red}{-4} & = & \color{red}{-27x} +6 \\\Leftrightarrow & 36x \color{red}{-4} \color{blue}{+4} \color{blue}{+27x} & = & \color{red}{-27x} +6 \color{blue}{+27x} \color{blue}{+4} \\\Leftrightarrow & 36x+27x& = & 6+4 \\\Leftrightarrow & \color{red}{63} x& = & 10 \\\Leftrightarrow & x = \frac{10}{63} & & \\ & V = \left\{ \frac{10}{63} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{5}{6})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -10x-\frac{25}{6}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-60}{ \color{blue}{6} }x- \frac{25}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -60x \color{red}{-25} & = & \color{red}{42x} +8 \\\Leftrightarrow & -60x \color{red}{-25} \color{blue}{+25} \color{blue}{-42x} & = & \color{red}{42x} +8 \color{blue}{-42x} \color{blue}{+25} \\\Leftrightarrow & -60x-42x& = & 8+25 \\\Leftrightarrow & \color{red}{-102} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-102} & & \\\Leftrightarrow & x = \frac{-11}{34} & & \\ & V = \left\{ \frac{-11}{34} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{2})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -10x+\frac{25}{2}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-60}{ \color{blue}{6} }x+ \frac{75}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -60x \color{red}{+75} & = & \color{red}{42x} +20 \\\Leftrightarrow & -60x \color{red}{+75} \color{blue}{-75} \color{blue}{-42x} & = & \color{red}{42x} +20 \color{blue}{-42x} \color{blue}{-75} \\\Leftrightarrow & -60x-42x& = & 20-75 \\\Leftrightarrow & \color{red}{-102} x& = & -55 \\\Leftrightarrow & x = \frac{-55}{-102} & & \\\Leftrightarrow & x = \frac{55}{102} & & \\ & V = \left\{ \frac{55}{102} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{4}{5})& = & -7x+\frac{2}{7} \\\Leftrightarrow & 12x-\frac{24}{5}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{168}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-168} & = & \color{red}{-245x} +10 \\\Leftrightarrow & 420x \color{red}{-168} \color{blue}{+168} \color{blue}{+245x} & = & \color{red}{-245x} +10 \color{blue}{+245x} \color{blue}{+168} \\\Leftrightarrow & 420x+245x& = & 10+168 \\\Leftrightarrow & \color{red}{665} x& = & 178 \\\Leftrightarrow & x = \frac{178}{665} & & \\ & V = \left\{ \frac{178}{665} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{3}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 18x+\frac{18}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{90}{ \color{blue}{5} }x+ \frac{18}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 90x \color{red}{+18} & = & \color{red}{35x} +6 \\\Leftrightarrow & 90x \color{red}{+18} \color{blue}{-18} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{-18} \\\Leftrightarrow & 90x-35x& = & 6-18 \\\Leftrightarrow & \color{red}{55} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{55} & & \\ & V = \left\{ \frac{-12}{55} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & -2x+\frac{8}{3} \\\Leftrightarrow & 21x-\frac{14}{3}& = & -2x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{63}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{-6}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 63x \color{red}{-14} & = & \color{red}{-6x} +8 \\\Leftrightarrow & 63x \color{red}{-14} \color{blue}{+14} \color{blue}{+6x} & = & \color{red}{-6x} +8 \color{blue}{+6x} \color{blue}{+14} \\\Leftrightarrow & 63x+6x& = & 8+14 \\\Leftrightarrow & \color{red}{69} x& = & 22 \\\Leftrightarrow & x = \frac{22}{69} & & \\ & V = \left\{ \frac{22}{69} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{4}{9})& = & 7x+\frac{8}{5} \\\Leftrightarrow & -16x+\frac{16}{9}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-720}{ \color{blue}{45} }x+ \frac{80}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{72}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -720x \color{red}{+80} & = & \color{red}{315x} +72 \\\Leftrightarrow & -720x \color{red}{+80} \color{blue}{-80} \color{blue}{-315x} & = & \color{red}{315x} +72 \color{blue}{-315x} \color{blue}{-80} \\\Leftrightarrow & -720x-315x& = & 72-80 \\\Leftrightarrow & \color{red}{-1035} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-1035} & & \\\Leftrightarrow & x = \frac{8}{1035} & & \\ & V = \left\{ \frac{8}{1035} \right\} & \\\end{align}\)
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