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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{3}{5})& = & 9x+\frac{8}{5} \\\Leftrightarrow & -8x+\frac{12}{5}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-40}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{45}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -40x \color{red}{+12} & = & \color{red}{45x} +8 \\\Leftrightarrow & -40x \color{red}{+12} \color{blue}{-12} \color{blue}{-45x} & = & \color{red}{45x} +8 \color{blue}{-45x} \color{blue}{-12} \\\Leftrightarrow & -40x-45x& = & 8-12 \\\Leftrightarrow & \color{red}{-85} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-85} & & \\\Leftrightarrow & x = \frac{4}{85} & & \\ & V = \left\{ \frac{4}{85} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{2}{3})& = & -9x+\frac{3}{10} \\\Leftrightarrow & -8x-\frac{4}{3}& = & -9x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-240}{ \color{blue}{30} }x- \frac{40}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -240x \color{red}{-40} & = & \color{red}{-270x} +9 \\\Leftrightarrow & -240x \color{red}{-40} \color{blue}{+40} \color{blue}{+270x} & = & \color{red}{-270x} +9 \color{blue}{+270x} \color{blue}{+40} \\\Leftrightarrow & -240x+270x& = & 9+40 \\\Leftrightarrow & \color{red}{30} x& = & 49 \\\Leftrightarrow & x = \frac{49}{30} & & \\ & V = \left\{ \frac{49}{30} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{3}{10})& = & 9x+\frac{5}{11} \\\Leftrightarrow & -35x-\frac{21}{10}& = & 9x+\frac{5}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-3850}{ \color{blue}{110} }x- \frac{231}{ \color{blue}{110} })& = & (\frac{990}{ \color{blue}{110} }x+ \frac{50}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -3850x \color{red}{-231} & = & \color{red}{990x} +50 \\\Leftrightarrow & -3850x \color{red}{-231} \color{blue}{+231} \color{blue}{-990x} & = & \color{red}{990x} +50 \color{blue}{-990x} \color{blue}{+231} \\\Leftrightarrow & -3850x-990x& = & 50+231 \\\Leftrightarrow & \color{red}{-4840} x& = & 281 \\\Leftrightarrow & x = \frac{281}{-4840} & & \\\Leftrightarrow & x = \frac{-281}{4840} & & \\ & V = \left\{ \frac{-281}{4840} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{5}{7})& = & 2x+\frac{9}{7} \\\Leftrightarrow & 15x+\frac{25}{7}& = & 2x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{105}{ \color{blue}{7} }x+ \frac{25}{ \color{blue}{7} })& = & (\frac{14}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 105x \color{red}{+25} & = & \color{red}{14x} +9 \\\Leftrightarrow & 105x \color{red}{+25} \color{blue}{-25} \color{blue}{-14x} & = & \color{red}{14x} +9 \color{blue}{-14x} \color{blue}{-25} \\\Leftrightarrow & 105x-14x& = & 9-25 \\\Leftrightarrow & \color{red}{91} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{91} & & \\ & V = \left\{ \frac{-16}{91} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{3})& = & -9x+\frac{9}{7} \\\Leftrightarrow & -8x+\frac{8}{3}& = & -9x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{+56} & = & \color{red}{-189x} +27 \\\Leftrightarrow & -168x \color{red}{+56} \color{blue}{-56} \color{blue}{+189x} & = & \color{red}{-189x} +27 \color{blue}{+189x} \color{blue}{-56} \\\Leftrightarrow & -168x+189x& = & 27-56 \\\Leftrightarrow & \color{red}{21} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{21} & & \\ & V = \left\{ \frac{-29}{21} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{5}{7})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -24x-\frac{30}{7}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-336}{ \color{blue}{14} }x- \frac{60}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -336x \color{red}{-60} & = & \color{red}{98x} +63 \\\Leftrightarrow & -336x \color{red}{-60} \color{blue}{+60} \color{blue}{-98x} & = & \color{red}{98x} +63 \color{blue}{-98x} \color{blue}{+60} \\\Leftrightarrow & -336x-98x& = & 63+60 \\\Leftrightarrow & \color{red}{-434} x& = & 123 \\\Leftrightarrow & x = \frac{123}{-434} & & \\\Leftrightarrow & x = \frac{-123}{434} & & \\ & V = \left\{ \frac{-123}{434} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{3}{2})& = & -2x+\frac{8}{7} \\\Leftrightarrow & 9x-\frac{9}{2}& = & -2x+\frac{8}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{126}{ \color{blue}{14} }x- \frac{63}{ \color{blue}{14} })& = & (\frac{-28}{ \color{blue}{14} }x+ \frac{16}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 126x \color{red}{-63} & = & \color{red}{-28x} +16 \\\Leftrightarrow & 126x \color{red}{-63} \color{blue}{+63} \color{blue}{+28x} & = & \color{red}{-28x} +16 \color{blue}{+28x} \color{blue}{+63} \\\Leftrightarrow & 126x+28x& = & 16+63 \\\Leftrightarrow & \color{red}{154} x& = & 79 \\\Leftrightarrow & x = \frac{79}{154} & & \\ & V = \left\{ \frac{79}{154} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{11})& = & 3x+\frac{8}{5} \\\Leftrightarrow & -20x-\frac{16}{11}& = & 3x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1100}{ \color{blue}{55} }x- \frac{80}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1100x \color{red}{-80} & = & \color{red}{165x} +88 \\\Leftrightarrow & -1100x \color{red}{-80} \color{blue}{+80} \color{blue}{-165x} & = & \color{red}{165x} +88 \color{blue}{-165x} \color{blue}{+80} \\\Leftrightarrow & -1100x-165x& = & 88+80 \\\Leftrightarrow & \color{red}{-1265} x& = & 168 \\\Leftrightarrow & x = \frac{168}{-1265} & & \\\Leftrightarrow & x = \frac{-168}{1265} & & \\ & V = \left\{ \frac{-168}{1265} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{8})& = & 7x+\frac{3}{4} \\\Leftrightarrow & 9x-\frac{15}{8}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{72}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{56}{ \color{blue}{8} }x+ \frac{6}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 72x \color{red}{-15} & = & \color{red}{56x} +6 \\\Leftrightarrow & 72x \color{red}{-15} \color{blue}{+15} \color{blue}{-56x} & = & \color{red}{56x} +6 \color{blue}{-56x} \color{blue}{+15} \\\Leftrightarrow & 72x-56x& = & 6+15 \\\Leftrightarrow & \color{red}{16} x& = & 21 \\\Leftrightarrow & x = \frac{21}{16} & & \\ & V = \left\{ \frac{21}{16} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{2}{5})& = & 7x+\frac{7}{2} \\\Leftrightarrow & 30x-\frac{12}{5}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{300}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 300x \color{red}{-24} & = & \color{red}{70x} +35 \\\Leftrightarrow & 300x \color{red}{-24} \color{blue}{+24} \color{blue}{-70x} & = & \color{red}{70x} +35 \color{blue}{-70x} \color{blue}{+24} \\\Leftrightarrow & 300x-70x& = & 35+24 \\\Leftrightarrow & \color{red}{230} x& = & 59 \\\Leftrightarrow & x = \frac{59}{230} & & \\ & V = \left\{ \frac{59}{230} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{5}{3})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -12x+\frac{20}{3}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{+220} & = & \color{red}{165x} +15 \\\Leftrightarrow & -396x \color{red}{+220} \color{blue}{-220} \color{blue}{-165x} & = & \color{red}{165x} +15 \color{blue}{-165x} \color{blue}{-220} \\\Leftrightarrow & -396x-165x& = & 15-220 \\\Leftrightarrow & \color{red}{-561} x& = & -205 \\\Leftrightarrow & x = \frac{-205}{-561} & & \\\Leftrightarrow & x = \frac{205}{561} & & \\ & V = \left\{ \frac{205}{561} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{5}{7})& = & -5x+\frac{8}{9} \\\Leftrightarrow & -24x+\frac{30}{7}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1512}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1512x \color{red}{+270} & = & \color{red}{-315x} +56 \\\Leftrightarrow & -1512x \color{red}{+270} \color{blue}{-270} \color{blue}{+315x} & = & \color{red}{-315x} +56 \color{blue}{+315x} \color{blue}{-270} \\\Leftrightarrow & -1512x+315x& = & 56-270 \\\Leftrightarrow & \color{red}{-1197} x& = & -214 \\\Leftrightarrow & x = \frac{-214}{-1197} & & \\\Leftrightarrow & x = \frac{214}{1197} & & \\ & V = \left\{ \frac{214}{1197} \right\} & \\\end{align}\)
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