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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{3}{5})& = & -7x+\frac{2}{7} \\\Leftrightarrow & -16x+\frac{12}{5}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-560}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -560x \color{red}{+84} & = & \color{red}{-245x} +10 \\\Leftrightarrow & -560x \color{red}{+84} \color{blue}{-84} \color{blue}{+245x} & = & \color{red}{-245x} +10 \color{blue}{+245x} \color{blue}{-84} \\\Leftrightarrow & -560x+245x& = & 10-84 \\\Leftrightarrow & \color{red}{-315} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{-315} & & \\\Leftrightarrow & x = \frac{74}{315} & & \\ & V = \left\{ \frac{74}{315} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{2}{5})& = & 2x+\frac{10}{9} \\\Leftrightarrow & 21x+\frac{14}{5}& = & 2x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{945}{ \color{blue}{45} }x+ \frac{126}{ \color{blue}{45} })& = & (\frac{90}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 945x \color{red}{+126} & = & \color{red}{90x} +50 \\\Leftrightarrow & 945x \color{red}{+126} \color{blue}{-126} \color{blue}{-90x} & = & \color{red}{90x} +50 \color{blue}{-90x} \color{blue}{-126} \\\Leftrightarrow & 945x-90x& = & 50-126 \\\Leftrightarrow & \color{red}{855} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{855} & & \\\Leftrightarrow & x = \frac{-4}{45} & & \\ & V = \left\{ \frac{-4}{45} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{7})& = & -5x+\frac{2}{11} \\\Leftrightarrow & 12x-\frac{15}{7}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{165}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-165} & = & \color{red}{-385x} +14 \\\Leftrightarrow & 924x \color{red}{-165} \color{blue}{+165} \color{blue}{+385x} & = & \color{red}{-385x} +14 \color{blue}{+385x} \color{blue}{+165} \\\Leftrightarrow & 924x+385x& = & 14+165 \\\Leftrightarrow & \color{red}{1309} x& = & 179 \\\Leftrightarrow & x = \frac{179}{1309} & & \\ & V = \left\{ \frac{179}{1309} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{2}{5})& = & -5x+\frac{7}{9} \\\Leftrightarrow & 18x+\frac{12}{5}& = & -5x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{810}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 810x \color{red}{+108} & = & \color{red}{-225x} +35 \\\Leftrightarrow & 810x \color{red}{+108} \color{blue}{-108} \color{blue}{+225x} & = & \color{red}{-225x} +35 \color{blue}{+225x} \color{blue}{-108} \\\Leftrightarrow & 810x+225x& = & 35-108 \\\Leftrightarrow & \color{red}{1035} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{1035} & & \\ & V = \left\{ \frac{-73}{1035} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{4})& = & 6x+\frac{8}{11} \\\Leftrightarrow & -28x+\frac{21}{4}& = & 6x+\frac{8}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1232}{ \color{blue}{44} }x+ \frac{231}{ \color{blue}{44} })& = & (\frac{264}{ \color{blue}{44} }x+ \frac{32}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1232x \color{red}{+231} & = & \color{red}{264x} +32 \\\Leftrightarrow & -1232x \color{red}{+231} \color{blue}{-231} \color{blue}{-264x} & = & \color{red}{264x} +32 \color{blue}{-264x} \color{blue}{-231} \\\Leftrightarrow & -1232x-264x& = & 32-231 \\\Leftrightarrow & \color{red}{-1496} x& = & -199 \\\Leftrightarrow & x = \frac{-199}{-1496} & & \\\Leftrightarrow & x = \frac{199}{1496} & & \\ & V = \left\{ \frac{199}{1496} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{7})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -12x+\frac{30}{7}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+330} & = & \color{red}{385x} +14 \\\Leftrightarrow & -924x \color{red}{+330} \color{blue}{-330} \color{blue}{-385x} & = & \color{red}{385x} +14 \color{blue}{-385x} \color{blue}{-330} \\\Leftrightarrow & -924x-385x& = & 14-330 \\\Leftrightarrow & \color{red}{-1309} x& = & -316 \\\Leftrightarrow & x = \frac{-316}{-1309} & & \\\Leftrightarrow & x = \frac{316}{1309} & & \\ & V = \left\{ \frac{316}{1309} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{2}{11})& = & -4x+\frac{3}{2} \\\Leftrightarrow & 9x-\frac{6}{11}& = & -4x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{198}{ \color{blue}{22} }x- \frac{12}{ \color{blue}{22} })& = & (\frac{-88}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 198x \color{red}{-12} & = & \color{red}{-88x} +33 \\\Leftrightarrow & 198x \color{red}{-12} \color{blue}{+12} \color{blue}{+88x} & = & \color{red}{-88x} +33 \color{blue}{+88x} \color{blue}{+12} \\\Leftrightarrow & 198x+88x& = & 33+12 \\\Leftrightarrow & \color{red}{286} x& = & 45 \\\Leftrightarrow & x = \frac{45}{286} & & \\ & V = \left\{ \frac{45}{286} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{4}{9})& = & 2x+\frac{10}{9} \\\Leftrightarrow & 35x-\frac{28}{9}& = & 2x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{315}{ \color{blue}{9} }x- \frac{28}{ \color{blue}{9} })& = & (\frac{18}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 315x \color{red}{-28} & = & \color{red}{18x} +10 \\\Leftrightarrow & 315x \color{red}{-28} \color{blue}{+28} \color{blue}{-18x} & = & \color{red}{18x} +10 \color{blue}{-18x} \color{blue}{+28} \\\Leftrightarrow & 315x-18x& = & 10+28 \\\Leftrightarrow & \color{red}{297} x& = & 38 \\\Leftrightarrow & x = \frac{38}{297} & & \\ & V = \left\{ \frac{38}{297} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{9})& = & 9x+\frac{2}{7} \\\Leftrightarrow & 16x+\frac{8}{9}& = & 9x+\frac{2}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1008}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{18}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1008x \color{red}{+56} & = & \color{red}{567x} +18 \\\Leftrightarrow & 1008x \color{red}{+56} \color{blue}{-56} \color{blue}{-567x} & = & \color{red}{567x} +18 \color{blue}{-567x} \color{blue}{-56} \\\Leftrightarrow & 1008x-567x& = & 18-56 \\\Leftrightarrow & \color{red}{441} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{441} & & \\ & V = \left\{ \frac{-38}{441} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{4}{11})& = & -3x+\frac{4}{7} \\\Leftrightarrow & -8x-\frac{8}{11}& = & -3x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x- \frac{56}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{-56} & = & \color{red}{-231x} +44 \\\Leftrightarrow & -616x \color{red}{-56} \color{blue}{+56} \color{blue}{+231x} & = & \color{red}{-231x} +44 \color{blue}{+231x} \color{blue}{+56} \\\Leftrightarrow & -616x+231x& = & 44+56 \\\Leftrightarrow & \color{red}{-385} x& = & 100 \\\Leftrightarrow & x = \frac{100}{-385} & & \\\Leftrightarrow & x = \frac{-20}{77} & & \\ & V = \left\{ \frac{-20}{77} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{11})& = & 6x+\frac{8}{9} \\\Leftrightarrow & -28x-\frac{28}{11}& = & 6x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2772}{ \color{blue}{99} }x- \frac{252}{ \color{blue}{99} })& = & (\frac{594}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2772x \color{red}{-252} & = & \color{red}{594x} +88 \\\Leftrightarrow & -2772x \color{red}{-252} \color{blue}{+252} \color{blue}{-594x} & = & \color{red}{594x} +88 \color{blue}{-594x} \color{blue}{+252} \\\Leftrightarrow & -2772x-594x& = & 88+252 \\\Leftrightarrow & \color{red}{-3366} x& = & 340 \\\Leftrightarrow & x = \frac{340}{-3366} & & \\\Leftrightarrow & x = \frac{-10}{99} & & \\ & V = \left\{ \frac{-10}{99} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{12})& = & 3x+\frac{6}{5} \\\Leftrightarrow & -20x-\frac{25}{12}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 12 en 5 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1200}{ \color{blue}{60} }x- \frac{125}{ \color{blue}{60} })& = & (\frac{180}{ \color{blue}{60} }x+ \frac{72}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1200x \color{red}{-125} & = & \color{red}{180x} +72 \\\Leftrightarrow & -1200x \color{red}{-125} \color{blue}{+125} \color{blue}{-180x} & = & \color{red}{180x} +72 \color{blue}{-180x} \color{blue}{+125} \\\Leftrightarrow & -1200x-180x& = & 72+125 \\\Leftrightarrow & \color{red}{-1380} x& = & 197 \\\Leftrightarrow & x = \frac{197}{-1380} & & \\\Leftrightarrow & x = \frac{-197}{1380} & & \\ & V = \left\{ \frac{-197}{1380} \right\} & \\\end{align}\)
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