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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{2}{7})& = & -7x+\frac{9}{11} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-66} & = & \color{red}{-539x} +63 \\\Leftrightarrow & -462x \color{red}{-66} \color{blue}{+66} \color{blue}{+539x} & = & \color{red}{-539x} +63 \color{blue}{+539x} \color{blue}{+66} \\\Leftrightarrow & -462x+539x& = & 63+66 \\\Leftrightarrow & \color{red}{77} x& = & 129 \\\Leftrightarrow & x = \frac{129}{77} & & \\ & V = \left\{ \frac{129}{77} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{5}{3})& = & 9x+\frac{3}{2} \\\Leftrightarrow & -28x+\frac{35}{3}& = & 9x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-168}{ \color{blue}{6} }x+ \frac{70}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -168x \color{red}{+70} & = & \color{red}{54x} +9 \\\Leftrightarrow & -168x \color{red}{+70} \color{blue}{-70} \color{blue}{-54x} & = & \color{red}{54x} +9 \color{blue}{-54x} \color{blue}{-70} \\\Leftrightarrow & -168x-54x& = & 9-70 \\\Leftrightarrow & \color{red}{-222} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{-222} & & \\\Leftrightarrow & x = \frac{61}{222} & & \\ & V = \left\{ \frac{61}{222} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{9})& = & -3x+\frac{10}{7} \\\Leftrightarrow & 28x-\frac{14}{9}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1764}{ \color{blue}{63} }x- \frac{98}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1764x \color{red}{-98} & = & \color{red}{-189x} +90 \\\Leftrightarrow & 1764x \color{red}{-98} \color{blue}{+98} \color{blue}{+189x} & = & \color{red}{-189x} +90 \color{blue}{+189x} \color{blue}{+98} \\\Leftrightarrow & 1764x+189x& = & 90+98 \\\Leftrightarrow & \color{red}{1953} x& = & 188 \\\Leftrightarrow & x = \frac{188}{1953} & & \\ & V = \left\{ \frac{188}{1953} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{5}{12})& = & 4x+\frac{3}{10} \\\Leftrightarrow & -25x+\frac{25}{12}& = & 4x+\frac{3}{10} \\ & & & \text{kgv van noemers 12 en 10 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1500}{ \color{blue}{60} }x+ \frac{125}{ \color{blue}{60} })& = & (\frac{240}{ \color{blue}{60} }x+ \frac{18}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1500x \color{red}{+125} & = & \color{red}{240x} +18 \\\Leftrightarrow & -1500x \color{red}{+125} \color{blue}{-125} \color{blue}{-240x} & = & \color{red}{240x} +18 \color{blue}{-240x} \color{blue}{-125} \\\Leftrightarrow & -1500x-240x& = & 18-125 \\\Leftrightarrow & \color{red}{-1740} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{-1740} & & \\\Leftrightarrow & x = \frac{107}{1740} & & \\ & V = \left\{ \frac{107}{1740} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{5}{11})& = & 7x+\frac{2}{9} \\\Leftrightarrow & 30x+\frac{30}{11}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2970}{ \color{blue}{99} }x+ \frac{270}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2970x \color{red}{+270} & = & \color{red}{693x} +22 \\\Leftrightarrow & 2970x \color{red}{+270} \color{blue}{-270} \color{blue}{-693x} & = & \color{red}{693x} +22 \color{blue}{-693x} \color{blue}{-270} \\\Leftrightarrow & 2970x-693x& = & 22-270 \\\Leftrightarrow & \color{red}{2277} x& = & -248 \\\Leftrightarrow & x = \frac{-248}{2277} & & \\ & V = \left\{ \frac{-248}{2277} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{2}{5})& = & 5x+\frac{3}{10} \\\Leftrightarrow & 24x-\frac{12}{5}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{240}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 240x \color{red}{-24} & = & \color{red}{50x} +3 \\\Leftrightarrow & 240x \color{red}{-24} \color{blue}{+24} \color{blue}{-50x} & = & \color{red}{50x} +3 \color{blue}{-50x} \color{blue}{+24} \\\Leftrightarrow & 240x-50x& = & 3+24 \\\Leftrightarrow & \color{red}{190} x& = & 27 \\\Leftrightarrow & x = \frac{27}{190} & & \\ & V = \left\{ \frac{27}{190} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{4}{5})& = & -7x+\frac{7}{8} \\\Leftrightarrow & 12x-\frac{24}{5}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x- \frac{192}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{-192} & = & \color{red}{-280x} +35 \\\Leftrightarrow & 480x \color{red}{-192} \color{blue}{+192} \color{blue}{+280x} & = & \color{red}{-280x} +35 \color{blue}{+280x} \color{blue}{+192} \\\Leftrightarrow & 480x+280x& = & 35+192 \\\Leftrightarrow & \color{red}{760} x& = & 227 \\\Leftrightarrow & x = \frac{227}{760} & & \\ & V = \left\{ \frac{227}{760} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{9})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 16x+\frac{8}{9}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1584}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1584x \color{red}{+88} & = & \color{red}{495x} +54 \\\Leftrightarrow & 1584x \color{red}{+88} \color{blue}{-88} \color{blue}{-495x} & = & \color{red}{495x} +54 \color{blue}{-495x} \color{blue}{-88} \\\Leftrightarrow & 1584x-495x& = & 54-88 \\\Leftrightarrow & \color{red}{1089} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{1089} & & \\ & V = \left\{ \frac{-34}{1089} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{2}{3})& = & -2x+\frac{3}{2} \\\Leftrightarrow & 35x+\frac{14}{3}& = & -2x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{210}{ \color{blue}{6} }x+ \frac{28}{ \color{blue}{6} })& = & (\frac{-12}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 210x \color{red}{+28} & = & \color{red}{-12x} +9 \\\Leftrightarrow & 210x \color{red}{+28} \color{blue}{-28} \color{blue}{+12x} & = & \color{red}{-12x} +9 \color{blue}{+12x} \color{blue}{-28} \\\Leftrightarrow & 210x+12x& = & 9-28 \\\Leftrightarrow & \color{red}{222} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{222} & & \\ & V = \left\{ \frac{-19}{222} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{2}{3})& = & -5x+\frac{8}{11} \\\Leftrightarrow & 12x-\frac{8}{3}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{-88} & = & \color{red}{-165x} +24 \\\Leftrightarrow & 396x \color{red}{-88} \color{blue}{+88} \color{blue}{+165x} & = & \color{red}{-165x} +24 \color{blue}{+165x} \color{blue}{+88} \\\Leftrightarrow & 396x+165x& = & 24+88 \\\Leftrightarrow & \color{red}{561} x& = & 112 \\\Leftrightarrow & x = \frac{112}{561} & & \\ & V = \left\{ \frac{112}{561} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{5}{11})& = & -5x+\frac{5}{6} \\\Leftrightarrow & -24x+\frac{30}{11}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1584}{ \color{blue}{66} }x+ \frac{180}{ \color{blue}{66} })& = & (\frac{-330}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1584x \color{red}{+180} & = & \color{red}{-330x} +55 \\\Leftrightarrow & -1584x \color{red}{+180} \color{blue}{-180} \color{blue}{+330x} & = & \color{red}{-330x} +55 \color{blue}{+330x} \color{blue}{-180} \\\Leftrightarrow & -1584x+330x& = & 55-180 \\\Leftrightarrow & \color{red}{-1254} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{-1254} & & \\\Leftrightarrow & x = \frac{125}{1254} & & \\ & V = \left\{ \frac{125}{1254} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{2}{5})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -30x+\frac{12}{5}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{+84} & = & \color{red}{245x} +50 \\\Leftrightarrow & -1050x \color{red}{+84} \color{blue}{-84} \color{blue}{-245x} & = & \color{red}{245x} +50 \color{blue}{-245x} \color{blue}{-84} \\\Leftrightarrow & -1050x-245x& = & 50-84 \\\Leftrightarrow & \color{red}{-1295} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-1295} & & \\\Leftrightarrow & x = \frac{34}{1295} & & \\ & V = \left\{ \frac{34}{1295} \right\} & \\\end{align}\)
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