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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{3}{10})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 12x+\frac{9}{10}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1320}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{100}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1320x \color{red}{+99} & = & \color{red}{-550x} +100 \\\Leftrightarrow & 1320x \color{red}{+99} \color{blue}{-99} \color{blue}{+550x} & = & \color{red}{-550x} +100 \color{blue}{+550x} \color{blue}{-99} \\\Leftrightarrow & 1320x+550x& = & 100-99 \\\Leftrightarrow & \color{red}{1870} x& = & 1 \\\Leftrightarrow & x = \frac{1}{1870} & & \\ & V = \left\{ \frac{1}{1870} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{4}{11})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -30x-\frac{24}{11}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x- \frac{168}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{-168} & = & \color{red}{539x} +44 \\\Leftrightarrow & -2310x \color{red}{-168} \color{blue}{+168} \color{blue}{-539x} & = & \color{red}{539x} +44 \color{blue}{-539x} \color{blue}{+168} \\\Leftrightarrow & -2310x-539x& = & 44+168 \\\Leftrightarrow & \color{red}{-2849} x& = & 212 \\\Leftrightarrow & x = \frac{212}{-2849} & & \\\Leftrightarrow & x = \frac{-212}{2849} & & \\ & V = \left\{ \frac{-212}{2849} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{3}{5})& = & 7x+\frac{3}{10} \\\Leftrightarrow & 6x-\frac{9}{5}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x- \frac{18}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{-18} & = & \color{red}{70x} +3 \\\Leftrightarrow & 60x \color{red}{-18} \color{blue}{+18} \color{blue}{-70x} & = & \color{red}{70x} +3 \color{blue}{-70x} \color{blue}{+18} \\\Leftrightarrow & 60x-70x& = & 3+18 \\\Leftrightarrow & \color{red}{-10} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-10} & & \\\Leftrightarrow & x = \frac{-21}{10} & & \\ & V = \left\{ \frac{-21}{10} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{4}{5})& = & -5x+\frac{5}{2} \\\Leftrightarrow & 6x+\frac{8}{5}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{+16} & = & \color{red}{-50x} +25 \\\Leftrightarrow & 60x \color{red}{+16} \color{blue}{-16} \color{blue}{+50x} & = & \color{red}{-50x} +25 \color{blue}{+50x} \color{blue}{-16} \\\Leftrightarrow & 60x+50x& = & 25-16 \\\Leftrightarrow & \color{red}{110} x& = & 9 \\\Leftrightarrow & x = \frac{9}{110} & & \\ & V = \left\{ \frac{9}{110} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{4}{7})& = & 8x+\frac{6}{5} \\\Leftrightarrow & -15x+\frac{12}{7}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x+ \frac{60}{ \color{blue}{35} })& = & (\frac{280}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{+60} & = & \color{red}{280x} +42 \\\Leftrightarrow & -525x \color{red}{+60} \color{blue}{-60} \color{blue}{-280x} & = & \color{red}{280x} +42 \color{blue}{-280x} \color{blue}{-60} \\\Leftrightarrow & -525x-280x& = & 42-60 \\\Leftrightarrow & \color{red}{-805} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-805} & & \\\Leftrightarrow & x = \frac{18}{805} & & \\ & V = \left\{ \frac{18}{805} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{3}{11})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 12x-\frac{18}{11}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{-54} & = & \color{red}{165x} +110 \\\Leftrightarrow & 396x \color{red}{-54} \color{blue}{+54} \color{blue}{-165x} & = & \color{red}{165x} +110 \color{blue}{-165x} \color{blue}{+54} \\\Leftrightarrow & 396x-165x& = & 110+54 \\\Leftrightarrow & \color{red}{231} x& = & 164 \\\Leftrightarrow & x = \frac{164}{231} & & \\ & V = \left\{ \frac{164}{231} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{3}{8})& = & 3x+\frac{9}{2} \\\Leftrightarrow & 28x+\frac{21}{8}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{224}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{24}{ \color{blue}{8} }x+ \frac{36}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 224x \color{red}{+21} & = & \color{red}{24x} +36 \\\Leftrightarrow & 224x \color{red}{+21} \color{blue}{-21} \color{blue}{-24x} & = & \color{red}{24x} +36 \color{blue}{-24x} \color{blue}{-21} \\\Leftrightarrow & 224x-24x& = & 36-21 \\\Leftrightarrow & \color{red}{200} x& = & 15 \\\Leftrightarrow & x = \frac{15}{200} & & \\\Leftrightarrow & x = \frac{3}{40} & & \\ & V = \left\{ \frac{3}{40} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{7})& = & 5x+\frac{5}{12} \\\Leftrightarrow & -24x+\frac{24}{7}& = & 5x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-2016}{ \color{blue}{84} }x+ \frac{288}{ \color{blue}{84} })& = & (\frac{420}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -2016x \color{red}{+288} & = & \color{red}{420x} +35 \\\Leftrightarrow & -2016x \color{red}{+288} \color{blue}{-288} \color{blue}{-420x} & = & \color{red}{420x} +35 \color{blue}{-420x} \color{blue}{-288} \\\Leftrightarrow & -2016x-420x& = & 35-288 \\\Leftrightarrow & \color{red}{-2436} x& = & -253 \\\Leftrightarrow & x = \frac{-253}{-2436} & & \\\Leftrightarrow & x = \frac{253}{2436} & & \\ & V = \left\{ \frac{253}{2436} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{3}{5})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 12x+\frac{9}{5}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{18}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+18} & = & \color{red}{-50x} +45 \\\Leftrightarrow & 120x \color{red}{+18} \color{blue}{-18} \color{blue}{+50x} & = & \color{red}{-50x} +45 \color{blue}{+50x} \color{blue}{-18} \\\Leftrightarrow & 120x+50x& = & 45-18 \\\Leftrightarrow & \color{red}{170} x& = & 27 \\\Leftrightarrow & x = \frac{27}{170} & & \\ & V = \left\{ \frac{27}{170} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{3})& = & -9x+\frac{10}{11} \\\Leftrightarrow & 20x+\frac{25}{3}& = & -9x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x+ \frac{275}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{+275} & = & \color{red}{-297x} +30 \\\Leftrightarrow & 660x \color{red}{+275} \color{blue}{-275} \color{blue}{+297x} & = & \color{red}{-297x} +30 \color{blue}{+297x} \color{blue}{-275} \\\Leftrightarrow & 660x+297x& = & 30-275 \\\Leftrightarrow & \color{red}{957} x& = & -245 \\\Leftrightarrow & x = \frac{-245}{957} & & \\ & V = \left\{ \frac{-245}{957} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{3}{5})& = & -3x+\frac{3}{10} \\\Leftrightarrow & 8x-\frac{6}{5}& = & -3x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{80}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 80x \color{red}{-12} & = & \color{red}{-30x} +3 \\\Leftrightarrow & 80x \color{red}{-12} \color{blue}{+12} \color{blue}{+30x} & = & \color{red}{-30x} +3 \color{blue}{+30x} \color{blue}{+12} \\\Leftrightarrow & 80x+30x& = & 3+12 \\\Leftrightarrow & \color{red}{110} x& = & 15 \\\Leftrightarrow & x = \frac{15}{110} & & \\\Leftrightarrow & x = \frac{3}{22} & & \\ & V = \left\{ \frac{3}{22} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{4}{7})& = & -5x+\frac{8}{7} \\\Leftrightarrow & -12x-\frac{16}{7}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{-16} & = & \color{red}{-35x} +8 \\\Leftrightarrow & -84x \color{red}{-16} \color{blue}{+16} \color{blue}{+35x} & = & \color{red}{-35x} +8 \color{blue}{+35x} \color{blue}{+16} \\\Leftrightarrow & -84x+35x& = & 8+16 \\\Leftrightarrow & \color{red}{-49} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-49} & & \\\Leftrightarrow & x = \frac{-24}{49} & & \\ & V = \left\{ \frac{-24}{49} \right\} & \\\end{align}\)
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