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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{4}{11})& = & 7x+\frac{2}{11} \\\Leftrightarrow & -6x+\frac{8}{11}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-66}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -66x \color{red}{+8} & = & \color{red}{77x} +2 \\\Leftrightarrow & -66x \color{red}{+8} \color{blue}{-8} \color{blue}{-77x} & = & \color{red}{77x} +2 \color{blue}{-77x} \color{blue}{-8} \\\Leftrightarrow & -66x-77x& = & 2-8 \\\Leftrightarrow & \color{red}{-143} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-143} & & \\\Leftrightarrow & x = \frac{6}{143} & & \\ & V = \left\{ \frac{6}{143} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{3}{5})& = & -7x+\frac{5}{8} \\\Leftrightarrow & -16x+\frac{12}{5}& = & -7x+\frac{5}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-640}{ \color{blue}{40} }x+ \frac{96}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{25}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -640x \color{red}{+96} & = & \color{red}{-280x} +25 \\\Leftrightarrow & -640x \color{red}{+96} \color{blue}{-96} \color{blue}{+280x} & = & \color{red}{-280x} +25 \color{blue}{+280x} \color{blue}{-96} \\\Leftrightarrow & -640x+280x& = & 25-96 \\\Leftrightarrow & \color{red}{-360} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{-360} & & \\\Leftrightarrow & x = \frac{71}{360} & & \\ & V = \left\{ \frac{71}{360} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{5}{7})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 30x-\frac{30}{7}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{420}{ \color{blue}{14} }x- \frac{60}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 420x \color{red}{-60} & = & \color{red}{98x} +21 \\\Leftrightarrow & 420x \color{red}{-60} \color{blue}{+60} \color{blue}{-98x} & = & \color{red}{98x} +21 \color{blue}{-98x} \color{blue}{+60} \\\Leftrightarrow & 420x-98x& = & 21+60 \\\Leftrightarrow & \color{red}{322} x& = & 81 \\\Leftrightarrow & x = \frac{81}{322} & & \\ & V = \left\{ \frac{81}{322} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{6})& = & -9x+\frac{8}{7} \\\Leftrightarrow & 14x-\frac{35}{6}& = & -9x+\frac{8}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{588}{ \color{blue}{42} }x- \frac{245}{ \color{blue}{42} })& = & (\frac{-378}{ \color{blue}{42} }x+ \frac{48}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 588x \color{red}{-245} & = & \color{red}{-378x} +48 \\\Leftrightarrow & 588x \color{red}{-245} \color{blue}{+245} \color{blue}{+378x} & = & \color{red}{-378x} +48 \color{blue}{+378x} \color{blue}{+245} \\\Leftrightarrow & 588x+378x& = & 48+245 \\\Leftrightarrow & \color{red}{966} x& = & 293 \\\Leftrightarrow & x = \frac{293}{966} & & \\ & V = \left\{ \frac{293}{966} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{2}{3})& = & 8x+\frac{5}{8} \\\Leftrightarrow & -28x-\frac{14}{3}& = & 8x+\frac{5}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-672}{ \color{blue}{24} }x- \frac{112}{ \color{blue}{24} })& = & (\frac{192}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -672x \color{red}{-112} & = & \color{red}{192x} +15 \\\Leftrightarrow & -672x \color{red}{-112} \color{blue}{+112} \color{blue}{-192x} & = & \color{red}{192x} +15 \color{blue}{-192x} \color{blue}{+112} \\\Leftrightarrow & -672x-192x& = & 15+112 \\\Leftrightarrow & \color{red}{-864} x& = & 127 \\\Leftrightarrow & x = \frac{127}{-864} & & \\\Leftrightarrow & x = \frac{-127}{864} & & \\ & V = \left\{ \frac{-127}{864} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{7})& = & -5x+\frac{7}{8} \\\Leftrightarrow & -12x-\frac{15}{7}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-672}{ \color{blue}{56} }x- \frac{120}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -672x \color{red}{-120} & = & \color{red}{-280x} +49 \\\Leftrightarrow & -672x \color{red}{-120} \color{blue}{+120} \color{blue}{+280x} & = & \color{red}{-280x} +49 \color{blue}{+280x} \color{blue}{+120} \\\Leftrightarrow & -672x+280x& = & 49+120 \\\Leftrightarrow & \color{red}{-392} x& = & 169 \\\Leftrightarrow & x = \frac{169}{-392} & & \\\Leftrightarrow & x = \frac{-169}{392} & & \\ & V = \left\{ \frac{-169}{392} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{3}{5})& = & 9x+\frac{4}{5} \\\Leftrightarrow & -8x-\frac{6}{5}& = & 9x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-40}{ \color{blue}{5} }x- \frac{6}{ \color{blue}{5} })& = & (\frac{45}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -40x \color{red}{-6} & = & \color{red}{45x} +4 \\\Leftrightarrow & -40x \color{red}{-6} \color{blue}{+6} \color{blue}{-45x} & = & \color{red}{45x} +4 \color{blue}{-45x} \color{blue}{+6} \\\Leftrightarrow & -40x-45x& = & 4+6 \\\Leftrightarrow & \color{red}{-85} x& = & 10 \\\Leftrightarrow & x = \frac{10}{-85} & & \\\Leftrightarrow & x = \frac{-2}{17} & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{2})& = & -7x+\frac{6}{7} \\\Leftrightarrow & 12x-\frac{15}{2}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x- \frac{105}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{-105} & = & \color{red}{-98x} +12 \\\Leftrightarrow & 168x \color{red}{-105} \color{blue}{+105} \color{blue}{+98x} & = & \color{red}{-98x} +12 \color{blue}{+98x} \color{blue}{+105} \\\Leftrightarrow & 168x+98x& = & 12+105 \\\Leftrightarrow & \color{red}{266} x& = & 117 \\\Leftrightarrow & x = \frac{117}{266} & & \\ & V = \left\{ \frac{117}{266} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{5}{7})& = & 7x+\frac{7}{12} \\\Leftrightarrow & 10x+\frac{25}{7}& = & 7x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{840}{ \color{blue}{84} }x+ \frac{300}{ \color{blue}{84} })& = & (\frac{588}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 840x \color{red}{+300} & = & \color{red}{588x} +49 \\\Leftrightarrow & 840x \color{red}{+300} \color{blue}{-300} \color{blue}{-588x} & = & \color{red}{588x} +49 \color{blue}{-588x} \color{blue}{-300} \\\Leftrightarrow & 840x-588x& = & 49-300 \\\Leftrightarrow & \color{red}{252} x& = & -251 \\\Leftrightarrow & x = \frac{-251}{252} & & \\ & V = \left\{ \frac{-251}{252} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{4}{9})& = & 9x+\frac{3}{7} \\\Leftrightarrow & -20x+\frac{20}{9}& = & 9x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x+ \frac{140}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{+140} & = & \color{red}{567x} +27 \\\Leftrightarrow & -1260x \color{red}{+140} \color{blue}{-140} \color{blue}{-567x} & = & \color{red}{567x} +27 \color{blue}{-567x} \color{blue}{-140} \\\Leftrightarrow & -1260x-567x& = & 27-140 \\\Leftrightarrow & \color{red}{-1827} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{-1827} & & \\\Leftrightarrow & x = \frac{113}{1827} & & \\ & V = \left\{ \frac{113}{1827} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{2}{7})& = & -4x+\frac{9}{2} \\\Leftrightarrow & -15x+\frac{6}{7}& = & -4x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-210}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{-56}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -210x \color{red}{+12} & = & \color{red}{-56x} +63 \\\Leftrightarrow & -210x \color{red}{+12} \color{blue}{-12} \color{blue}{+56x} & = & \color{red}{-56x} +63 \color{blue}{+56x} \color{blue}{-12} \\\Leftrightarrow & -210x+56x& = & 63-12 \\\Leftrightarrow & \color{red}{-154} x& = & 51 \\\Leftrightarrow & x = \frac{51}{-154} & & \\\Leftrightarrow & x = \frac{-51}{154} & & \\ & V = \left\{ \frac{-51}{154} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{4}{11})& = & 3x+\frac{6}{5} \\\Leftrightarrow & -8x+\frac{16}{11}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x+ \frac{80}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{+80} & = & \color{red}{165x} +66 \\\Leftrightarrow & -440x \color{red}{+80} \color{blue}{-80} \color{blue}{-165x} & = & \color{red}{165x} +66 \color{blue}{-165x} \color{blue}{-80} \\\Leftrightarrow & -440x-165x& = & 66-80 \\\Leftrightarrow & \color{red}{-605} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-605} & & \\\Leftrightarrow & x = \frac{14}{605} & & \\ & V = \left\{ \frac{14}{605} \right\} & \\\end{align}\)
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