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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{5}{11})& = & -8x+\frac{9}{7} \\\Leftrightarrow & -21x-\frac{35}{11}& = & -8x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1617}{ \color{blue}{77} }x- \frac{245}{ \color{blue}{77} })& = & (\frac{-616}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1617x \color{red}{-245} & = & \color{red}{-616x} +99 \\\Leftrightarrow & -1617x \color{red}{-245} \color{blue}{+245} \color{blue}{+616x} & = & \color{red}{-616x} +99 \color{blue}{+616x} \color{blue}{+245} \\\Leftrightarrow & -1617x+616x& = & 99+245 \\\Leftrightarrow & \color{red}{-1001} x& = & 344 \\\Leftrightarrow & x = \frac{344}{-1001} & & \\\Leftrightarrow & x = \frac{-344}{1001} & & \\ & V = \left\{ \frac{-344}{1001} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{2}{5})& = & 7x+\frac{9}{4} \\\Leftrightarrow & 30x-\frac{12}{5}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{600}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 600x \color{red}{-48} & = & \color{red}{140x} +45 \\\Leftrightarrow & 600x \color{red}{-48} \color{blue}{+48} \color{blue}{-140x} & = & \color{red}{140x} +45 \color{blue}{-140x} \color{blue}{+48} \\\Leftrightarrow & 600x-140x& = & 45+48 \\\Leftrightarrow & \color{red}{460} x& = & 93 \\\Leftrightarrow & x = \frac{93}{460} & & \\ & V = \left\{ \frac{93}{460} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{3})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 16x+\frac{8}{3}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{240}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 240x \color{red}{+40} & = & \color{red}{45x} +18 \\\Leftrightarrow & 240x \color{red}{+40} \color{blue}{-40} \color{blue}{-45x} & = & \color{red}{45x} +18 \color{blue}{-45x} \color{blue}{-40} \\\Leftrightarrow & 240x-45x& = & 18-40 \\\Leftrightarrow & \color{red}{195} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{195} & & \\ & V = \left\{ \frac{-22}{195} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{4}{9})& = & -8x+\frac{7}{9} \\\Leftrightarrow & -21x+\frac{28}{9}& = & -8x+\frac{7}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-189}{ \color{blue}{9} }x+ \frac{28}{ \color{blue}{9} })& = & (\frac{-72}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -189x \color{red}{+28} & = & \color{red}{-72x} +7 \\\Leftrightarrow & -189x \color{red}{+28} \color{blue}{-28} \color{blue}{+72x} & = & \color{red}{-72x} +7 \color{blue}{+72x} \color{blue}{-28} \\\Leftrightarrow & -189x+72x& = & 7-28 \\\Leftrightarrow & \color{red}{-117} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-117} & & \\\Leftrightarrow & x = \frac{7}{39} & & \\ & V = \left\{ \frac{7}{39} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{4}{11})& = & -7x+\frac{3}{11} \\\Leftrightarrow & 12x+\frac{24}{11}& = & -7x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x+ \frac{24}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{+24} & = & \color{red}{-77x} +3 \\\Leftrightarrow & 132x \color{red}{+24} \color{blue}{-24} \color{blue}{+77x} & = & \color{red}{-77x} +3 \color{blue}{+77x} \color{blue}{-24} \\\Leftrightarrow & 132x+77x& = & 3-24 \\\Leftrightarrow & \color{red}{209} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{209} & & \\ & V = \left\{ \frac{-21}{209} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{3}{11})& = & -5x+\frac{7}{6} \\\Leftrightarrow & 24x-\frac{18}{11}& = & -5x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{1584}{ \color{blue}{66} }x- \frac{108}{ \color{blue}{66} })& = & (\frac{-330}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 1584x \color{red}{-108} & = & \color{red}{-330x} +77 \\\Leftrightarrow & 1584x \color{red}{-108} \color{blue}{+108} \color{blue}{+330x} & = & \color{red}{-330x} +77 \color{blue}{+330x} \color{blue}{+108} \\\Leftrightarrow & 1584x+330x& = & 77+108 \\\Leftrightarrow & \color{red}{1914} x& = & 185 \\\Leftrightarrow & x = \frac{185}{1914} & & \\ & V = \left\{ \frac{185}{1914} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & -7x+\frac{8}{11} \\\Leftrightarrow & 15x-\frac{6}{7}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{-66} & = & \color{red}{-539x} +56 \\\Leftrightarrow & 1155x \color{red}{-66} \color{blue}{+66} \color{blue}{+539x} & = & \color{red}{-539x} +56 \color{blue}{+539x} \color{blue}{+66} \\\Leftrightarrow & 1155x+539x& = & 56+66 \\\Leftrightarrow & \color{red}{1694} x& = & 122 \\\Leftrightarrow & x = \frac{122}{1694} & & \\\Leftrightarrow & x = \frac{61}{847} & & \\ & V = \left\{ \frac{61}{847} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{3}{5})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -12x-\frac{9}{5}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{27}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-27} & = & \color{red}{-75x} +20 \\\Leftrightarrow & -180x \color{red}{-27} \color{blue}{+27} \color{blue}{+75x} & = & \color{red}{-75x} +20 \color{blue}{+75x} \color{blue}{+27} \\\Leftrightarrow & -180x+75x& = & 20+27 \\\Leftrightarrow & \color{red}{-105} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-105} & & \\\Leftrightarrow & x = \frac{-47}{105} & & \\ & V = \left\{ \frac{-47}{105} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{4}{9})& = & -8x+\frac{6}{5} \\\Leftrightarrow & -15x+\frac{20}{9}& = & -8x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-675}{ \color{blue}{45} }x+ \frac{100}{ \color{blue}{45} })& = & (\frac{-360}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -675x \color{red}{+100} & = & \color{red}{-360x} +54 \\\Leftrightarrow & -675x \color{red}{+100} \color{blue}{-100} \color{blue}{+360x} & = & \color{red}{-360x} +54 \color{blue}{+360x} \color{blue}{-100} \\\Leftrightarrow & -675x+360x& = & 54-100 \\\Leftrightarrow & \color{red}{-315} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{-315} & & \\\Leftrightarrow & x = \frac{46}{315} & & \\ & V = \left\{ \frac{46}{315} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{3}{11})& = & -4x+\frac{7}{9} \\\Leftrightarrow & -25x-\frac{15}{11}& = & -4x+\frac{7}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2475}{ \color{blue}{99} }x- \frac{135}{ \color{blue}{99} })& = & (\frac{-396}{ \color{blue}{99} }x+ \frac{77}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2475x \color{red}{-135} & = & \color{red}{-396x} +77 \\\Leftrightarrow & -2475x \color{red}{-135} \color{blue}{+135} \color{blue}{+396x} & = & \color{red}{-396x} +77 \color{blue}{+396x} \color{blue}{+135} \\\Leftrightarrow & -2475x+396x& = & 77+135 \\\Leftrightarrow & \color{red}{-2079} x& = & 212 \\\Leftrightarrow & x = \frac{212}{-2079} & & \\\Leftrightarrow & x = \frac{-212}{2079} & & \\ & V = \left\{ \frac{-212}{2079} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{7})& = & 5x+\frac{9}{10} \\\Leftrightarrow & -12x-\frac{20}{7}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-840}{ \color{blue}{70} }x- \frac{200}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -840x \color{red}{-200} & = & \color{red}{350x} +63 \\\Leftrightarrow & -840x \color{red}{-200} \color{blue}{+200} \color{blue}{-350x} & = & \color{red}{350x} +63 \color{blue}{-350x} \color{blue}{+200} \\\Leftrightarrow & -840x-350x& = & 63+200 \\\Leftrightarrow & \color{red}{-1190} x& = & 263 \\\Leftrightarrow & x = \frac{263}{-1190} & & \\\Leftrightarrow & x = \frac{-263}{1190} & & \\ & V = \left\{ \frac{-263}{1190} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{2}{9})& = & -7x+\frac{7}{4} \\\Leftrightarrow & -6x-\frac{4}{9}& = & -7x+\frac{7}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-216}{ \color{blue}{36} }x- \frac{16}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{63}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -216x \color{red}{-16} & = & \color{red}{-252x} +63 \\\Leftrightarrow & -216x \color{red}{-16} \color{blue}{+16} \color{blue}{+252x} & = & \color{red}{-252x} +63 \color{blue}{+252x} \color{blue}{+16} \\\Leftrightarrow & -216x+252x& = & 63+16 \\\Leftrightarrow & \color{red}{36} x& = & 79 \\\Leftrightarrow & x = \frac{79}{36} & & \\ & V = \left\{ \frac{79}{36} \right\} & \\\end{align}\)
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