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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -24x+\frac{18}{11}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1056}{ \color{blue}{44} }x+ \frac{72}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1056x \color{red}{+72} & = & \color{red}{-308x} +33 \\\Leftrightarrow & -1056x \color{red}{+72} \color{blue}{-72} \color{blue}{+308x} & = & \color{red}{-308x} +33 \color{blue}{+308x} \color{blue}{-72} \\\Leftrightarrow & -1056x+308x& = & 33-72 \\\Leftrightarrow & \color{red}{-748} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{-748} & & \\\Leftrightarrow & x = \frac{39}{748} & & \\ & V = \left\{ \frac{39}{748} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{4}{9})& = & 3x+\frac{10}{9} \\\Leftrightarrow & 35x+\frac{28}{9}& = & 3x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{315}{ \color{blue}{9} }x+ \frac{28}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 315x \color{red}{+28} & = & \color{red}{27x} +10 \\\Leftrightarrow & 315x \color{red}{+28} \color{blue}{-28} \color{blue}{-27x} & = & \color{red}{27x} +10 \color{blue}{-27x} \color{blue}{-28} \\\Leftrightarrow & 315x-27x& = & 10-28 \\\Leftrightarrow & \color{red}{288} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{288} & & \\\Leftrightarrow & x = \frac{-1}{16} & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{4}{5})& = & -7x+\frac{3}{5} \\\Leftrightarrow & -9x+\frac{12}{5}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-45}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -45x \color{red}{+12} & = & \color{red}{-35x} +3 \\\Leftrightarrow & -45x \color{red}{+12} \color{blue}{-12} \color{blue}{+35x} & = & \color{red}{-35x} +3 \color{blue}{+35x} \color{blue}{-12} \\\Leftrightarrow & -45x+35x& = & 3-12 \\\Leftrightarrow & \color{red}{-10} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-10} & & \\\Leftrightarrow & x = \frac{9}{10} & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{5}{7})& = & 3x+\frac{7}{11} \\\Leftrightarrow & 8x+\frac{10}{7}& = & 3x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{+110} & = & \color{red}{231x} +49 \\\Leftrightarrow & 616x \color{red}{+110} \color{blue}{-110} \color{blue}{-231x} & = & \color{red}{231x} +49 \color{blue}{-231x} \color{blue}{-110} \\\Leftrightarrow & 616x-231x& = & 49-110 \\\Leftrightarrow & \color{red}{385} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{385} & & \\ & V = \left\{ \frac{-61}{385} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{3}{7})& = & -9x+\frac{10}{7} \\\Leftrightarrow & -20x+\frac{15}{7}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-140}{ \color{blue}{7} }x+ \frac{15}{ \color{blue}{7} })& = & (\frac{-63}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -140x \color{red}{+15} & = & \color{red}{-63x} +10 \\\Leftrightarrow & -140x \color{red}{+15} \color{blue}{-15} \color{blue}{+63x} & = & \color{red}{-63x} +10 \color{blue}{+63x} \color{blue}{-15} \\\Leftrightarrow & -140x+63x& = & 10-15 \\\Leftrightarrow & \color{red}{-77} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-77} & & \\\Leftrightarrow & x = \frac{5}{77} & & \\ & V = \left\{ \frac{5}{77} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{11})& = & 9x+\frac{9}{10} \\\Leftrightarrow & 20x+\frac{20}{11}& = & 9x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{2200}{ \color{blue}{110} }x+ \frac{200}{ \color{blue}{110} })& = & (\frac{990}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 2200x \color{red}{+200} & = & \color{red}{990x} +99 \\\Leftrightarrow & 2200x \color{red}{+200} \color{blue}{-200} \color{blue}{-990x} & = & \color{red}{990x} +99 \color{blue}{-990x} \color{blue}{-200} \\\Leftrightarrow & 2200x-990x& = & 99-200 \\\Leftrightarrow & \color{red}{1210} x& = & -101 \\\Leftrightarrow & x = \frac{-101}{1210} & & \\ & V = \left\{ \frac{-101}{1210} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{2}{5})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -24x+\frac{12}{5}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1080}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1080x \color{red}{+108} & = & \color{red}{-315x} +50 \\\Leftrightarrow & -1080x \color{red}{+108} \color{blue}{-108} \color{blue}{+315x} & = & \color{red}{-315x} +50 \color{blue}{+315x} \color{blue}{-108} \\\Leftrightarrow & -1080x+315x& = & 50-108 \\\Leftrightarrow & \color{red}{-765} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{-765} & & \\\Leftrightarrow & x = \frac{58}{765} & & \\ & V = \left\{ \frac{58}{765} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{5}{8})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -28x+\frac{35}{8}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1120}{ \color{blue}{40} }x+ \frac{175}{ \color{blue}{40} })& = & (\frac{360}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1120x \color{red}{+175} & = & \color{red}{360x} +48 \\\Leftrightarrow & -1120x \color{red}{+175} \color{blue}{-175} \color{blue}{-360x} & = & \color{red}{360x} +48 \color{blue}{-360x} \color{blue}{-175} \\\Leftrightarrow & -1120x-360x& = & 48-175 \\\Leftrightarrow & \color{red}{-1480} x& = & -127 \\\Leftrightarrow & x = \frac{-127}{-1480} & & \\\Leftrightarrow & x = \frac{127}{1480} & & \\ & V = \left\{ \frac{127}{1480} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{3})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 16x+\frac{8}{3}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{48}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 48x \color{red}{+8} & = & \color{red}{9x} +4 \\\Leftrightarrow & 48x \color{red}{+8} \color{blue}{-8} \color{blue}{-9x} & = & \color{red}{9x} +4 \color{blue}{-9x} \color{blue}{-8} \\\Leftrightarrow & 48x-9x& = & 4-8 \\\Leftrightarrow & \color{red}{39} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{39} & & \\ & V = \left\{ \frac{-4}{39} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{4})& = & -4x+\frac{10}{11} \\\Leftrightarrow & -28x+\frac{21}{4}& = & -4x+\frac{10}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1232}{ \color{blue}{44} }x+ \frac{231}{ \color{blue}{44} })& = & (\frac{-176}{ \color{blue}{44} }x+ \frac{40}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1232x \color{red}{+231} & = & \color{red}{-176x} +40 \\\Leftrightarrow & -1232x \color{red}{+231} \color{blue}{-231} \color{blue}{+176x} & = & \color{red}{-176x} +40 \color{blue}{+176x} \color{blue}{-231} \\\Leftrightarrow & -1232x+176x& = & 40-231 \\\Leftrightarrow & \color{red}{-1056} x& = & -191 \\\Leftrightarrow & x = \frac{-191}{-1056} & & \\\Leftrightarrow & x = \frac{191}{1056} & & \\ & V = \left\{ \frac{191}{1056} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{3}{5})& = & 7x+\frac{8}{11} \\\Leftrightarrow & 30x-\frac{18}{5}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x- \frac{198}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{-198} & = & \color{red}{385x} +40 \\\Leftrightarrow & 1650x \color{red}{-198} \color{blue}{+198} \color{blue}{-385x} & = & \color{red}{385x} +40 \color{blue}{-385x} \color{blue}{+198} \\\Leftrightarrow & 1650x-385x& = & 40+198 \\\Leftrightarrow & \color{red}{1265} x& = & 238 \\\Leftrightarrow & x = \frac{238}{1265} & & \\ & V = \left\{ \frac{238}{1265} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{5}{11})& = & -8x+\frac{7}{10} \\\Leftrightarrow & -15x-\frac{25}{11}& = & -8x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1650}{ \color{blue}{110} }x- \frac{250}{ \color{blue}{110} })& = & (\frac{-880}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1650x \color{red}{-250} & = & \color{red}{-880x} +77 \\\Leftrightarrow & -1650x \color{red}{-250} \color{blue}{+250} \color{blue}{+880x} & = & \color{red}{-880x} +77 \color{blue}{+880x} \color{blue}{+250} \\\Leftrightarrow & -1650x+880x& = & 77+250 \\\Leftrightarrow & \color{red}{-770} x& = & 327 \\\Leftrightarrow & x = \frac{327}{-770} & & \\\Leftrightarrow & x = \frac{-327}{770} & & \\ & V = \left\{ \frac{-327}{770} \right\} & \\\end{align}\)
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