Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{2}{11})& = & 5x+\frac{9}{10} \\\Leftrightarrow & 12x+\frac{12}{11}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1320}{ \color{blue}{110} }x+ \frac{120}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1320x \color{red}{+120} & = & \color{red}{550x} +99 \\\Leftrightarrow & 1320x \color{red}{+120} \color{blue}{-120} \color{blue}{-550x} & = & \color{red}{550x} +99 \color{blue}{-550x} \color{blue}{-120} \\\Leftrightarrow & 1320x-550x& = & 99-120 \\\Leftrightarrow & \color{red}{770} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{770} & & \\\Leftrightarrow & x = \frac{-3}{110} & & \\ & V = \left\{ \frac{-3}{110} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{2}{5})& = & 5x+\frac{5}{2} \\\Leftrightarrow & -12x-\frac{6}{5}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{-12} & = & \color{red}{50x} +25 \\\Leftrightarrow & -120x \color{red}{-12} \color{blue}{+12} \color{blue}{-50x} & = & \color{red}{50x} +25 \color{blue}{-50x} \color{blue}{+12} \\\Leftrightarrow & -120x-50x& = & 25+12 \\\Leftrightarrow & \color{red}{-170} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-170} & & \\\Leftrightarrow & x = \frac{-37}{170} & & \\ & V = \left\{ \frac{-37}{170} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{4}{9})& = & -8x+\frac{2}{3} \\\Leftrightarrow & -15x-\frac{20}{9}& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-135}{ \color{blue}{9} }x- \frac{20}{ \color{blue}{9} })& = & (\frac{-72}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -135x \color{red}{-20} & = & \color{red}{-72x} +6 \\\Leftrightarrow & -135x \color{red}{-20} \color{blue}{+20} \color{blue}{+72x} & = & \color{red}{-72x} +6 \color{blue}{+72x} \color{blue}{+20} \\\Leftrightarrow & -135x+72x& = & 6+20 \\\Leftrightarrow & \color{red}{-63} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-63} & & \\\Leftrightarrow & x = \frac{-26}{63} & & \\ & V = \left\{ \frac{-26}{63} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{4}{7})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 16x-\frac{16}{7}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{672}{ \color{blue}{42} }x- \frac{96}{ \color{blue}{42} })& = & (\frac{-210}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 672x \color{red}{-96} & = & \color{red}{-210x} +35 \\\Leftrightarrow & 672x \color{red}{-96} \color{blue}{+96} \color{blue}{+210x} & = & \color{red}{-210x} +35 \color{blue}{+210x} \color{blue}{+96} \\\Leftrightarrow & 672x+210x& = & 35+96 \\\Leftrightarrow & \color{red}{882} x& = & 131 \\\Leftrightarrow & x = \frac{131}{882} & & \\ & V = \left\{ \frac{131}{882} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{3}{11})& = & -7x+\frac{3}{5} \\\Leftrightarrow & 12x-\frac{12}{11}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-60} & = & \color{red}{-385x} +33 \\\Leftrightarrow & 660x \color{red}{-60} \color{blue}{+60} \color{blue}{+385x} & = & \color{red}{-385x} +33 \color{blue}{+385x} \color{blue}{+60} \\\Leftrightarrow & 660x+385x& = & 33+60 \\\Leftrightarrow & \color{red}{1045} x& = & 93 \\\Leftrightarrow & x = \frac{93}{1045} & & \\ & V = \left\{ \frac{93}{1045} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{2}{3})& = & -3x+\frac{8}{11} \\\Leftrightarrow & -14x-\frac{14}{3}& = & -3x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-462}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -462x \color{red}{-154} & = & \color{red}{-99x} +24 \\\Leftrightarrow & -462x \color{red}{-154} \color{blue}{+154} \color{blue}{+99x} & = & \color{red}{-99x} +24 \color{blue}{+99x} \color{blue}{+154} \\\Leftrightarrow & -462x+99x& = & 24+154 \\\Leftrightarrow & \color{red}{-363} x& = & 178 \\\Leftrightarrow & x = \frac{178}{-363} & & \\\Leftrightarrow & x = \frac{-178}{363} & & \\ & V = \left\{ \frac{-178}{363} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{2}{7})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{+18} & = & \color{red}{147x} +56 \\\Leftrightarrow & -126x \color{red}{+18} \color{blue}{-18} \color{blue}{-147x} & = & \color{red}{147x} +56 \color{blue}{-147x} \color{blue}{-18} \\\Leftrightarrow & -126x-147x& = & 56-18 \\\Leftrightarrow & \color{red}{-273} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-273} & & \\\Leftrightarrow & x = \frac{-38}{273} & & \\ & V = \left\{ \frac{-38}{273} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{5}{7})& = & 5x+\frac{4}{9} \\\Leftrightarrow & 24x+\frac{30}{7}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1512}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1512x \color{red}{+270} & = & \color{red}{315x} +28 \\\Leftrightarrow & 1512x \color{red}{+270} \color{blue}{-270} \color{blue}{-315x} & = & \color{red}{315x} +28 \color{blue}{-315x} \color{blue}{-270} \\\Leftrightarrow & 1512x-315x& = & 28-270 \\\Leftrightarrow & \color{red}{1197} x& = & -242 \\\Leftrightarrow & x = \frac{-242}{1197} & & \\ & V = \left\{ \frac{-242}{1197} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{2}{7})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -20x+\frac{10}{7}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{+110} & = & \color{red}{539x} +56 \\\Leftrightarrow & -1540x \color{red}{+110} \color{blue}{-110} \color{blue}{-539x} & = & \color{red}{539x} +56 \color{blue}{-539x} \color{blue}{-110} \\\Leftrightarrow & -1540x-539x& = & 56-110 \\\Leftrightarrow & \color{red}{-2079} x& = & -54 \\\Leftrightarrow & x = \frac{-54}{-2079} & & \\\Leftrightarrow & x = \frac{2}{77} & & \\ & V = \left\{ \frac{2}{77} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{3}{8})& = & 9x+\frac{5}{2} \\\Leftrightarrow & -35x-\frac{21}{8}& = & 9x+\frac{5}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-280}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{72}{ \color{blue}{8} }x+ \frac{20}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -280x \color{red}{-21} & = & \color{red}{72x} +20 \\\Leftrightarrow & -280x \color{red}{-21} \color{blue}{+21} \color{blue}{-72x} & = & \color{red}{72x} +20 \color{blue}{-72x} \color{blue}{+21} \\\Leftrightarrow & -280x-72x& = & 20+21 \\\Leftrightarrow & \color{red}{-352} x& = & 41 \\\Leftrightarrow & x = \frac{41}{-352} & & \\\Leftrightarrow & x = \frac{-41}{352} & & \\ & V = \left\{ \frac{-41}{352} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{4}{3})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 25x-\frac{20}{3}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{525}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 525x \color{red}{-140} & = & \color{red}{-147x} +30 \\\Leftrightarrow & 525x \color{red}{-140} \color{blue}{+140} \color{blue}{+147x} & = & \color{red}{-147x} +30 \color{blue}{+147x} \color{blue}{+140} \\\Leftrightarrow & 525x+147x& = & 30+140 \\\Leftrightarrow & \color{red}{672} x& = & 170 \\\Leftrightarrow & x = \frac{170}{672} & & \\\Leftrightarrow & x = \frac{85}{336} & & \\ & V = \left\{ \frac{85}{336} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{2}{3})& = & 9x+\frac{10}{3} \\\Leftrightarrow & -28x+\frac{14}{3}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-84}{ \color{blue}{3} }x+ \frac{14}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -84x \color{red}{+14} & = & \color{red}{27x} +10 \\\Leftrightarrow & -84x \color{red}{+14} \color{blue}{-14} \color{blue}{-27x} & = & \color{red}{27x} +10 \color{blue}{-27x} \color{blue}{-14} \\\Leftrightarrow & -84x-27x& = & 10-14 \\\Leftrightarrow & \color{red}{-111} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-111} & & \\\Leftrightarrow & x = \frac{4}{111} & & \\ & V = \left\{ \frac{4}{111} \right\} & \\\end{align}\)
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