Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{2}{3})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -10x-\frac{10}{3}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{70}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-70} & = & \color{red}{-147x} +30 \\\Leftrightarrow & -210x \color{red}{-70} \color{blue}{+70} \color{blue}{+147x} & = & \color{red}{-147x} +30 \color{blue}{+147x} \color{blue}{+70} \\\Leftrightarrow & -210x+147x& = & 30+70 \\\Leftrightarrow & \color{red}{-63} x& = & 100 \\\Leftrightarrow & x = \frac{100}{-63} & & \\\Leftrightarrow & x = \frac{-100}{63} & & \\ & V = \left\{ \frac{-100}{63} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{2}{3})& = & -3x+\frac{2}{7} \\\Leftrightarrow & 20x-\frac{8}{3}& = & -3x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{-56} & = & \color{red}{-63x} +6 \\\Leftrightarrow & 420x \color{red}{-56} \color{blue}{+56} \color{blue}{+63x} & = & \color{red}{-63x} +6 \color{blue}{+63x} \color{blue}{+56} \\\Leftrightarrow & 420x+63x& = & 6+56 \\\Leftrightarrow & \color{red}{483} x& = & 62 \\\Leftrightarrow & x = \frac{62}{483} & & \\ & V = \left\{ \frac{62}{483} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{3}{5})& = & 5x+\frac{9}{4} \\\Leftrightarrow & 12x-\frac{18}{5}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{240}{ \color{blue}{20} }x- \frac{72}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 240x \color{red}{-72} & = & \color{red}{100x} +45 \\\Leftrightarrow & 240x \color{red}{-72} \color{blue}{+72} \color{blue}{-100x} & = & \color{red}{100x} +45 \color{blue}{-100x} \color{blue}{+72} \\\Leftrightarrow & 240x-100x& = & 45+72 \\\Leftrightarrow & \color{red}{140} x& = & 117 \\\Leftrightarrow & x = \frac{117}{140} & & \\ & V = \left\{ \frac{117}{140} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{2}{3})& = & -3x+\frac{9}{2} \\\Leftrightarrow & 16x-\frac{8}{3}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{96}{ \color{blue}{6} }x- \frac{16}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 96x \color{red}{-16} & = & \color{red}{-18x} +27 \\\Leftrightarrow & 96x \color{red}{-16} \color{blue}{+16} \color{blue}{+18x} & = & \color{red}{-18x} +27 \color{blue}{+18x} \color{blue}{+16} \\\Leftrightarrow & 96x+18x& = & 27+16 \\\Leftrightarrow & \color{red}{114} x& = & 43 \\\Leftrightarrow & x = \frac{43}{114} & & \\ & V = \left\{ \frac{43}{114} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{12})& = & 9x+\frac{3}{7} \\\Leftrightarrow & 14x-\frac{35}{12}& = & 9x+\frac{3}{7} \\ & & & \text{kgv van noemers 12 en 7 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{1176}{ \color{blue}{84} }x- \frac{245}{ \color{blue}{84} })& = & (\frac{756}{ \color{blue}{84} }x+ \frac{36}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 1176x \color{red}{-245} & = & \color{red}{756x} +36 \\\Leftrightarrow & 1176x \color{red}{-245} \color{blue}{+245} \color{blue}{-756x} & = & \color{red}{756x} +36 \color{blue}{-756x} \color{blue}{+245} \\\Leftrightarrow & 1176x-756x& = & 36+245 \\\Leftrightarrow & \color{red}{420} x& = & 281 \\\Leftrightarrow & x = \frac{281}{420} & & \\ & V = \left\{ \frac{281}{420} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{4}{7})& = & 9x+\frac{9}{10} \\\Leftrightarrow & 20x+\frac{20}{7}& = & 9x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1400}{ \color{blue}{70} }x+ \frac{200}{ \color{blue}{70} })& = & (\frac{630}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1400x \color{red}{+200} & = & \color{red}{630x} +63 \\\Leftrightarrow & 1400x \color{red}{+200} \color{blue}{-200} \color{blue}{-630x} & = & \color{red}{630x} +63 \color{blue}{-630x} \color{blue}{-200} \\\Leftrightarrow & 1400x-630x& = & 63-200 \\\Leftrightarrow & \color{red}{770} x& = & -137 \\\Leftrightarrow & x = \frac{-137}{770} & & \\ & V = \left\{ \frac{-137}{770} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{2}{5})& = & -4x+\frac{6}{11} \\\Leftrightarrow & 9x+\frac{6}{5}& = & -4x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{495}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{-220}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 495x \color{red}{+66} & = & \color{red}{-220x} +30 \\\Leftrightarrow & 495x \color{red}{+66} \color{blue}{-66} \color{blue}{+220x} & = & \color{red}{-220x} +30 \color{blue}{+220x} \color{blue}{-66} \\\Leftrightarrow & 495x+220x& = & 30-66 \\\Leftrightarrow & \color{red}{715} x& = & -36 \\\Leftrightarrow & x = \frac{-36}{715} & & \\ & V = \left\{ \frac{-36}{715} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{3}{5})& = & -9x+\frac{9}{8} \\\Leftrightarrow & -8x-\frac{12}{5}& = & -9x+\frac{9}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-320}{ \color{blue}{40} }x- \frac{96}{ \color{blue}{40} })& = & (\frac{-360}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -320x \color{red}{-96} & = & \color{red}{-360x} +45 \\\Leftrightarrow & -320x \color{red}{-96} \color{blue}{+96} \color{blue}{+360x} & = & \color{red}{-360x} +45 \color{blue}{+360x} \color{blue}{+96} \\\Leftrightarrow & -320x+360x& = & 45+96 \\\Leftrightarrow & \color{red}{40} x& = & 141 \\\Leftrightarrow & x = \frac{141}{40} & & \\ & V = \left\{ \frac{141}{40} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{4}{9})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 20x-\frac{16}{9}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x- \frac{16}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{-16} & = & \color{red}{-63x} +6 \\\Leftrightarrow & 180x \color{red}{-16} \color{blue}{+16} \color{blue}{+63x} & = & \color{red}{-63x} +6 \color{blue}{+63x} \color{blue}{+16} \\\Leftrightarrow & 180x+63x& = & 6+16 \\\Leftrightarrow & \color{red}{243} x& = & 22 \\\Leftrightarrow & x = \frac{22}{243} & & \\ & V = \left\{ \frac{22}{243} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{5}{7})& = & 7x+\frac{5}{11} \\\Leftrightarrow & -16x-\frac{20}{7}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1232}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{-220} & = & \color{red}{539x} +35 \\\Leftrightarrow & -1232x \color{red}{-220} \color{blue}{+220} \color{blue}{-539x} & = & \color{red}{539x} +35 \color{blue}{-539x} \color{blue}{+220} \\\Leftrightarrow & -1232x-539x& = & 35+220 \\\Leftrightarrow & \color{red}{-1771} x& = & 255 \\\Leftrightarrow & x = \frac{255}{-1771} & & \\\Leftrightarrow & x = \frac{-255}{1771} & & \\ & V = \left\{ \frac{-255}{1771} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{3}{11})& = & -9x+\frac{4}{3} \\\Leftrightarrow & -8x-\frac{12}{11}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x- \frac{36}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{-36} & = & \color{red}{-297x} +44 \\\Leftrightarrow & -264x \color{red}{-36} \color{blue}{+36} \color{blue}{+297x} & = & \color{red}{-297x} +44 \color{blue}{+297x} \color{blue}{+36} \\\Leftrightarrow & -264x+297x& = & 44+36 \\\Leftrightarrow & \color{red}{33} x& = & 80 \\\Leftrightarrow & x = \frac{80}{33} & & \\ & V = \left\{ \frac{80}{33} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{5}{7})& = & -4x+\frac{8}{5} \\\Leftrightarrow & -18x-\frac{30}{7}& = & -4x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{-140}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{-150} & = & \color{red}{-140x} +56 \\\Leftrightarrow & -630x \color{red}{-150} \color{blue}{+150} \color{blue}{+140x} & = & \color{red}{-140x} +56 \color{blue}{+140x} \color{blue}{+150} \\\Leftrightarrow & -630x+140x& = & 56+150 \\\Leftrightarrow & \color{red}{-490} x& = & 206 \\\Leftrightarrow & x = \frac{206}{-490} & & \\\Leftrightarrow & x = \frac{-103}{245} & & \\ & V = \left\{ \frac{-103}{245} \right\} & \\\end{align}\)
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