Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{2}{9})& = & 9x+\frac{7}{5} \\\Leftrightarrow & -25x+\frac{10}{9}& = & 9x+\frac{7}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1125}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{63}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1125x \color{red}{+50} & = & \color{red}{405x} +63 \\\Leftrightarrow & -1125x \color{red}{+50} \color{blue}{-50} \color{blue}{-405x} & = & \color{red}{405x} +63 \color{blue}{-405x} \color{blue}{-50} \\\Leftrightarrow & -1125x-405x& = & 63-50 \\\Leftrightarrow & \color{red}{-1530} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-1530} & & \\\Leftrightarrow & x = \frac{-13}{1530} & & \\ & V = \left\{ \frac{-13}{1530} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{3}{8})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -25x-\frac{15}{8}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-200}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{56}{ \color{blue}{8} }x+ \frac{28}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -200x \color{red}{-15} & = & \color{red}{56x} +28 \\\Leftrightarrow & -200x \color{red}{-15} \color{blue}{+15} \color{blue}{-56x} & = & \color{red}{56x} +28 \color{blue}{-56x} \color{blue}{+15} \\\Leftrightarrow & -200x-56x& = & 28+15 \\\Leftrightarrow & \color{red}{-256} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-256} & & \\\Leftrightarrow & x = \frac{-43}{256} & & \\ & V = \left\{ \frac{-43}{256} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{4}{11})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 12x-\frac{24}{11}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1188}{ \color{blue}{99} }x- \frac{216}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1188x \color{red}{-216} & = & \color{red}{-495x} +88 \\\Leftrightarrow & 1188x \color{red}{-216} \color{blue}{+216} \color{blue}{+495x} & = & \color{red}{-495x} +88 \color{blue}{+495x} \color{blue}{+216} \\\Leftrightarrow & 1188x+495x& = & 88+216 \\\Leftrightarrow & \color{red}{1683} x& = & 304 \\\Leftrightarrow & x = \frac{304}{1683} & & \\ & V = \left\{ \frac{304}{1683} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & 9x+\frac{4}{3} \\\Leftrightarrow & -28x+\frac{21}{8}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-672}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{216}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -672x \color{red}{+63} & = & \color{red}{216x} +32 \\\Leftrightarrow & -672x \color{red}{+63} \color{blue}{-63} \color{blue}{-216x} & = & \color{red}{216x} +32 \color{blue}{-216x} \color{blue}{-63} \\\Leftrightarrow & -672x-216x& = & 32-63 \\\Leftrightarrow & \color{red}{-888} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-888} & & \\\Leftrightarrow & x = \frac{31}{888} & & \\ & V = \left\{ \frac{31}{888} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{2}{5})& = & -2x+\frac{3}{7} \\\Leftrightarrow & -18x-\frac{12}{5}& = & -2x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-70}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{-84} & = & \color{red}{-70x} +15 \\\Leftrightarrow & -630x \color{red}{-84} \color{blue}{+84} \color{blue}{+70x} & = & \color{red}{-70x} +15 \color{blue}{+70x} \color{blue}{+84} \\\Leftrightarrow & -630x+70x& = & 15+84 \\\Leftrightarrow & \color{red}{-560} x& = & 99 \\\Leftrightarrow & x = \frac{99}{-560} & & \\\Leftrightarrow & x = \frac{-99}{560} & & \\ & V = \left\{ \frac{-99}{560} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{2}{3})& = & -3x+\frac{3}{8} \\\Leftrightarrow & -35x-\frac{14}{3}& = & -3x+\frac{3}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-840}{ \color{blue}{24} }x- \frac{112}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{9}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -840x \color{red}{-112} & = & \color{red}{-72x} +9 \\\Leftrightarrow & -840x \color{red}{-112} \color{blue}{+112} \color{blue}{+72x} & = & \color{red}{-72x} +9 \color{blue}{+72x} \color{blue}{+112} \\\Leftrightarrow & -840x+72x& = & 9+112 \\\Leftrightarrow & \color{red}{-768} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-768} & & \\\Leftrightarrow & x = \frac{-121}{768} & & \\ & V = \left\{ \frac{-121}{768} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{5}{11})& = & 2x+\frac{10}{11} \\\Leftrightarrow & 15x-\frac{25}{11}& = & 2x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{165}{ \color{blue}{11} }x- \frac{25}{ \color{blue}{11} })& = & (\frac{22}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 165x \color{red}{-25} & = & \color{red}{22x} +10 \\\Leftrightarrow & 165x \color{red}{-25} \color{blue}{+25} \color{blue}{-22x} & = & \color{red}{22x} +10 \color{blue}{-22x} \color{blue}{+25} \\\Leftrightarrow & 165x-22x& = & 10+25 \\\Leftrightarrow & \color{red}{143} x& = & 35 \\\Leftrightarrow & x = \frac{35}{143} & & \\ & V = \left\{ \frac{35}{143} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{2}{5})& = & 3x+\frac{8}{3} \\\Leftrightarrow & 10x-\frac{4}{5}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{150}{ \color{blue}{15} }x- \frac{12}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 150x \color{red}{-12} & = & \color{red}{45x} +40 \\\Leftrightarrow & 150x \color{red}{-12} \color{blue}{+12} \color{blue}{-45x} & = & \color{red}{45x} +40 \color{blue}{-45x} \color{blue}{+12} \\\Leftrightarrow & 150x-45x& = & 40+12 \\\Leftrightarrow & \color{red}{105} x& = & 52 \\\Leftrightarrow & x = \frac{52}{105} & & \\ & V = \left\{ \frac{52}{105} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{3}{7})& = & -2x+\frac{9}{10} \\\Leftrightarrow & -25x-\frac{15}{7}& = & -2x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1750}{ \color{blue}{70} }x- \frac{150}{ \color{blue}{70} })& = & (\frac{-140}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1750x \color{red}{-150} & = & \color{red}{-140x} +63 \\\Leftrightarrow & -1750x \color{red}{-150} \color{blue}{+150} \color{blue}{+140x} & = & \color{red}{-140x} +63 \color{blue}{+140x} \color{blue}{+150} \\\Leftrightarrow & -1750x+140x& = & 63+150 \\\Leftrightarrow & \color{red}{-1610} x& = & 213 \\\Leftrightarrow & x = \frac{213}{-1610} & & \\\Leftrightarrow & x = \frac{-213}{1610} & & \\ & V = \left\{ \frac{-213}{1610} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{4}{9})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -25x-\frac{20}{9}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-450}{ \color{blue}{18} }x- \frac{40}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -450x \color{red}{-40} & = & \color{red}{126x} +81 \\\Leftrightarrow & -450x \color{red}{-40} \color{blue}{+40} \color{blue}{-126x} & = & \color{red}{126x} +81 \color{blue}{-126x} \color{blue}{+40} \\\Leftrightarrow & -450x-126x& = & 81+40 \\\Leftrightarrow & \color{red}{-576} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-576} & & \\\Leftrightarrow & x = \frac{-121}{576} & & \\ & V = \left\{ \frac{-121}{576} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{3}{11})& = & 3x+\frac{4}{9} \\\Leftrightarrow & -8x-\frac{12}{11}& = & 3x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-792}{ \color{blue}{99} }x- \frac{108}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -792x \color{red}{-108} & = & \color{red}{297x} +44 \\\Leftrightarrow & -792x \color{red}{-108} \color{blue}{+108} \color{blue}{-297x} & = & \color{red}{297x} +44 \color{blue}{-297x} \color{blue}{+108} \\\Leftrightarrow & -792x-297x& = & 44+108 \\\Leftrightarrow & \color{red}{-1089} x& = & 152 \\\Leftrightarrow & x = \frac{152}{-1089} & & \\\Leftrightarrow & x = \frac{-152}{1089} & & \\ & V = \left\{ \frac{-152}{1089} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{4}{7})& = & 3x+\frac{5}{11} \\\Leftrightarrow & -20x+\frac{16}{7}& = & 3x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x+ \frac{176}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{+176} & = & \color{red}{231x} +35 \\\Leftrightarrow & -1540x \color{red}{+176} \color{blue}{-176} \color{blue}{-231x} & = & \color{red}{231x} +35 \color{blue}{-231x} \color{blue}{-176} \\\Leftrightarrow & -1540x-231x& = & 35-176 \\\Leftrightarrow & \color{red}{-1771} x& = & -141 \\\Leftrightarrow & x = \frac{-141}{-1771} & & \\\Leftrightarrow & x = \frac{141}{1771} & & \\ & V = \left\{ \frac{141}{1771} \right\} & \\\end{align}\)
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