Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{3}{5})& = & 9x+\frac{4}{3} \\\Leftrightarrow & -8x+\frac{6}{5}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{+18} & = & \color{red}{135x} +20 \\\Leftrightarrow & -120x \color{red}{+18} \color{blue}{-18} \color{blue}{-135x} & = & \color{red}{135x} +20 \color{blue}{-135x} \color{blue}{-18} \\\Leftrightarrow & -120x-135x& = & 20-18 \\\Leftrightarrow & \color{red}{-255} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-255} & & \\\Leftrightarrow & x = \frac{-2}{255} & & \\ & V = \left\{ \frac{-2}{255} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{5})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 6x-\frac{6}{5}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{42}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-42} & = & \color{red}{175x} +40 \\\Leftrightarrow & 210x \color{red}{-42} \color{blue}{+42} \color{blue}{-175x} & = & \color{red}{175x} +40 \color{blue}{-175x} \color{blue}{+42} \\\Leftrightarrow & 210x-175x& = & 40+42 \\\Leftrightarrow & \color{red}{35} x& = & 82 \\\Leftrightarrow & x = \frac{82}{35} & & \\ & V = \left\{ \frac{82}{35} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{2}{3})& = & -7x+\frac{7}{5} \\\Leftrightarrow & -10x-\frac{4}{3}& = & -7x+\frac{7}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x- \frac{20}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{21}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{-20} & = & \color{red}{-105x} +21 \\\Leftrightarrow & -150x \color{red}{-20} \color{blue}{+20} \color{blue}{+105x} & = & \color{red}{-105x} +21 \color{blue}{+105x} \color{blue}{+20} \\\Leftrightarrow & -150x+105x& = & 21+20 \\\Leftrightarrow & \color{red}{-45} x& = & 41 \\\Leftrightarrow & x = \frac{41}{-45} & & \\\Leftrightarrow & x = \frac{-41}{45} & & \\ & V = \left\{ \frac{-41}{45} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{5})& = & -3x+\frac{9}{2} \\\Leftrightarrow & 8x-\frac{4}{5}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{80}{ \color{blue}{10} }x- \frac{8}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 80x \color{red}{-8} & = & \color{red}{-30x} +45 \\\Leftrightarrow & 80x \color{red}{-8} \color{blue}{+8} \color{blue}{+30x} & = & \color{red}{-30x} +45 \color{blue}{+30x} \color{blue}{+8} \\\Leftrightarrow & 80x+30x& = & 45+8 \\\Leftrightarrow & \color{red}{110} x& = & 53 \\\Leftrightarrow & x = \frac{53}{110} & & \\ & V = \left\{ \frac{53}{110} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -28x+\frac{21}{8}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-672}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -672x \color{red}{+63} & = & \color{red}{-72x} +64 \\\Leftrightarrow & -672x \color{red}{+63} \color{blue}{-63} \color{blue}{+72x} & = & \color{red}{-72x} +64 \color{blue}{+72x} \color{blue}{-63} \\\Leftrightarrow & -672x+72x& = & 64-63 \\\Leftrightarrow & \color{red}{-600} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-600} & & \\\Leftrightarrow & x = \frac{-1}{600} & & \\ & V = \left\{ \frac{-1}{600} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{4}{7})& = & -7x+\frac{4}{5} \\\Leftrightarrow & -10x+\frac{20}{7}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{+100} & = & \color{red}{-245x} +28 \\\Leftrightarrow & -350x \color{red}{+100} \color{blue}{-100} \color{blue}{+245x} & = & \color{red}{-245x} +28 \color{blue}{+245x} \color{blue}{-100} \\\Leftrightarrow & -350x+245x& = & 28-100 \\\Leftrightarrow & \color{red}{-105} x& = & -72 \\\Leftrightarrow & x = \frac{-72}{-105} & & \\\Leftrightarrow & x = \frac{24}{35} & & \\ & V = \left\{ \frac{24}{35} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{5}{3})& = & -7x+\frac{7}{10} \\\Leftrightarrow & 8x-\frac{20}{3}& = & -7x+\frac{7}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{240}{ \color{blue}{30} }x- \frac{200}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{21}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 240x \color{red}{-200} & = & \color{red}{-210x} +21 \\\Leftrightarrow & 240x \color{red}{-200} \color{blue}{+200} \color{blue}{+210x} & = & \color{red}{-210x} +21 \color{blue}{+210x} \color{blue}{+200} \\\Leftrightarrow & 240x+210x& = & 21+200 \\\Leftrightarrow & \color{red}{450} x& = & 221 \\\Leftrightarrow & x = \frac{221}{450} & & \\ & V = \left\{ \frac{221}{450} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{3}{11})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{18}{11}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-90} & = & \color{red}{275x} +66 \\\Leftrightarrow & 660x \color{red}{-90} \color{blue}{+90} \color{blue}{-275x} & = & \color{red}{275x} +66 \color{blue}{-275x} \color{blue}{+90} \\\Leftrightarrow & 660x-275x& = & 66+90 \\\Leftrightarrow & \color{red}{385} x& = & 156 \\\Leftrightarrow & x = \frac{156}{385} & & \\ & V = \left\{ \frac{156}{385} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{11})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -12x-\frac{30}{11}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{90}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-90} & = & \color{red}{165x} +110 \\\Leftrightarrow & -396x \color{red}{-90} \color{blue}{+90} \color{blue}{-165x} & = & \color{red}{165x} +110 \color{blue}{-165x} \color{blue}{+90} \\\Leftrightarrow & -396x-165x& = & 110+90 \\\Leftrightarrow & \color{red}{-561} x& = & 200 \\\Leftrightarrow & x = \frac{200}{-561} & & \\\Leftrightarrow & x = \frac{-200}{561} & & \\ & V = \left\{ \frac{-200}{561} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{11})& = & -4x+\frac{7}{2} \\\Leftrightarrow & -15x-\frac{15}{11}& = & -4x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-330}{ \color{blue}{22} }x- \frac{30}{ \color{blue}{22} })& = & (\frac{-88}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -330x \color{red}{-30} & = & \color{red}{-88x} +77 \\\Leftrightarrow & -330x \color{red}{-30} \color{blue}{+30} \color{blue}{+88x} & = & \color{red}{-88x} +77 \color{blue}{+88x} \color{blue}{+30} \\\Leftrightarrow & -330x+88x& = & 77+30 \\\Leftrightarrow & \color{red}{-242} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-242} & & \\\Leftrightarrow & x = \frac{-107}{242} & & \\ & V = \left\{ \frac{-107}{242} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{4}{3})& = & 9x+\frac{10}{3} \\\Leftrightarrow & 20x-\frac{20}{3}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{60}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 60x \color{red}{-20} & = & \color{red}{27x} +10 \\\Leftrightarrow & 60x \color{red}{-20} \color{blue}{+20} \color{blue}{-27x} & = & \color{red}{27x} +10 \color{blue}{-27x} \color{blue}{+20} \\\Leftrightarrow & 60x-27x& = & 10+20 \\\Leftrightarrow & \color{red}{33} x& = & 30 \\\Leftrightarrow & x = \frac{30}{33} & & \\\Leftrightarrow & x = \frac{10}{11} & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{5}{12})& = & 8x+\frac{5}{4} \\\Leftrightarrow & 15x-\frac{25}{12}& = & 8x+\frac{5}{4} \\ & & & \text{kgv van noemers 12 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x- \frac{25}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{-25} & = & \color{red}{96x} +15 \\\Leftrightarrow & 180x \color{red}{-25} \color{blue}{+25} \color{blue}{-96x} & = & \color{red}{96x} +15 \color{blue}{-96x} \color{blue}{+25} \\\Leftrightarrow & 180x-96x& = & 15+25 \\\Leftrightarrow & \color{red}{84} x& = & 40 \\\Leftrightarrow & x = \frac{40}{84} & & \\\Leftrightarrow & x = \frac{10}{21} & & \\ & V = \left\{ \frac{10}{21} \right\} & \\\end{align}\)
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