Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{3}{7})& = & 7x+\frac{8}{9} \\\Leftrightarrow & -10x+\frac{6}{7}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{+54} & = & \color{red}{441x} +56 \\\Leftrightarrow & -630x \color{red}{+54} \color{blue}{-54} \color{blue}{-441x} & = & \color{red}{441x} +56 \color{blue}{-441x} \color{blue}{-54} \\\Leftrightarrow & -630x-441x& = & 56-54 \\\Leftrightarrow & \color{red}{-1071} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-1071} & & \\\Leftrightarrow & x = \frac{-2}{1071} & & \\ & V = \left\{ \frac{-2}{1071} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{5})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -6x+\frac{8}{5}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{+24} & = & \color{red}{105x} +50 \\\Leftrightarrow & -90x \color{red}{+24} \color{blue}{-24} \color{blue}{-105x} & = & \color{red}{105x} +50 \color{blue}{-105x} \color{blue}{-24} \\\Leftrightarrow & -90x-105x& = & 50-24 \\\Leftrightarrow & \color{red}{-195} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-195} & & \\\Leftrightarrow & x = \frac{-2}{15} & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{4}{3})& = & 8x+\frac{4}{3} \\\Leftrightarrow & 21x+\frac{28}{3}& = & 8x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{63}{ \color{blue}{3} }x+ \frac{28}{ \color{blue}{3} })& = & (\frac{24}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 63x \color{red}{+28} & = & \color{red}{24x} +4 \\\Leftrightarrow & 63x \color{red}{+28} \color{blue}{-28} \color{blue}{-24x} & = & \color{red}{24x} +4 \color{blue}{-24x} \color{blue}{-28} \\\Leftrightarrow & 63x-24x& = & 4-28 \\\Leftrightarrow & \color{red}{39} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{39} & & \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{4}{7})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 20x-\frac{20}{7}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{-100} & = & \color{red}{105x} +42 \\\Leftrightarrow & 700x \color{red}{-100} \color{blue}{+100} \color{blue}{-105x} & = & \color{red}{105x} +42 \color{blue}{-105x} \color{blue}{+100} \\\Leftrightarrow & 700x-105x& = & 42+100 \\\Leftrightarrow & \color{red}{595} x& = & 142 \\\Leftrightarrow & x = \frac{142}{595} & & \\ & V = \left\{ \frac{142}{595} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{3}{11})& = & 9x+\frac{9}{11} \\\Leftrightarrow & -4x-\frac{6}{11}& = & 9x+\frac{9}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-44}{ \color{blue}{11} }x- \frac{6}{ \color{blue}{11} })& = & (\frac{99}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -44x \color{red}{-6} & = & \color{red}{99x} +9 \\\Leftrightarrow & -44x \color{red}{-6} \color{blue}{+6} \color{blue}{-99x} & = & \color{red}{99x} +9 \color{blue}{-99x} \color{blue}{+6} \\\Leftrightarrow & -44x-99x& = & 9+6 \\\Leftrightarrow & \color{red}{-143} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-143} & & \\\Leftrightarrow & x = \frac{-15}{143} & & \\ & V = \left\{ \frac{-15}{143} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{9})& = & -7x+\frac{9}{11} \\\Leftrightarrow & -16x+\frac{8}{9}& = & -7x+\frac{9}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1584}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{81}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1584x \color{red}{+88} & = & \color{red}{-693x} +81 \\\Leftrightarrow & -1584x \color{red}{+88} \color{blue}{-88} \color{blue}{+693x} & = & \color{red}{-693x} +81 \color{blue}{+693x} \color{blue}{-88} \\\Leftrightarrow & -1584x+693x& = & 81-88 \\\Leftrightarrow & \color{red}{-891} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-891} & & \\\Leftrightarrow & x = \frac{7}{891} & & \\ & V = \left\{ \frac{7}{891} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{5}{11})& = & 7x+\frac{4}{5} \\\Leftrightarrow & -6x-\frac{10}{11}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x- \frac{50}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{-50} & = & \color{red}{385x} +44 \\\Leftrightarrow & -330x \color{red}{-50} \color{blue}{+50} \color{blue}{-385x} & = & \color{red}{385x} +44 \color{blue}{-385x} \color{blue}{+50} \\\Leftrightarrow & -330x-385x& = & 44+50 \\\Leftrightarrow & \color{red}{-715} x& = & 94 \\\Leftrightarrow & x = \frac{94}{-715} & & \\\Leftrightarrow & x = \frac{-94}{715} & & \\ & V = \left\{ \frac{-94}{715} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{3}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x-\frac{18}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x- \frac{18}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{-18} & = & \color{red}{25x} +6 \\\Leftrightarrow & -60x \color{red}{-18} \color{blue}{+18} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{+18} \\\Leftrightarrow & -60x-25x& = & 6+18 \\\Leftrightarrow & \color{red}{-85} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-85} & & \\\Leftrightarrow & x = \frac{-24}{85} & & \\ & V = \left\{ \frac{-24}{85} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{2}{11})& = & 7x+\frac{10}{9} \\\Leftrightarrow & 30x+\frac{12}{11}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2970}{ \color{blue}{99} }x+ \frac{108}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2970x \color{red}{+108} & = & \color{red}{693x} +110 \\\Leftrightarrow & 2970x \color{red}{+108} \color{blue}{-108} \color{blue}{-693x} & = & \color{red}{693x} +110 \color{blue}{-693x} \color{blue}{-108} \\\Leftrightarrow & 2970x-693x& = & 110-108 \\\Leftrightarrow & \color{red}{2277} x& = & 2 \\\Leftrightarrow & x = \frac{2}{2277} & & \\ & V = \left\{ \frac{2}{2277} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{4}{11})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 18x-\frac{24}{11}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{594}{ \color{blue}{33} }x- \frac{72}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 594x \color{red}{-72} & = & \color{red}{165x} +110 \\\Leftrightarrow & 594x \color{red}{-72} \color{blue}{+72} \color{blue}{-165x} & = & \color{red}{165x} +110 \color{blue}{-165x} \color{blue}{+72} \\\Leftrightarrow & 594x-165x& = & 110+72 \\\Leftrightarrow & \color{red}{429} x& = & 182 \\\Leftrightarrow & x = \frac{182}{429} & & \\\Leftrightarrow & x = \frac{14}{33} & & \\ & V = \left\{ \frac{14}{33} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{11})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 18x+\frac{24}{11}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{594}{ \color{blue}{33} }x+ \frac{72}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 594x \color{red}{+72} & = & \color{red}{-165x} +44 \\\Leftrightarrow & 594x \color{red}{+72} \color{blue}{-72} \color{blue}{+165x} & = & \color{red}{-165x} +44 \color{blue}{+165x} \color{blue}{-72} \\\Leftrightarrow & 594x+165x& = & 44-72 \\\Leftrightarrow & \color{red}{759} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{759} & & \\ & V = \left\{ \frac{-28}{759} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{11})& = & -9x+\frac{9}{11} \\\Leftrightarrow & -8x+\frac{8}{11}& = & -9x+\frac{9}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-88}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -88x \color{red}{+8} & = & \color{red}{-99x} +9 \\\Leftrightarrow & -88x \color{red}{+8} \color{blue}{-8} \color{blue}{+99x} & = & \color{red}{-99x} +9 \color{blue}{+99x} \color{blue}{-8} \\\Leftrightarrow & -88x+99x& = & 9-8 \\\Leftrightarrow & \color{red}{11} x& = & 1 \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
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