Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

  1. \(-6(5x-\frac{4}{15})=7x+\frac{5}{7}\)
  2. \(-7(x-\frac{4}{11})=-2x+\frac{8}{15}\)
  3. \(5(5x+\frac{2}{5})=-7x+\frac{7}{4}\)
  4. \(-(2x+\frac{4}{11})=3x+\frac{8}{11}\)
  5. \(-2(-3x+\frac{4}{5})=x+\frac{7}{10}\)
  6. \((-4x-\frac{3}{11})=3x+\frac{2}{11}\)
  7. \(-(4x+\frac{2}{9})=-3x+\frac{2}{13}\)
  8. \(-7(-x-\frac{3}{7})=-10x+\frac{8}{15}\)
  9. \(3(-3x-\frac{5}{7})=-2x+\frac{2}{13}\)
  10. \(-4(-2x-\frac{2}{7})=-7x+\frac{5}{4}\)
  11. \(7(-4x+\frac{4}{7})=27x+\frac{3}{7}\)
  12. \(-3(-3x+\frac{5}{8})=x+\frac{9}{8}\)

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{15})& = & 7x+\frac{5}{7} \\\Leftrightarrow & -30x+\frac{8}{5}& = & 7x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(-30x+\frac{8}{5})& = & (7x+\frac{5}{7}). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{+56} & = & \color{red}{245x} +25 \\\Leftrightarrow & -1050x \color{red}{+56} \color{blue}{-56} \color{blue}{-245x} & = & \color{red}{245x} +25 \color{blue}{-245x} \color{blue}{-56} \\\Leftrightarrow & -1050x-245x& = & 25-56 \\\Leftrightarrow & \color{red}{-1295} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-1295} & & \\\Leftrightarrow & x = \frac{31}{1295} & & \\ & V = \left\{ \frac{31}{1295} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (x-\frac{4}{11})& = & -2x+\frac{8}{15} \\\Leftrightarrow & -7x+\frac{28}{11}& = & -2x+\frac{8}{15} \\ & & & \text{kgv van noemers 11 en 15 is 165} \\\Leftrightarrow & \color{blue}{165} .(-7x+\frac{28}{11})& = & (-2x+\frac{8}{15}). \color{blue}{165} \\\Leftrightarrow & -1155x \color{red}{+420} & = & \color{red}{-330x} +88 \\\Leftrightarrow & -1155x \color{red}{+420} \color{blue}{-420} \color{blue}{+330x} & = & \color{red}{-330x} +88 \color{blue}{+330x} \color{blue}{-420} \\\Leftrightarrow & -1155x+330x& = & 88-420 \\\Leftrightarrow & \color{red}{-825} x& = & -332 \\\Leftrightarrow & x = \frac{-332}{-825} & & \\\Leftrightarrow & x = \frac{332}{825} & & \\ & V = \left\{ \frac{332}{825} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{2}{5})& = & -7x+\frac{7}{4} \\\Leftrightarrow & 25x+2& = & -7x+\frac{7}{4} \\ & & & \text{kgv van noemers 1 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(25x+2)& = & (-7x+\frac{7}{4}). \color{blue}{4} \\\Leftrightarrow & 100x \color{red}{+8} & = & \color{red}{-28x} +7 \\\Leftrightarrow & 100x \color{red}{+8} \color{blue}{-8} \color{blue}{+28x} & = & \color{red}{-28x} +7 \color{blue}{+28x} \color{blue}{-8} \\\Leftrightarrow & 100x+28x& = & 7-8 \\\Leftrightarrow & \color{red}{128} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{128} & & \\ & V = \left\{ \frac{-1}{128} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-} (2x+\frac{4}{11})& = & 3x+\frac{8}{11} \\\Leftrightarrow & -2x-\frac{4}{11}& = & 3x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(-2x-\frac{4}{11})& = & (3x+\frac{8}{11}). \color{blue}{11} \\\Leftrightarrow & -22x \color{red}{-4} & = & \color{red}{33x} +8 \\\Leftrightarrow & -22x \color{red}{-4} \color{blue}{+4} \color{blue}{-33x} & = & \color{red}{33x} +8 \color{blue}{-33x} \color{blue}{+4} \\\Leftrightarrow & -22x-33x& = & 8+4 \\\Leftrightarrow & \color{red}{-55} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-55} & & \\\Leftrightarrow & x = \frac{-12}{55} & & \\ & V = \left\{ \frac{-12}{55} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{4}{5})& = & x+\frac{7}{10} \\\Leftrightarrow & 6x-\frac{8}{5}& = & x+\frac{7}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(6x-\frac{8}{5})& = & (x+\frac{7}{10}). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{-16} & = & \color{red}{10x} +7 \\\Leftrightarrow & 60x \color{red}{-16} \color{blue}{+16} \color{blue}{-10x} & = & \color{red}{10x} +7 \color{blue}{-10x} \color{blue}{+16} \\\Leftrightarrow & 60x-10x& = & 7+16 \\\Leftrightarrow & \color{red}{50} x& = & 23 \\\Leftrightarrow & x = \frac{23}{50} & & \\ & V = \left\{ \frac{23}{50} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (-4x-\frac{3}{11})& = & 3x+\frac{2}{11} \\\Leftrightarrow & -4x-\frac{3}{11}& = & 3x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(-4x-\frac{3}{11})& = & (3x+\frac{2}{11}). \color{blue}{11} \\\Leftrightarrow & -44x \color{red}{-3} & = & \color{red}{33x} +2 \\\Leftrightarrow & -44x \color{red}{-3} \color{blue}{+3} \color{blue}{-33x} & = & \color{red}{33x} +2 \color{blue}{-33x} \color{blue}{+3} \\\Leftrightarrow & -44x-33x& = & 2+3 \\\Leftrightarrow & \color{red}{-77} x& = & 5 \\\Leftrightarrow & x = \frac{5}{-77} & & \\\Leftrightarrow & x = \frac{-5}{77} & & \\ & V = \left\{ \frac{-5}{77} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-} (4x+\frac{2}{9})& = & -3x+\frac{2}{13} \\\Leftrightarrow & -4x-\frac{2}{9}& = & -3x+\frac{2}{13} \\ & & & \text{kgv van noemers 9 en 13 is 117} \\\Leftrightarrow & \color{blue}{117} .(-4x-\frac{2}{9})& = & (-3x+\frac{2}{13}). \color{blue}{117} \\\Leftrightarrow & -468x \color{red}{-26} & = & \color{red}{-351x} +18 \\\Leftrightarrow & -468x \color{red}{-26} \color{blue}{+26} \color{blue}{+351x} & = & \color{red}{-351x} +18 \color{blue}{+351x} \color{blue}{+26} \\\Leftrightarrow & -468x+351x& = & 18+26 \\\Leftrightarrow & \color{red}{-117} x& = & 44 \\\Leftrightarrow & x = \frac{44}{-117} & & \\\Leftrightarrow & x = \frac{-44}{117} & & \\ & V = \left\{ \frac{-44}{117} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-x-\frac{3}{7})& = & -10x+\frac{8}{15} \\\Leftrightarrow & 7x+3& = & -10x+\frac{8}{15} \\ & & & \text{kgv van noemers 1 en 15 is 15} \\\Leftrightarrow & \color{blue}{15} .(7x+3)& = & (-10x+\frac{8}{15}). \color{blue}{15} \\\Leftrightarrow & 105x \color{red}{+45} & = & \color{red}{-150x} +8 \\\Leftrightarrow & 105x \color{red}{+45} \color{blue}{-45} \color{blue}{+150x} & = & \color{red}{-150x} +8 \color{blue}{+150x} \color{blue}{-45} \\\Leftrightarrow & 105x+150x& = & 8-45 \\\Leftrightarrow & \color{red}{255} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{255} & & \\ & V = \left\{ \frac{-37}{255} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{5}{7})& = & -2x+\frac{2}{13} \\\Leftrightarrow & -9x-\frac{15}{7}& = & -2x+\frac{2}{13} \\ & & & \text{kgv van noemers 7 en 13 is 91} \\\Leftrightarrow & \color{blue}{91} .(-9x-\frac{15}{7})& = & (-2x+\frac{2}{13}). \color{blue}{91} \\\Leftrightarrow & -819x \color{red}{-195} & = & \color{red}{-182x} +14 \\\Leftrightarrow & -819x \color{red}{-195} \color{blue}{+195} \color{blue}{+182x} & = & \color{red}{-182x} +14 \color{blue}{+182x} \color{blue}{+195} \\\Leftrightarrow & -819x+182x& = & 14+195 \\\Leftrightarrow & \color{red}{-637} x& = & 209 \\\Leftrightarrow & x = \frac{209}{-637} & & \\\Leftrightarrow & x = \frac{-209}{637} & & \\ & V = \left\{ \frac{-209}{637} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{2}{7})& = & -7x+\frac{5}{4} \\\Leftrightarrow & 8x+\frac{8}{7}& = & -7x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(8x+\frac{8}{7})& = & (-7x+\frac{5}{4}). \color{blue}{28} \\\Leftrightarrow & 224x \color{red}{+32} & = & \color{red}{-196x} +35 \\\Leftrightarrow & 224x \color{red}{+32} \color{blue}{-32} \color{blue}{+196x} & = & \color{red}{-196x} +35 \color{blue}{+196x} \color{blue}{-32} \\\Leftrightarrow & 224x+196x& = & 35-32 \\\Leftrightarrow & \color{red}{420} x& = & 3 \\\Leftrightarrow & x = \frac{3}{420} & & \\\Leftrightarrow & x = \frac{1}{140} & & \\ & V = \left\{ \frac{1}{140} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{4}{7})& = & 27x+\frac{3}{7} \\\Leftrightarrow & -28x+4& = & 27x+\frac{3}{7} \\ & & & \text{kgv van noemers 1 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(-28x+4)& = & (27x+\frac{3}{7}). \color{blue}{7} \\\Leftrightarrow & -196x \color{red}{+28} & = & \color{red}{189x} +3 \\\Leftrightarrow & -196x \color{red}{+28} \color{blue}{-28} \color{blue}{-189x} & = & \color{red}{189x} +3 \color{blue}{-189x} \color{blue}{-28} \\\Leftrightarrow & -196x-189x& = & 3-28 \\\Leftrightarrow & \color{red}{-385} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{-385} & & \\\Leftrightarrow & x = \frac{5}{77} & & \\ & V = \left\{ \frac{5}{77} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{8})& = & x+\frac{9}{8} \\\Leftrightarrow & 9x-\frac{15}{8}& = & x+\frac{9}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(9x-\frac{15}{8})& = & (x+\frac{9}{8}). \color{blue}{8} \\\Leftrightarrow & 72x \color{red}{-15} & = & \color{red}{8x} +9 \\\Leftrightarrow & 72x \color{red}{-15} \color{blue}{+15} \color{blue}{-8x} & = & \color{red}{8x} +9 \color{blue}{-8x} \color{blue}{+15} \\\Leftrightarrow & 72x-8x& = & 9+15 \\\Leftrightarrow & \color{red}{64} x& = & 24 \\\Leftrightarrow & x = \frac{24}{64} & & \\\Leftrightarrow & x = \frac{3}{8} & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-04-02 10:53:04