Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

  1. \(6(-3x+\frac{3}{16})=-7x+\frac{9}{10}\)
  2. \(-3(-5x-\frac{4}{5})=-2x+\frac{7}{6}\)
  3. \(6(-x-\frac{5}{11})=7x+\frac{6}{13}\)
  4. \(2(x+\frac{2}{3})=9x+\frac{9}{16}\)
  5. \(-7(4x-\frac{3}{14})=5x+\frac{4}{13}\)
  6. \((3x-\frac{3}{13})=5x+\frac{8}{15}\)
  7. \(3(-x+\frac{2}{3})=8x+\frac{9}{8}\)
  8. \(-4(-2x+\frac{4}{11})=3x+\frac{6}{11}\)
  9. \(-7(-3x+\frac{2}{5})=2x+\frac{2}{7}\)
  10. \(-6(x-\frac{4}{3})=7x+\frac{2}{3}\)
  11. \(-4(-5x-\frac{4}{3})=x+\frac{7}{12}\)
  12. \(7(-5x-\frac{4}{13})=x+\frac{5}{11}\)

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{3}{16})& = & -7x+\frac{9}{10} \\\Leftrightarrow & -18x+\frac{9}{8}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(-18x+\frac{9}{8})& = & (-7x+\frac{9}{10}). \color{blue}{40} \\\Leftrightarrow & -720x \color{red}{+45} & = & \color{red}{-280x} +36 \\\Leftrightarrow & -720x \color{red}{+45} \color{blue}{-45} \color{blue}{+280x} & = & \color{red}{-280x} +36 \color{blue}{+280x} \color{blue}{-45} \\\Leftrightarrow & -720x+280x& = & 36-45 \\\Leftrightarrow & \color{red}{-440} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-440} & & \\\Leftrightarrow & x = \frac{9}{440} & & \\ & V = \left\{ \frac{9}{440} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & -2x+\frac{7}{6} \\\Leftrightarrow & 15x+\frac{12}{5}& = & -2x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(15x+\frac{12}{5})& = & (-2x+\frac{7}{6}). \color{blue}{30} \\\Leftrightarrow & 450x \color{red}{+72} & = & \color{red}{-60x} +35 \\\Leftrightarrow & 450x \color{red}{+72} \color{blue}{-72} \color{blue}{+60x} & = & \color{red}{-60x} +35 \color{blue}{+60x} \color{blue}{-72} \\\Leftrightarrow & 450x+60x& = & 35-72 \\\Leftrightarrow & \color{red}{510} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{510} & & \\ & V = \left\{ \frac{-37}{510} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-x-\frac{5}{11})& = & 7x+\frac{6}{13} \\\Leftrightarrow & -6x-\frac{30}{11}& = & 7x+\frac{6}{13} \\ & & & \text{kgv van noemers 11 en 13 is 143} \\\Leftrightarrow & \color{blue}{143} .(-6x-\frac{30}{11})& = & (7x+\frac{6}{13}). \color{blue}{143} \\\Leftrightarrow & -858x \color{red}{-390} & = & \color{red}{1001x} +66 \\\Leftrightarrow & -858x \color{red}{-390} \color{blue}{+390} \color{blue}{-1001x} & = & \color{red}{1001x} +66 \color{blue}{-1001x} \color{blue}{+390} \\\Leftrightarrow & -858x-1001x& = & 66+390 \\\Leftrightarrow & \color{red}{-1859} x& = & 456 \\\Leftrightarrow & x = \frac{456}{-1859} & & \\\Leftrightarrow & x = \frac{-456}{1859} & & \\ & V = \left\{ \frac{-456}{1859} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (x+\frac{2}{3})& = & 9x+\frac{9}{16} \\\Leftrightarrow & 2x+\frac{4}{3}& = & 9x+\frac{9}{16} \\ & & & \text{kgv van noemers 3 en 16 is 48} \\\Leftrightarrow & \color{blue}{48} .(2x+\frac{4}{3})& = & (9x+\frac{9}{16}). \color{blue}{48} \\\Leftrightarrow & 96x \color{red}{+64} & = & \color{red}{432x} +27 \\\Leftrightarrow & 96x \color{red}{+64} \color{blue}{-64} \color{blue}{-432x} & = & \color{red}{432x} +27 \color{blue}{-432x} \color{blue}{-64} \\\Leftrightarrow & 96x-432x& = & 27-64 \\\Leftrightarrow & \color{red}{-336} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-336} & & \\\Leftrightarrow & x = \frac{37}{336} & & \\ & V = \left\{ \frac{37}{336} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{14})& = & 5x+\frac{4}{13} \\\Leftrightarrow & -28x+\frac{3}{2}& = & 5x+\frac{4}{13} \\ & & & \text{kgv van noemers 2 en 13 is 26} \\\Leftrightarrow & \color{blue}{26} .(-28x+\frac{3}{2})& = & (5x+\frac{4}{13}). \color{blue}{26} \\\Leftrightarrow & -728x \color{red}{+39} & = & \color{red}{130x} +8 \\\Leftrightarrow & -728x \color{red}{+39} \color{blue}{-39} \color{blue}{-130x} & = & \color{red}{130x} +8 \color{blue}{-130x} \color{blue}{-39} \\\Leftrightarrow & -728x-130x& = & 8-39 \\\Leftrightarrow & \color{red}{-858} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-858} & & \\\Leftrightarrow & x = \frac{31}{858} & & \\ & V = \left\{ \frac{31}{858} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (3x-\frac{3}{13})& = & 5x+\frac{8}{15} \\\Leftrightarrow & 3x-\frac{3}{13}& = & 5x+\frac{8}{15} \\ & & & \text{kgv van noemers 13 en 15 is 195} \\\Leftrightarrow & \color{blue}{195} .(3x-\frac{3}{13})& = & (5x+\frac{8}{15}). \color{blue}{195} \\\Leftrightarrow & 585x \color{red}{-45} & = & \color{red}{975x} +104 \\\Leftrightarrow & 585x \color{red}{-45} \color{blue}{+45} \color{blue}{-975x} & = & \color{red}{975x} +104 \color{blue}{-975x} \color{blue}{+45} \\\Leftrightarrow & 585x-975x& = & 104+45 \\\Leftrightarrow & \color{red}{-390} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-390} & & \\\Leftrightarrow & x = \frac{-149}{390} & & \\ & V = \left\{ \frac{-149}{390} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-x+\frac{2}{3})& = & 8x+\frac{9}{8} \\\Leftrightarrow & -3x+2& = & 8x+\frac{9}{8} \\ & & & \text{kgv van noemers 1 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(-3x+2)& = & (8x+\frac{9}{8}). \color{blue}{8} \\\Leftrightarrow & -24x \color{red}{+16} & = & \color{red}{64x} +9 \\\Leftrightarrow & -24x \color{red}{+16} \color{blue}{-16} \color{blue}{-64x} & = & \color{red}{64x} +9 \color{blue}{-64x} \color{blue}{-16} \\\Leftrightarrow & -24x-64x& = & 9-16 \\\Leftrightarrow & \color{red}{-88} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-88} & & \\\Leftrightarrow & x = \frac{7}{88} & & \\ & V = \left\{ \frac{7}{88} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{4}{11})& = & 3x+\frac{6}{11} \\\Leftrightarrow & 8x-\frac{16}{11}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(8x-\frac{16}{11})& = & (3x+\frac{6}{11}). \color{blue}{11} \\\Leftrightarrow & 88x \color{red}{-16} & = & \color{red}{33x} +6 \\\Leftrightarrow & 88x \color{red}{-16} \color{blue}{+16} \color{blue}{-33x} & = & \color{red}{33x} +6 \color{blue}{-33x} \color{blue}{+16} \\\Leftrightarrow & 88x-33x& = & 6+16 \\\Leftrightarrow & \color{red}{55} x& = & 22 \\\Leftrightarrow & x = \frac{22}{55} & & \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{5})& = & 2x+\frac{2}{7} \\\Leftrightarrow & 21x-\frac{14}{5}& = & 2x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(21x-\frac{14}{5})& = & (2x+\frac{2}{7}). \color{blue}{35} \\\Leftrightarrow & 735x \color{red}{-98} & = & \color{red}{70x} +10 \\\Leftrightarrow & 735x \color{red}{-98} \color{blue}{+98} \color{blue}{-70x} & = & \color{red}{70x} +10 \color{blue}{-70x} \color{blue}{+98} \\\Leftrightarrow & 735x-70x& = & 10+98 \\\Leftrightarrow & \color{red}{665} x& = & 108 \\\Leftrightarrow & x = \frac{108}{665} & & \\ & V = \left\{ \frac{108}{665} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (x-\frac{4}{3})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -6x+8& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 1 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(-6x+8)& = & (7x+\frac{2}{3}). \color{blue}{3} \\\Leftrightarrow & -18x \color{red}{+24} & = & \color{red}{21x} +2 \\\Leftrightarrow & -18x \color{red}{+24} \color{blue}{-24} \color{blue}{-21x} & = & \color{red}{21x} +2 \color{blue}{-21x} \color{blue}{-24} \\\Leftrightarrow & -18x-21x& = & 2-24 \\\Leftrightarrow & \color{red}{-39} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-39} & & \\\Leftrightarrow & x = \frac{22}{39} & & \\ & V = \left\{ \frac{22}{39} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{4}{3})& = & x+\frac{7}{12} \\\Leftrightarrow & 20x+\frac{16}{3}& = & x+\frac{7}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(20x+\frac{16}{3})& = & (x+\frac{7}{12}). \color{blue}{12} \\\Leftrightarrow & 240x \color{red}{+64} & = & \color{red}{12x} +7 \\\Leftrightarrow & 240x \color{red}{+64} \color{blue}{-64} \color{blue}{-12x} & = & \color{red}{12x} +7 \color{blue}{-12x} \color{blue}{-64} \\\Leftrightarrow & 240x-12x& = & 7-64 \\\Leftrightarrow & \color{red}{228} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{228} & & \\\Leftrightarrow & x = \frac{-1}{4} & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{4}{13})& = & x+\frac{5}{11} \\\Leftrightarrow & -35x-\frac{28}{13}& = & x+\frac{5}{11} \\ & & & \text{kgv van noemers 13 en 11 is 143} \\\Leftrightarrow & \color{blue}{143} .(-35x-\frac{28}{13})& = & (x+\frac{5}{11}). \color{blue}{143} \\\Leftrightarrow & -5005x \color{red}{-308} & = & \color{red}{143x} +65 \\\Leftrightarrow & -5005x \color{red}{-308} \color{blue}{+308} \color{blue}{-143x} & = & \color{red}{143x} +65 \color{blue}{-143x} \color{blue}{+308} \\\Leftrightarrow & -5005x-143x& = & 65+308 \\\Leftrightarrow & \color{red}{-5148} x& = & 373 \\\Leftrightarrow & x = \frac{373}{-5148} & & \\\Leftrightarrow & x = \frac{-373}{5148} & & \\ & V = \left\{ \frac{-373}{5148} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-05-02 09:20:01