Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{2}{11})& = & 11x+\frac{2}{5} \\\Leftrightarrow & 12x-\frac{6}{11}& = & 11x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(12x-\frac{6}{11})& = & (11x+\frac{2}{5}). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-30} & = & \color{red}{605x} +22 \\\Leftrightarrow & 660x \color{red}{-30} \color{blue}{+30} \color{blue}{-605x} & = & \color{red}{605x} +22 \color{blue}{-605x} \color{blue}{+30} \\\Leftrightarrow & 660x-605x& = & 22+30 \\\Leftrightarrow & \color{red}{55} x& = & 52 \\\Leftrightarrow & x = \frac{52}{55} & & \\ & V = \left\{ \frac{52}{55} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{5}{12})& = & 5x+\frac{2}{15} \\\Leftrightarrow & -14x+\frac{35}{12}& = & 5x+\frac{2}{15} \\ & & & \text{kgv van noemers 12 en 15 is 60} \\\Leftrightarrow & \color{blue}{60} .(-14x+\frac{35}{12})& = & (5x+\frac{2}{15}). \color{blue}{60} \\\Leftrightarrow & -840x \color{red}{+175} & = & \color{red}{300x} +8 \\\Leftrightarrow & -840x \color{red}{+175} \color{blue}{-175} \color{blue}{-300x} & = & \color{red}{300x} +8 \color{blue}{-300x} \color{blue}{-175} \\\Leftrightarrow & -840x-300x& = & 8-175 \\\Leftrightarrow & \color{red}{-1140} x& = & -167 \\\Leftrightarrow & x = \frac{-167}{-1140} & & \\\Leftrightarrow & x = \frac{167}{1140} & & \\ & V = \left\{ \frac{167}{1140} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{2}{3})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -10x-\frac{4}{3}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(-10x-\frac{4}{3})& = & (-9x+\frac{6}{5}). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{-20} & = & \color{red}{-135x} +18 \\\Leftrightarrow & -150x \color{red}{-20} \color{blue}{+20} \color{blue}{+135x} & = & \color{red}{-135x} +18 \color{blue}{+135x} \color{blue}{+20} \\\Leftrightarrow & -150x+135x& = & 18+20 \\\Leftrightarrow & \color{red}{-15} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-15} & & \\\Leftrightarrow & x = \frac{-38}{15} & & \\ & V = \left\{ \frac{-38}{15} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{5}{13})& = & 8x+\frac{8}{13} \\\Leftrightarrow & 15x-\frac{15}{13}& = & 8x+\frac{8}{13} \\ & & & \text{kgv van noemers 13 en 13 is 13} \\\Leftrightarrow & \color{blue}{13} .(15x-\frac{15}{13})& = & (8x+\frac{8}{13}). \color{blue}{13} \\\Leftrightarrow & 195x \color{red}{-15} & = & \color{red}{104x} +8 \\\Leftrightarrow & 195x \color{red}{-15} \color{blue}{+15} \color{blue}{-104x} & = & \color{red}{104x} +8 \color{blue}{-104x} \color{blue}{+15} \\\Leftrightarrow & 195x-104x& = & 8+15 \\\Leftrightarrow & \color{red}{91} x& = & 23 \\\Leftrightarrow & x = \frac{23}{91} & & \\ & V = \left\{ \frac{23}{91} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{4}{7})& = & -7x+\frac{8}{9} \\\Leftrightarrow & 12x+\frac{16}{7}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(12x+\frac{16}{7})& = & (-7x+\frac{8}{9}). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{+144} & = & \color{red}{-441x} +56 \\\Leftrightarrow & 756x \color{red}{+144} \color{blue}{-144} \color{blue}{+441x} & = & \color{red}{-441x} +56 \color{blue}{+441x} \color{blue}{-144} \\\Leftrightarrow & 756x+441x& = & 56-144 \\\Leftrightarrow & \color{red}{1197} x& = & -88 \\\Leftrightarrow & x = \frac{-88}{1197} & & \\ & V = \left\{ \frac{-88}{1197} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{4}{11})& = & 5x+\frac{8}{9} \\\Leftrightarrow & -18x-\frac{24}{11}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(-18x-\frac{24}{11})& = & (5x+\frac{8}{9}). \color{blue}{99} \\\Leftrightarrow & -1782x \color{red}{-216} & = & \color{red}{495x} +88 \\\Leftrightarrow & -1782x \color{red}{-216} \color{blue}{+216} \color{blue}{-495x} & = & \color{red}{495x} +88 \color{blue}{-495x} \color{blue}{+216} \\\Leftrightarrow & -1782x-495x& = & 88+216 \\\Leftrightarrow & \color{red}{-2277} x& = & 304 \\\Leftrightarrow & x = \frac{304}{-2277} & & \\\Leftrightarrow & x = \frac{-304}{2277} & & \\ & V = \left\{ \frac{-304}{2277} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{5}{14})& = & x+\frac{8}{13} \\\Leftrightarrow & 25x+\frac{25}{14}& = & x+\frac{8}{13} \\ & & & \text{kgv van noemers 14 en 13 is 182} \\\Leftrightarrow & \color{blue}{182} .(25x+\frac{25}{14})& = & (x+\frac{8}{13}). \color{blue}{182} \\\Leftrightarrow & 4550x \color{red}{+325} & = & \color{red}{182x} +112 \\\Leftrightarrow & 4550x \color{red}{+325} \color{blue}{-325} \color{blue}{-182x} & = & \color{red}{182x} +112 \color{blue}{-182x} \color{blue}{-325} \\\Leftrightarrow & 4550x-182x& = & 112-325 \\\Leftrightarrow & \color{red}{4368} x& = & -213 \\\Leftrightarrow & x = \frac{-213}{4368} & & \\\Leftrightarrow & x = \frac{-71}{1456} & & \\ & V = \left\{ \frac{-71}{1456} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{2}{13})& = & 5x+\frac{3}{11} \\\Leftrightarrow & 12x+\frac{8}{13}& = & 5x+\frac{3}{11} \\ & & & \text{kgv van noemers 13 en 11 is 143} \\\Leftrightarrow & \color{blue}{143} .(12x+\frac{8}{13})& = & (5x+\frac{3}{11}). \color{blue}{143} \\\Leftrightarrow & 1716x \color{red}{+88} & = & \color{red}{715x} +39 \\\Leftrightarrow & 1716x \color{red}{+88} \color{blue}{-88} \color{blue}{-715x} & = & \color{red}{715x} +39 \color{blue}{-715x} \color{blue}{-88} \\\Leftrightarrow & 1716x-715x& = & 39-88 \\\Leftrightarrow & \color{red}{1001} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{1001} & & \\\Leftrightarrow & x = \frac{-7}{143} & & \\ & V = \left\{ \frac{-7}{143} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{2}{11})& = & 11x+\frac{8}{7} \\\Leftrightarrow & 12x-\frac{6}{11}& = & 11x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(12x-\frac{6}{11})& = & (11x+\frac{8}{7}). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-42} & = & \color{red}{847x} +88 \\\Leftrightarrow & 924x \color{red}{-42} \color{blue}{+42} \color{blue}{-847x} & = & \color{red}{847x} +88 \color{blue}{-847x} \color{blue}{+42} \\\Leftrightarrow & 924x-847x& = & 88+42 \\\Leftrightarrow & \color{red}{77} x& = & 130 \\\Leftrightarrow & x = \frac{130}{77} & & \\ & V = \left\{ \frac{130}{77} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{4})& = & -9x+\frac{6}{7} \\\Leftrightarrow & -10x+\frac{25}{4}& = & -9x+\frac{6}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(-10x+\frac{25}{4})& = & (-9x+\frac{6}{7}). \color{blue}{28} \\\Leftrightarrow & -280x \color{red}{+175} & = & \color{red}{-252x} +24 \\\Leftrightarrow & -280x \color{red}{+175} \color{blue}{-175} \color{blue}{+252x} & = & \color{red}{-252x} +24 \color{blue}{+252x} \color{blue}{-175} \\\Leftrightarrow & -280x+252x& = & 24-175 \\\Leftrightarrow & \color{red}{-28} x& = & -151 \\\Leftrightarrow & x = \frac{-151}{-28} & & \\\Leftrightarrow & x = \frac{151}{28} & & \\ & V = \left\{ \frac{151}{28} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-x+\frac{2}{7})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -6x+\frac{12}{7}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(-6x+\frac{12}{7})& = & (-5x+\frac{6}{5}). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+60} & = & \color{red}{-175x} +42 \\\Leftrightarrow & -210x \color{red}{+60} \color{blue}{-60} \color{blue}{+175x} & = & \color{red}{-175x} +42 \color{blue}{+175x} \color{blue}{-60} \\\Leftrightarrow & -210x+175x& = & 42-60 \\\Leftrightarrow & \color{red}{-35} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-35} & & \\\Leftrightarrow & x = \frac{18}{35} & & \\ & V = \left\{ \frac{18}{35} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{3}{10})& = & 7x+\frac{6}{7} \\\Leftrightarrow & -6x+\frac{3}{5}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(-6x+\frac{3}{5})& = & (7x+\frac{6}{7}). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+21} & = & \color{red}{245x} +30 \\\Leftrightarrow & -210x \color{red}{+21} \color{blue}{-21} \color{blue}{-245x} & = & \color{red}{245x} +30 \color{blue}{-245x} \color{blue}{-21} \\\Leftrightarrow & -210x-245x& = & 30-21 \\\Leftrightarrow & \color{red}{-455} x& = & 9 \\\Leftrightarrow & x = \frac{9}{-455} & & \\\Leftrightarrow & x = \frac{-9}{455} & & \\ & V = \left\{ \frac{-9}{455} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-05-14 11:00:03