Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{5}{14})& = & 7x+\frac{6}{7} \\\Leftrightarrow & -16x+\frac{10}{7}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(-16x+\frac{10}{7})& = & (7x+\frac{6}{7}). \color{blue}{7} \\\Leftrightarrow & -112x \color{red}{+10} & = & \color{red}{49x} +6 \\\Leftrightarrow & -112x \color{red}{+10} \color{blue}{-10} \color{blue}{-49x} & = & \color{red}{49x} +6 \color{blue}{-49x} \color{blue}{-10} \\\Leftrightarrow & -112x-49x& = & 6-10 \\\Leftrightarrow & \color{red}{-161} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-161} & & \\\Leftrightarrow & x = \frac{4}{161} & & \\ & V = \left\{ \frac{4}{161} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-} (2x-\frac{4}{3})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -2x+\frac{4}{3}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(-2x+\frac{4}{3})& = & (5x+\frac{4}{3}). \color{blue}{3} \\\Leftrightarrow & -6x \color{red}{+4} & = & \color{red}{15x} +4 \\\Leftrightarrow & -6x \color{red}{+4} \color{blue}{-4} \color{blue}{-15x} & = & \color{red}{15x} +4 \color{blue}{-15x} \color{blue}{-4} \\\Leftrightarrow & -6x-15x& = & 4-4 \\\Leftrightarrow & \color{red}{-21} x& = & 0 \\\Leftrightarrow & x = \frac{0}{-21} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (x-\frac{3}{16})& = & x+\frac{6}{13} \\\Leftrightarrow & 4x-\frac{3}{4}& = & x+\frac{6}{13} \\ & & & \text{kgv van noemers 4 en 13 is 52} \\\Leftrightarrow & \color{blue}{52} .(4x-\frac{3}{4})& = & (x+\frac{6}{13}). \color{blue}{52} \\\Leftrightarrow & 208x \color{red}{-39} & = & \color{red}{52x} +24 \\\Leftrightarrow & 208x \color{red}{-39} \color{blue}{+39} \color{blue}{-52x} & = & \color{red}{52x} +24 \color{blue}{-52x} \color{blue}{+39} \\\Leftrightarrow & 208x-52x& = & 24+39 \\\Leftrightarrow & \color{red}{156} x& = & 63 \\\Leftrightarrow & x = \frac{63}{156} & & \\\Leftrightarrow & x = \frac{21}{52} & & \\ & V = \left\{ \frac{21}{52} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{4}{9})& = & 7x+\frac{2}{13} \\\Leftrightarrow & -12x-\frac{4}{3}& = & 7x+\frac{2}{13} \\ & & & \text{kgv van noemers 3 en 13 is 39} \\\Leftrightarrow & \color{blue}{39} .(-12x-\frac{4}{3})& = & (7x+\frac{2}{13}). \color{blue}{39} \\\Leftrightarrow & -468x \color{red}{-52} & = & \color{red}{273x} +6 \\\Leftrightarrow & -468x \color{red}{-52} \color{blue}{+52} \color{blue}{-273x} & = & \color{red}{273x} +6 \color{blue}{-273x} \color{blue}{+52} \\\Leftrightarrow & -468x-273x& = & 6+52 \\\Leftrightarrow & \color{red}{-741} x& = & 58 \\\Leftrightarrow & x = \frac{58}{-741} & & \\\Leftrightarrow & x = \frac{-58}{741} & & \\ & V = \left\{ \frac{-58}{741} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{4}{11})& = & 9x+\frac{7}{12} \\\Leftrightarrow & -14x+\frac{28}{11}& = & 9x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(-14x+\frac{28}{11})& = & (9x+\frac{7}{12}). \color{blue}{132} \\\Leftrightarrow & -1848x \color{red}{+336} & = & \color{red}{1188x} +77 \\\Leftrightarrow & -1848x \color{red}{+336} \color{blue}{-336} \color{blue}{-1188x} & = & \color{red}{1188x} +77 \color{blue}{-1188x} \color{blue}{-336} \\\Leftrightarrow & -1848x-1188x& = & 77-336 \\\Leftrightarrow & \color{red}{-3036} x& = & -259 \\\Leftrightarrow & x = \frac{-259}{-3036} & & \\\Leftrightarrow & x = \frac{259}{3036} & & \\ & V = \left\{ \frac{259}{3036} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{2}{15})& = & -2x+\frac{6}{5} \\\Leftrightarrow & 25x+\frac{2}{3}& = & -2x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(25x+\frac{2}{3})& = & (-2x+\frac{6}{5}). \color{blue}{15} \\\Leftrightarrow & 375x \color{red}{+10} & = & \color{red}{-30x} +18 \\\Leftrightarrow & 375x \color{red}{+10} \color{blue}{-10} \color{blue}{+30x} & = & \color{red}{-30x} +18 \color{blue}{+30x} \color{blue}{-10} \\\Leftrightarrow & 375x+30x& = & 18-10 \\\Leftrightarrow & \color{red}{405} x& = & 8 \\\Leftrightarrow & x = \frac{8}{405} & & \\ & V = \left\{ \frac{8}{405} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{2}{3})& = & 3x+\frac{2}{11} \\\Leftrightarrow & -8x+\frac{8}{3}& = & 3x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(-8x+\frac{8}{3})& = & (3x+\frac{2}{11}). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+88} & = & \color{red}{99x} +6 \\\Leftrightarrow & -264x \color{red}{+88} \color{blue}{-88} \color{blue}{-99x} & = & \color{red}{99x} +6 \color{blue}{-99x} \color{blue}{-88} \\\Leftrightarrow & -264x-99x& = & 6-88 \\\Leftrightarrow & \color{red}{-363} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-363} & & \\\Leftrightarrow & x = \frac{82}{363} & & \\ & V = \left\{ \frac{82}{363} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (-5x+\frac{2}{13})& = & 8x+\frac{10}{3} \\\Leftrightarrow & -5x+\frac{2}{13}& = & 8x+\frac{10}{3} \\ & & & \text{kgv van noemers 13 en 3 is 39} \\\Leftrightarrow & \color{blue}{39} .(-5x+\frac{2}{13})& = & (8x+\frac{10}{3}). \color{blue}{39} \\\Leftrightarrow & -195x \color{red}{+6} & = & \color{red}{312x} +130 \\\Leftrightarrow & -195x \color{red}{+6} \color{blue}{-6} \color{blue}{-312x} & = & \color{red}{312x} +130 \color{blue}{-312x} \color{blue}{-6} \\\Leftrightarrow & -195x-312x& = & 130-6 \\\Leftrightarrow & \color{red}{-507} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-507} & & \\\Leftrightarrow & x = \frac{-124}{507} & & \\ & V = \left\{ \frac{-124}{507} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{2}{5})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 24x+\frac{12}{5}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(24x+\frac{12}{5})& = & (5x+\frac{5}{11}). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{+132} & = & \color{red}{275x} +25 \\\Leftrightarrow & 1320x \color{red}{+132} \color{blue}{-132} \color{blue}{-275x} & = & \color{red}{275x} +25 \color{blue}{-275x} \color{blue}{-132} \\\Leftrightarrow & 1320x-275x& = & 25-132 \\\Leftrightarrow & \color{red}{1045} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{1045} & & \\ & V = \left\{ \frac{-107}{1045} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (-x+\frac{3}{7})& = & -3x+\frac{2}{15} \\\Leftrightarrow & -x+\frac{3}{7}& = & -3x+\frac{2}{15} \\ & & & \text{kgv van noemers 7 en 15 is 105} \\\Leftrightarrow & \color{blue}{105} .(-x+\frac{3}{7})& = & (-3x+\frac{2}{15}). \color{blue}{105} \\\Leftrightarrow & -105x \color{red}{+45} & = & \color{red}{-315x} +14 \\\Leftrightarrow & -105x \color{red}{+45} \color{blue}{-45} \color{blue}{+315x} & = & \color{red}{-315x} +14 \color{blue}{+315x} \color{blue}{-45} \\\Leftrightarrow & -105x+315x& = & 14-45 \\\Leftrightarrow & \color{red}{210} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{210} & & \\ & V = \left\{ \frac{-31}{210} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{5})& = & x+\frac{8}{11} \\\Leftrightarrow & -20x+\frac{16}{5}& = & x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(-20x+\frac{16}{5})& = & (x+\frac{8}{11}). \color{blue}{55} \\\Leftrightarrow & -1100x \color{red}{+176} & = & \color{red}{55x} +40 \\\Leftrightarrow & -1100x \color{red}{+176} \color{blue}{-176} \color{blue}{-55x} & = & \color{red}{55x} +40 \color{blue}{-55x} \color{blue}{-176} \\\Leftrightarrow & -1100x-55x& = & 40-176 \\\Leftrightarrow & \color{red}{-1155} x& = & -136 \\\Leftrightarrow & x = \frac{-136}{-1155} & & \\\Leftrightarrow & x = \frac{136}{1155} & & \\ & V = \left\{ \frac{136}{1155} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{3}{2})& = & 3x+\frac{10}{7} \\\Leftrightarrow & -20x+\frac{15}{2}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(-20x+\frac{15}{2})& = & (3x+\frac{10}{7}). \color{blue}{14} \\\Leftrightarrow & -280x \color{red}{+105} & = & \color{red}{42x} +20 \\\Leftrightarrow & -280x \color{red}{+105} \color{blue}{-105} \color{blue}{-42x} & = & \color{red}{42x} +20 \color{blue}{-42x} \color{blue}{-105} \\\Leftrightarrow & -280x-42x& = & 20-105 \\\Leftrightarrow & \color{red}{-322} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{-322} & & \\\Leftrightarrow & x = \frac{85}{322} & & \\ & V = \left\{ \frac{85}{322} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-05-19 10:47:57