Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{4}{7})& = & x+\frac{10}{13} \\\Leftrightarrow & 6x-\frac{8}{7}& = & x+\frac{10}{13} \\ & & & \text{kgv van noemers 7 en 13 is 91} \\\Leftrightarrow & \color{blue}{91} .(6x-\frac{8}{7})& = & (x+\frac{10}{13}). \color{blue}{91} \\\Leftrightarrow & 546x \color{red}{-104} & = & \color{red}{91x} +70 \\\Leftrightarrow & 546x \color{red}{-104} \color{blue}{+104} \color{blue}{-91x} & = & \color{red}{91x} +70 \color{blue}{-91x} \color{blue}{+104} \\\Leftrightarrow & 546x-91x& = & 70+104 \\\Leftrightarrow & \color{red}{455} x& = & 174 \\\Leftrightarrow & x = \frac{174}{455} & & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{3})& = & 3x+\frac{9}{13} \\\Leftrightarrow & 8x+\frac{4}{3}& = & 3x+\frac{9}{13} \\ & & & \text{kgv van noemers 3 en 13 is 39} \\\Leftrightarrow & \color{blue}{39} .(8x+\frac{4}{3})& = & (3x+\frac{9}{13}). \color{blue}{39} \\\Leftrightarrow & 312x \color{red}{+52} & = & \color{red}{117x} +27 \\\Leftrightarrow & 312x \color{red}{+52} \color{blue}{-52} \color{blue}{-117x} & = & \color{red}{117x} +27 \color{blue}{-117x} \color{blue}{-52} \\\Leftrightarrow & 312x-117x& = & 27-52 \\\Leftrightarrow & \color{red}{195} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{195} & & \\\Leftrightarrow & x = \frac{-5}{39} & & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{3}{8})& = & 2x+\frac{6}{7} \\\Leftrightarrow & -15x-\frac{9}{8}& = & 2x+\frac{6}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(-15x-\frac{9}{8})& = & (2x+\frac{6}{7}). \color{blue}{56} \\\Leftrightarrow & -840x \color{red}{-63} & = & \color{red}{112x} +48 \\\Leftrightarrow & -840x \color{red}{-63} \color{blue}{+63} \color{blue}{-112x} & = & \color{red}{112x} +48 \color{blue}{-112x} \color{blue}{+63} \\\Leftrightarrow & -840x-112x& = & 48+63 \\\Leftrightarrow & \color{red}{-952} x& = & 111 \\\Leftrightarrow & x = \frac{111}{-952} & & \\\Leftrightarrow & x = \frac{-111}{952} & & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{2}{5})& = & -7x+\frac{6}{13} \\\Leftrightarrow & -12x+\frac{6}{5}& = & -7x+\frac{6}{13} \\ & & & \text{kgv van noemers 5 en 13 is 65} \\\Leftrightarrow & \color{blue}{65} .(-12x+\frac{6}{5})& = & (-7x+\frac{6}{13}). \color{blue}{65} \\\Leftrightarrow & -780x \color{red}{+78} & = & \color{red}{-455x} +30 \\\Leftrightarrow & -780x \color{red}{+78} \color{blue}{-78} \color{blue}{+455x} & = & \color{red}{-455x} +30 \color{blue}{+455x} \color{blue}{-78} \\\Leftrightarrow & -780x+455x& = & 30-78 \\\Leftrightarrow & \color{red}{-325} x& = & -48 \\\Leftrightarrow & x = \frac{-48}{-325} & & \\\Leftrightarrow & x = \frac{48}{325} & & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{9})& = & 8x+\frac{9}{11} \\\Leftrightarrow & 15x+\frac{2}{3}& = & 8x+\frac{9}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(15x+\frac{2}{3})& = & (8x+\frac{9}{11}). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{+22} & = & \color{red}{264x} +27 \\\Leftrightarrow & 495x \color{red}{+22} \color{blue}{-22} \color{blue}{-264x} & = & \color{red}{264x} +27 \color{blue}{-264x} \color{blue}{-22} \\\Leftrightarrow & 495x-264x& = & 27-22 \\\Leftrightarrow & \color{red}{231} x& = & 5 \\\Leftrightarrow & x = \frac{5}{231} & & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{5})& = & x+\frac{3}{10} \\\Leftrightarrow & -10x+\frac{4}{5}& = & x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(-10x+\frac{4}{5})& = & (x+\frac{3}{10}). \color{blue}{10} \\\Leftrightarrow & -100x \color{red}{+8} & = & \color{red}{10x} +3 \\\Leftrightarrow & -100x \color{red}{+8} \color{blue}{-8} \color{blue}{-10x} & = & \color{red}{10x} +3 \color{blue}{-10x} \color{blue}{-8} \\\Leftrightarrow & -100x-10x& = & 3-8 \\\Leftrightarrow & \color{red}{-110} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-110} & & \\\Leftrightarrow & x = \frac{1}{22} & & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-} (-3x+\frac{4}{11})& = & 8x+\frac{8}{15} \\\Leftrightarrow & 3x-\frac{4}{11}& = & 8x+\frac{8}{15} \\ & & & \text{kgv van noemers 11 en 15 is 165} \\\Leftrightarrow & \color{blue}{165} .(3x-\frac{4}{11})& = & (8x+\frac{8}{15}). \color{blue}{165} \\\Leftrightarrow & 495x \color{red}{-60} & = & \color{red}{1320x} +88 \\\Leftrightarrow & 495x \color{red}{-60} \color{blue}{+60} \color{blue}{-1320x} & = & \color{red}{1320x} +88 \color{blue}{-1320x} \color{blue}{+60} \\\Leftrightarrow & 495x-1320x& = & 88+60 \\\Leftrightarrow & \color{red}{-825} x& = & 148 \\\Leftrightarrow & x = \frac{148}{-825} & & \\\Leftrightarrow & x = \frac{-148}{825} & & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{3}{13})& = & x+\frac{3}{4} \\\Leftrightarrow & 20x+\frac{15}{13}& = & x+\frac{3}{4} \\ & & & \text{kgv van noemers 13 en 4 is 52} \\\Leftrightarrow & \color{blue}{52} .(20x+\frac{15}{13})& = & (x+\frac{3}{4}). \color{blue}{52} \\\Leftrightarrow & 1040x \color{red}{+60} & = & \color{red}{52x} +39 \\\Leftrightarrow & 1040x \color{red}{+60} \color{blue}{-60} \color{blue}{-52x} & = & \color{red}{52x} +39 \color{blue}{-52x} \color{blue}{-60} \\\Leftrightarrow & 1040x-52x& = & 39-60 \\\Leftrightarrow & \color{red}{988} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{988} & & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (x+\frac{2}{3})& = & 3x+\frac{7}{13} \\\Leftrightarrow & 2x+\frac{4}{3}& = & 3x+\frac{7}{13} \\ & & & \text{kgv van noemers 3 en 13 is 39} \\\Leftrightarrow & \color{blue}{39} .(2x+\frac{4}{3})& = & (3x+\frac{7}{13}). \color{blue}{39} \\\Leftrightarrow & 78x \color{red}{+52} & = & \color{red}{117x} +21 \\\Leftrightarrow & 78x \color{red}{+52} \color{blue}{-52} \color{blue}{-117x} & = & \color{red}{117x} +21 \color{blue}{-117x} \color{blue}{-52} \\\Leftrightarrow & 78x-117x& = & 21-52 \\\Leftrightarrow & \color{red}{-39} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-39} & & \\\Leftrightarrow & x = \frac{31}{39} & & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{2}{11})& = & 3x+\frac{7}{9} \\\Leftrightarrow & 10x+\frac{4}{11}& = & 3x+\frac{7}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(10x+\frac{4}{11})& = & (3x+\frac{7}{9}). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{+36} & = & \color{red}{297x} +77 \\\Leftrightarrow & 990x \color{red}{+36} \color{blue}{-36} \color{blue}{-297x} & = & \color{red}{297x} +77 \color{blue}{-297x} \color{blue}{-36} \\\Leftrightarrow & 990x-297x& = & 77-36 \\\Leftrightarrow & \color{red}{693} x& = & 41 \\\Leftrightarrow & x = \frac{41}{693} & & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{5}{6})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{5}{2}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(-12x+\frac{5}{2})& = & (-7x+\frac{6}{5}). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{+25} & = & \color{red}{-70x} +12 \\\Leftrightarrow & -120x \color{red}{+25} \color{blue}{-25} \color{blue}{+70x} & = & \color{red}{-70x} +12 \color{blue}{+70x} \color{blue}{-25} \\\Leftrightarrow & -120x+70x& = & 12-25 \\\Leftrightarrow & \color{red}{-50} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-50} & & \\\Leftrightarrow & x = \frac{13}{50} & & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{3}{2})& = & x+\frac{8}{3} \\\Leftrightarrow & -15x+\frac{15}{2}& = & x+\frac{8}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(-15x+\frac{15}{2})& = & (x+\frac{8}{3}). \color{blue}{6} \\\Leftrightarrow & -90x \color{red}{+45} & = & \color{red}{6x} +16 \\\Leftrightarrow & -90x \color{red}{+45} \color{blue}{-45} \color{blue}{-6x} & = & \color{red}{6x} +16 \color{blue}{-6x} \color{blue}{-45} \\\Leftrightarrow & -90x-6x& = & 16-45 \\\Leftrightarrow & \color{red}{-96} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-96} & & \\\Leftrightarrow & x = \frac{29}{96} & & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2021-12-02 00:52:46