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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (-5x+\frac{3}{10})& = & 9x+\frac{7}{3} \\\Leftrightarrow & -5x+\frac{3}{10}& = & 9x+\frac{7}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(-5x+\frac{3}{10})& = & (9x+\frac{7}{3}). \color{blue}{30} \\\Leftrightarrow & -150x \color{red}{+9} & = & \color{red}{270x} +70 \\\Leftrightarrow & -150x \color{red}{+9} \color{blue}{-9} \color{blue}{-270x} & = & \color{red}{270x} +70 \color{blue}{-270x} \color{blue}{-9} \\\Leftrightarrow & -150x-270x& = & 70-9 \\\Leftrightarrow & \color{red}{-420} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-420} & & \\\Leftrightarrow & x = \frac{-61}{420} & & \\ & V = \left\{ \frac{-61}{420} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{5}{2})& = & -3x+\frac{3}{7} \\\Leftrightarrow & 25x-\frac{25}{2}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(25x-\frac{25}{2})& = & (-3x+\frac{3}{7}). \color{blue}{14} \\\Leftrightarrow & 350x \color{red}{-175} & = & \color{red}{-42x} +6 \\\Leftrightarrow & 350x \color{red}{-175} \color{blue}{+175} \color{blue}{+42x} & = & \color{red}{-42x} +6 \color{blue}{+42x} \color{blue}{+175} \\\Leftrightarrow & 350x+42x& = & 6+175 \\\Leftrightarrow & \color{red}{392} x& = & 181 \\\Leftrightarrow & x = \frac{181}{392} & & \\ & V = \left\{ \frac{181}{392} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (x-\frac{5}{3})& = & x+\frac{3}{11} \\\Leftrightarrow & 5x-\frac{25}{3}& = & x+\frac{3}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(5x-\frac{25}{3})& = & (x+\frac{3}{11}). \color{blue}{33} \\\Leftrightarrow & 165x \color{red}{-275} & = & \color{red}{33x} +9 \\\Leftrightarrow & 165x \color{red}{-275} \color{blue}{+275} \color{blue}{-33x} & = & \color{red}{33x} +9 \color{blue}{-33x} \color{blue}{+275} \\\Leftrightarrow & 165x-33x& = & 9+275 \\\Leftrightarrow & \color{red}{132} x& = & 284 \\\Leftrightarrow & x = \frac{284}{132} & & \\\Leftrightarrow & x = \frac{71}{33} & & \\ & V = \left\{ \frac{71}{33} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (x+\frac{2}{9})& = & -3x+\frac{4}{3} \\\Leftrightarrow & 4x+\frac{8}{9}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(4x+\frac{8}{9})& = & (-3x+\frac{4}{3}). \color{blue}{9} \\\Leftrightarrow & 36x \color{red}{+8} & = & \color{red}{-27x} +12 \\\Leftrightarrow & 36x \color{red}{+8} \color{blue}{-8} \color{blue}{+27x} & = & \color{red}{-27x} +12 \color{blue}{+27x} \color{blue}{-8} \\\Leftrightarrow & 36x+27x& = & 12-8 \\\Leftrightarrow & \color{red}{63} x& = & 4 \\\Leftrightarrow & x = \frac{4}{63} & & \\ & V = \left\{ \frac{4}{63} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-} (-3x+\frac{3}{16})& = & 4x+\frac{8}{3} \\\Leftrightarrow & 3x-\frac{3}{16}& = & 4x+\frac{8}{3} \\ & & & \text{kgv van noemers 16 en 3 is 48} \\\Leftrightarrow & \color{blue}{48} .(3x-\frac{3}{16})& = & (4x+\frac{8}{3}). \color{blue}{48} \\\Leftrightarrow & 144x \color{red}{-9} & = & \color{red}{192x} +128 \\\Leftrightarrow & 144x \color{red}{-9} \color{blue}{+9} \color{blue}{-192x} & = & \color{red}{192x} +128 \color{blue}{-192x} \color{blue}{+9} \\\Leftrightarrow & 144x-192x& = & 128+9 \\\Leftrightarrow & \color{red}{-48} x& = & 137 \\\Leftrightarrow & x = \frac{137}{-48} & & \\\Leftrightarrow & x = \frac{-137}{48} & & \\ & V = \left\{ \frac{-137}{48} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{3}{7})& = & 9x+\frac{6}{5} \\\Leftrightarrow & 28x+3& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 1 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(28x+3)& = & (9x+\frac{6}{5}). \color{blue}{5} \\\Leftrightarrow & 140x \color{red}{+15} & = & \color{red}{45x} +6 \\\Leftrightarrow & 140x \color{red}{+15} \color{blue}{-15} \color{blue}{-45x} & = & \color{red}{45x} +6 \color{blue}{-45x} \color{blue}{-15} \\\Leftrightarrow & 140x-45x& = & 6-15 \\\Leftrightarrow & \color{red}{95} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{95} & & \\ & V = \left\{ \frac{-9}{95} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-x-\frac{5}{13})& = & 4x+\frac{7}{5} \\\Leftrightarrow & -5x-\frac{25}{13}& = & 4x+\frac{7}{5} \\ & & & \text{kgv van noemers 13 en 5 is 65} \\\Leftrightarrow & \color{blue}{65} .(-5x-\frac{25}{13})& = & (4x+\frac{7}{5}). \color{blue}{65} \\\Leftrightarrow & -325x \color{red}{-125} & = & \color{red}{260x} +91 \\\Leftrightarrow & -325x \color{red}{-125} \color{blue}{+125} \color{blue}{-260x} & = & \color{red}{260x} +91 \color{blue}{-260x} \color{blue}{+125} \\\Leftrightarrow & -325x-260x& = & 91+125 \\\Leftrightarrow & \color{red}{-585} x& = & 216 \\\Leftrightarrow & x = \frac{216}{-585} & & \\\Leftrightarrow & x = \frac{-24}{65} & & \\ & V = \left\{ \frac{-24}{65} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-x-\frac{4}{15})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 6x+\frac{8}{5}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(6x+\frac{8}{5})& = & (7x+\frac{9}{2}). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{+16} & = & \color{red}{70x} +45 \\\Leftrightarrow & 60x \color{red}{+16} \color{blue}{-16} \color{blue}{-70x} & = & \color{red}{70x} +45 \color{blue}{-70x} \color{blue}{-16} \\\Leftrightarrow & 60x-70x& = & 45-16 \\\Leftrightarrow & \color{red}{-10} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-10} & & \\\Leftrightarrow & x = \frac{-29}{10} & & \\ & V = \left\{ \frac{-29}{10} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{2}{13})& = & 7x+\frac{5}{7} \\\Leftrightarrow & -6x+\frac{6}{13}& = & 7x+\frac{5}{7} \\ & & & \text{kgv van noemers 13 en 7 is 91} \\\Leftrightarrow & \color{blue}{91} .(-6x+\frac{6}{13})& = & (7x+\frac{5}{7}). \color{blue}{91} \\\Leftrightarrow & -546x \color{red}{+42} & = & \color{red}{637x} +65 \\\Leftrightarrow & -546x \color{red}{+42} \color{blue}{-42} \color{blue}{-637x} & = & \color{red}{637x} +65 \color{blue}{-637x} \color{blue}{-42} \\\Leftrightarrow & -546x-637x& = & 65-42 \\\Leftrightarrow & \color{red}{-1183} x& = & 23 \\\Leftrightarrow & x = \frac{23}{-1183} & & \\\Leftrightarrow & x = \frac{-23}{1183} & & \\ & V = \left\{ \frac{-23}{1183} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{3}{11})& = & -3x+\frac{4}{7} \\\Leftrightarrow & -10x-\frac{6}{11}& = & -3x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(-10x-\frac{6}{11})& = & (-3x+\frac{4}{7}). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{-42} & = & \color{red}{-231x} +44 \\\Leftrightarrow & -770x \color{red}{-42} \color{blue}{+42} \color{blue}{+231x} & = & \color{red}{-231x} +44 \color{blue}{+231x} \color{blue}{+42} \\\Leftrightarrow & -770x+231x& = & 44+42 \\\Leftrightarrow & \color{red}{-539} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-539} & & \\\Leftrightarrow & x = \frac{-86}{539} & & \\ & V = \left\{ \frac{-86}{539} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (x+\frac{4}{5})& = & 8x+\frac{5}{14} \\\Leftrightarrow & -7x-\frac{28}{5}& = & 8x+\frac{5}{14} \\ & & & \text{kgv van noemers 5 en 14 is 70} \\\Leftrightarrow & \color{blue}{70} .(-7x-\frac{28}{5})& = & (8x+\frac{5}{14}). \color{blue}{70} \\\Leftrightarrow & -490x \color{red}{-392} & = & \color{red}{560x} +25 \\\Leftrightarrow & -490x \color{red}{-392} \color{blue}{+392} \color{blue}{-560x} & = & \color{red}{560x} +25 \color{blue}{-560x} \color{blue}{+392} \\\Leftrightarrow & -490x-560x& = & 25+392 \\\Leftrightarrow & \color{red}{-1050} x& = & 417 \\\Leftrightarrow & x = \frac{417}{-1050} & & \\\Leftrightarrow & x = \frac{-139}{350} & & \\ & V = \left\{ \frac{-139}{350} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{4}{13})& = & 3x+\frac{2}{9} \\\Leftrightarrow & 10x-\frac{8}{13}& = & 3x+\frac{2}{9} \\ & & & \text{kgv van noemers 13 en 9 is 117} \\\Leftrightarrow & \color{blue}{117} .(10x-\frac{8}{13})& = & (3x+\frac{2}{9}). \color{blue}{117} \\\Leftrightarrow & 1170x \color{red}{-72} & = & \color{red}{351x} +26 \\\Leftrightarrow & 1170x \color{red}{-72} \color{blue}{+72} \color{blue}{-351x} & = & \color{red}{351x} +26 \color{blue}{-351x} \color{blue}{+72} \\\Leftrightarrow & 1170x-351x& = & 26+72 \\\Leftrightarrow & \color{red}{819} x& = & 98 \\\Leftrightarrow & x = \frac{98}{819} & & \\\Leftrightarrow & x = \frac{14}{117} & & \\ & V = \left\{ \frac{14}{117} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-05-03 10:56:12