Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{6})& = & 3x+\frac{2}{3} \\\Leftrightarrow & 10x+\frac{25}{6}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{60}{ \color{blue}{6} }x+ \frac{25}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 60x \color{red}{+25} & = & \color{red}{18x} +4 \\\Leftrightarrow & 60x \color{red}{+25} \color{blue}{-25} \color{blue}{-18x} & = & \color{red}{18x} +4 \color{blue}{-18x} \color{blue}{-25} \\\Leftrightarrow & 60x-18x& = & 4-25 \\\Leftrightarrow & \color{red}{42} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{42} & & \\\Leftrightarrow & x = \frac{-1}{2} & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{5}{11})& = & -5x+\frac{4}{9} \\\Leftrightarrow & 6x+\frac{10}{11}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{594}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 594x \color{red}{+90} & = & \color{red}{-495x} +44 \\\Leftrightarrow & 594x \color{red}{+90} \color{blue}{-90} \color{blue}{+495x} & = & \color{red}{-495x} +44 \color{blue}{+495x} \color{blue}{-90} \\\Leftrightarrow & 594x+495x& = & 44-90 \\\Leftrightarrow & \color{red}{1089} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{1089} & & \\ & V = \left\{ \frac{-46}{1089} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{3})& = & 7x+\frac{5}{9} \\\Leftrightarrow & 20x+\frac{25}{3}& = & 7x+\frac{5}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{75}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+75} & = & \color{red}{63x} +5 \\\Leftrightarrow & 180x \color{red}{+75} \color{blue}{-75} \color{blue}{-63x} & = & \color{red}{63x} +5 \color{blue}{-63x} \color{blue}{-75} \\\Leftrightarrow & 180x-63x& = & 5-75 \\\Leftrightarrow & \color{red}{117} x& = & -70 \\\Leftrightarrow & x = \frac{-70}{117} & & \\ & V = \left\{ \frac{-70}{117} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{4}{7})& = & 6x+\frac{3}{2} \\\Leftrightarrow & -25x+\frac{20}{7}& = & 6x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-350}{ \color{blue}{14} }x+ \frac{40}{ \color{blue}{14} })& = & (\frac{84}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -350x \color{red}{+40} & = & \color{red}{84x} +21 \\\Leftrightarrow & -350x \color{red}{+40} \color{blue}{-40} \color{blue}{-84x} & = & \color{red}{84x} +21 \color{blue}{-84x} \color{blue}{-40} \\\Leftrightarrow & -350x-84x& = & 21-40 \\\Leftrightarrow & \color{red}{-434} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{-434} & & \\\Leftrightarrow & x = \frac{19}{434} & & \\ & V = \left\{ \frac{19}{434} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{2}{5})& = & 7x+\frac{2}{9} \\\Leftrightarrow & -10x+\frac{4}{5}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-450}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -450x \color{red}{+36} & = & \color{red}{315x} +10 \\\Leftrightarrow & -450x \color{red}{+36} \color{blue}{-36} \color{blue}{-315x} & = & \color{red}{315x} +10 \color{blue}{-315x} \color{blue}{-36} \\\Leftrightarrow & -450x-315x& = & 10-36 \\\Leftrightarrow & \color{red}{-765} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-765} & & \\\Leftrightarrow & x = \frac{26}{765} & & \\ & V = \left\{ \frac{26}{765} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{5}{9})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -10x-\frac{25}{9}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-450}{ \color{blue}{45} }x- \frac{125}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -450x \color{red}{-125} & = & \color{red}{315x} +54 \\\Leftrightarrow & -450x \color{red}{-125} \color{blue}{+125} \color{blue}{-315x} & = & \color{red}{315x} +54 \color{blue}{-315x} \color{blue}{+125} \\\Leftrightarrow & -450x-315x& = & 54+125 \\\Leftrightarrow & \color{red}{-765} x& = & 179 \\\Leftrightarrow & x = \frac{179}{-765} & & \\\Leftrightarrow & x = \frac{-179}{765} & & \\ & V = \left\{ \frac{-179}{765} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{5}{3})& = & -2x+\frac{4}{7} \\\Leftrightarrow & 21x-\frac{35}{3}& = & -2x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{441}{ \color{blue}{21} }x- \frac{245}{ \color{blue}{21} })& = & (\frac{-42}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 441x \color{red}{-245} & = & \color{red}{-42x} +12 \\\Leftrightarrow & 441x \color{red}{-245} \color{blue}{+245} \color{blue}{+42x} & = & \color{red}{-42x} +12 \color{blue}{+42x} \color{blue}{+245} \\\Leftrightarrow & 441x+42x& = & 12+245 \\\Leftrightarrow & \color{red}{483} x& = & 257 \\\Leftrightarrow & x = \frac{257}{483} & & \\ & V = \left\{ \frac{257}{483} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{3}{11})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 12x+\frac{12}{11}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{+12} & = & \color{red}{55x} +6 \\\Leftrightarrow & 132x \color{red}{+12} \color{blue}{-12} \color{blue}{-55x} & = & \color{red}{55x} +6 \color{blue}{-55x} \color{blue}{-12} \\\Leftrightarrow & 132x-55x& = & 6-12 \\\Leftrightarrow & \color{red}{77} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{77} & & \\ & V = \left\{ \frac{-6}{77} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{4}{5})& = & -5x+\frac{9}{10} \\\Leftrightarrow & -12x-\frac{24}{5}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x- \frac{48}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{-48} & = & \color{red}{-50x} +9 \\\Leftrightarrow & -120x \color{red}{-48} \color{blue}{+48} \color{blue}{+50x} & = & \color{red}{-50x} +9 \color{blue}{+50x} \color{blue}{+48} \\\Leftrightarrow & -120x+50x& = & 9+48 \\\Leftrightarrow & \color{red}{-70} x& = & 57 \\\Leftrightarrow & x = \frac{57}{-70} & & \\\Leftrightarrow & x = \frac{-57}{70} & & \\ & V = \left\{ \frac{-57}{70} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{11})& = & -3x+\frac{7}{2} \\\Leftrightarrow & 16x+\frac{8}{11}& = & -3x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{352}{ \color{blue}{22} }x+ \frac{16}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 352x \color{red}{+16} & = & \color{red}{-66x} +77 \\\Leftrightarrow & 352x \color{red}{+16} \color{blue}{-16} \color{blue}{+66x} & = & \color{red}{-66x} +77 \color{blue}{+66x} \color{blue}{-16} \\\Leftrightarrow & 352x+66x& = & 77-16 \\\Leftrightarrow & \color{red}{418} x& = & 61 \\\Leftrightarrow & x = \frac{61}{418} & & \\ & V = \left\{ \frac{61}{418} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{4}{3})& = & 8x+\frac{6}{5} \\\Leftrightarrow & -15x+\frac{20}{3}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{+100} & = & \color{red}{120x} +18 \\\Leftrightarrow & -225x \color{red}{+100} \color{blue}{-100} \color{blue}{-120x} & = & \color{red}{120x} +18 \color{blue}{-120x} \color{blue}{-100} \\\Leftrightarrow & -225x-120x& = & 18-100 \\\Leftrightarrow & \color{red}{-345} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-345} & & \\\Leftrightarrow & x = \frac{82}{345} & & \\ & V = \left\{ \frac{82}{345} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{5})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -4x+\frac{4}{5}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-60}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -60x \color{red}{+12} & = & \color{red}{75x} +40 \\\Leftrightarrow & -60x \color{red}{+12} \color{blue}{-12} \color{blue}{-75x} & = & \color{red}{75x} +40 \color{blue}{-75x} \color{blue}{-12} \\\Leftrightarrow & -60x-75x& = & 40-12 \\\Leftrightarrow & \color{red}{-135} x& = & 28 \\\Leftrightarrow & x = \frac{28}{-135} & & \\\Leftrightarrow & x = \frac{-28}{135} & & \\ & V = \left\{ \frac{-28}{135} \right\} & \\\end{align}\)
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