Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{4}{7})& = & -3x+\frac{9}{10} \\\Leftrightarrow & 10x-\frac{20}{7}& = & -3x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{700}{ \color{blue}{70} }x- \frac{200}{ \color{blue}{70} })& = & (\frac{-210}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 700x \color{red}{-200} & = & \color{red}{-210x} +63 \\\Leftrightarrow & 700x \color{red}{-200} \color{blue}{+200} \color{blue}{+210x} & = & \color{red}{-210x} +63 \color{blue}{+210x} \color{blue}{+200} \\\Leftrightarrow & 700x+210x& = & 63+200 \\\Leftrightarrow & \color{red}{910} x& = & 263 \\\Leftrightarrow & x = \frac{263}{910} & & \\ & V = \left\{ \frac{263}{910} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{10})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -12x+\frac{9}{10}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1320}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{60}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1320x \color{red}{+99} & = & \color{red}{-550x} +60 \\\Leftrightarrow & -1320x \color{red}{+99} \color{blue}{-99} \color{blue}{+550x} & = & \color{red}{-550x} +60 \color{blue}{+550x} \color{blue}{-99} \\\Leftrightarrow & -1320x+550x& = & 60-99 \\\Leftrightarrow & \color{red}{-770} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{-770} & & \\\Leftrightarrow & x = \frac{39}{770} & & \\ & V = \left\{ \frac{39}{770} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{4}{5})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -8x-\frac{8}{5}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-40}{ \color{blue}{5} }x- \frac{8}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -40x \color{red}{-8} & = & \color{red}{-45x} +6 \\\Leftrightarrow & -40x \color{red}{-8} \color{blue}{+8} \color{blue}{+45x} & = & \color{red}{-45x} +6 \color{blue}{+45x} \color{blue}{+8} \\\Leftrightarrow & -40x+45x& = & 6+8 \\\Leftrightarrow & \color{red}{5} x& = & 14 \\\Leftrightarrow & x = \frac{14}{5} & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{9})& = & 6x+\frac{7}{11} \\\Leftrightarrow & -28x-\frac{28}{9}& = & 6x+\frac{7}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2772}{ \color{blue}{99} }x- \frac{308}{ \color{blue}{99} })& = & (\frac{594}{ \color{blue}{99} }x+ \frac{63}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2772x \color{red}{-308} & = & \color{red}{594x} +63 \\\Leftrightarrow & -2772x \color{red}{-308} \color{blue}{+308} \color{blue}{-594x} & = & \color{red}{594x} +63 \color{blue}{-594x} \color{blue}{+308} \\\Leftrightarrow & -2772x-594x& = & 63+308 \\\Leftrightarrow & \color{red}{-3366} x& = & 371 \\\Leftrightarrow & x = \frac{371}{-3366} & & \\\Leftrightarrow & x = \frac{-371}{3366} & & \\ & V = \left\{ \frac{-371}{3366} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{5}{7})& = & -7x+\frac{6}{7} \\\Leftrightarrow & 10x+\frac{10}{7}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{70}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 70x \color{red}{+10} & = & \color{red}{-49x} +6 \\\Leftrightarrow & 70x \color{red}{+10} \color{blue}{-10} \color{blue}{+49x} & = & \color{red}{-49x} +6 \color{blue}{+49x} \color{blue}{-10} \\\Leftrightarrow & 70x+49x& = & 6-10 \\\Leftrightarrow & \color{red}{119} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{119} & & \\ & V = \left\{ \frac{-4}{119} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{4}{7})& = & 5x+\frac{7}{6} \\\Leftrightarrow & 12x+\frac{16}{7}& = & 5x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{504}{ \color{blue}{42} }x+ \frac{96}{ \color{blue}{42} })& = & (\frac{210}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 504x \color{red}{+96} & = & \color{red}{210x} +49 \\\Leftrightarrow & 504x \color{red}{+96} \color{blue}{-96} \color{blue}{-210x} & = & \color{red}{210x} +49 \color{blue}{-210x} \color{blue}{-96} \\\Leftrightarrow & 504x-210x& = & 49-96 \\\Leftrightarrow & \color{red}{294} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{294} & & \\ & V = \left\{ \frac{-47}{294} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{3}{7})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -12x-\frac{12}{7}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-168}{ \color{blue}{14} }x- \frac{24}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -168x \color{red}{-24} & = & \color{red}{-70x} +21 \\\Leftrightarrow & -168x \color{red}{-24} \color{blue}{+24} \color{blue}{+70x} & = & \color{red}{-70x} +21 \color{blue}{+70x} \color{blue}{+24} \\\Leftrightarrow & -168x+70x& = & 21+24 \\\Leftrightarrow & \color{red}{-98} x& = & 45 \\\Leftrightarrow & x = \frac{45}{-98} & & \\\Leftrightarrow & x = \frac{-45}{98} & & \\ & V = \left\{ \frac{-45}{98} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{2}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{-6} & = & \color{red}{-49x} +10 \\\Leftrightarrow & -42x \color{red}{-6} \color{blue}{+6} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{+6} \\\Leftrightarrow & -42x+49x& = & 10+6 \\\Leftrightarrow & \color{red}{7} x& = & 16 \\\Leftrightarrow & x = \frac{16}{7} & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{8})& = & -9x+\frac{9}{4} \\\Leftrightarrow & 14x+\frac{21}{8}& = & -9x+\frac{9}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{112}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{-72}{ \color{blue}{8} }x+ \frac{18}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 112x \color{red}{+21} & = & \color{red}{-72x} +18 \\\Leftrightarrow & 112x \color{red}{+21} \color{blue}{-21} \color{blue}{+72x} & = & \color{red}{-72x} +18 \color{blue}{+72x} \color{blue}{-21} \\\Leftrightarrow & 112x+72x& = & 18-21 \\\Leftrightarrow & \color{red}{184} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{184} & & \\ & V = \left\{ \frac{-3}{184} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{3}{11})& = & -7x+\frac{3}{10} \\\Leftrightarrow & -20x+\frac{15}{11}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-2200}{ \color{blue}{110} }x+ \frac{150}{ \color{blue}{110} })& = & (\frac{-770}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -2200x \color{red}{+150} & = & \color{red}{-770x} +33 \\\Leftrightarrow & -2200x \color{red}{+150} \color{blue}{-150} \color{blue}{+770x} & = & \color{red}{-770x} +33 \color{blue}{+770x} \color{blue}{-150} \\\Leftrightarrow & -2200x+770x& = & 33-150 \\\Leftrightarrow & \color{red}{-1430} x& = & -117 \\\Leftrightarrow & x = \frac{-117}{-1430} & & \\\Leftrightarrow & x = \frac{9}{110} & & \\ & V = \left\{ \frac{9}{110} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{9})& = & -6x+\frac{2}{7} \\\Leftrightarrow & -35x-\frac{35}{9}& = & -6x+\frac{2}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-2205}{ \color{blue}{63} }x- \frac{245}{ \color{blue}{63} })& = & (\frac{-378}{ \color{blue}{63} }x+ \frac{18}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -2205x \color{red}{-245} & = & \color{red}{-378x} +18 \\\Leftrightarrow & -2205x \color{red}{-245} \color{blue}{+245} \color{blue}{+378x} & = & \color{red}{-378x} +18 \color{blue}{+378x} \color{blue}{+245} \\\Leftrightarrow & -2205x+378x& = & 18+245 \\\Leftrightarrow & \color{red}{-1827} x& = & 263 \\\Leftrightarrow & x = \frac{263}{-1827} & & \\\Leftrightarrow & x = \frac{-263}{1827} & & \\ & V = \left\{ \frac{-263}{1827} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{5}{11})& = & -3x+\frac{8}{7} \\\Leftrightarrow & 28x+\frac{35}{11}& = & -3x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2156}{ \color{blue}{77} }x+ \frac{245}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2156x \color{red}{+245} & = & \color{red}{-231x} +88 \\\Leftrightarrow & 2156x \color{red}{+245} \color{blue}{-245} \color{blue}{+231x} & = & \color{red}{-231x} +88 \color{blue}{+231x} \color{blue}{-245} \\\Leftrightarrow & 2156x+231x& = & 88-245 \\\Leftrightarrow & \color{red}{2387} x& = & -157 \\\Leftrightarrow & x = \frac{-157}{2387} & & \\ & V = \left\{ \frac{-157}{2387} \right\} & \\\end{align}\)
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