Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{4}{5})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 8x-\frac{8}{5}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(8x-\frac{8}{5})& = & (-5x+\frac{4}{3}). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{-24} & = & \color{red}{-75x} +20 \\\Leftrightarrow & 120x \color{red}{-24} \color{blue}{+24} \color{blue}{+75x} & = & \color{red}{-75x} +20 \color{blue}{+75x} \color{blue}{+24} \\\Leftrightarrow & 120x+75x& = & 20+24 \\\Leftrightarrow & \color{red}{195} x& = & 44 \\\Leftrightarrow & x = \frac{44}{195} & & \\ & V = \left\{ \frac{44}{195} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{3})& = & -3x+\frac{6}{7} \\\Leftrightarrow & -10x-\frac{8}{3}& = & -3x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(-10x-\frac{8}{3})& = & (-3x+\frac{6}{7}). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-56} & = & \color{red}{-63x} +18 \\\Leftrightarrow & -210x \color{red}{-56} \color{blue}{+56} \color{blue}{+63x} & = & \color{red}{-63x} +18 \color{blue}{+63x} \color{blue}{+56} \\\Leftrightarrow & -210x+63x& = & 18+56 \\\Leftrightarrow & \color{red}{-147} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-147} & & \\\Leftrightarrow & x = \frac{-74}{147} & & \\ & V = \left\{ \frac{-74}{147} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (x+\frac{5}{14})& = & 7x+\frac{6}{7} \\\Leftrightarrow & 2x+\frac{5}{7}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(2x+\frac{5}{7})& = & (7x+\frac{6}{7}). \color{blue}{7} \\\Leftrightarrow & 14x \color{red}{+5} & = & \color{red}{49x} +6 \\\Leftrightarrow & 14x \color{red}{+5} \color{blue}{-5} \color{blue}{-49x} & = & \color{red}{49x} +6 \color{blue}{-49x} \color{blue}{-5} \\\Leftrightarrow & 14x-49x& = & 6-5 \\\Leftrightarrow & \color{red}{-35} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-35} & & \\\Leftrightarrow & x = \frac{-1}{35} & & \\ & V = \left\{ \frac{-1}{35} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{2}{3})& = & 7x+\frac{7}{4} \\\Leftrightarrow & -8x-\frac{8}{3}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(-8x-\frac{8}{3})& = & (7x+\frac{7}{4}). \color{blue}{12} \\\Leftrightarrow & -96x \color{red}{-32} & = & \color{red}{84x} +21 \\\Leftrightarrow & -96x \color{red}{-32} \color{blue}{+32} \color{blue}{-84x} & = & \color{red}{84x} +21 \color{blue}{-84x} \color{blue}{+32} \\\Leftrightarrow & -96x-84x& = & 21+32 \\\Leftrightarrow & \color{red}{-180} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-180} & & \\\Leftrightarrow & x = \frac{-53}{180} & & \\ & V = \left\{ \frac{-53}{180} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{5}{3})& = & 6x+\frac{2}{13} \\\Leftrightarrow & 35x+\frac{35}{3}& = & 6x+\frac{2}{13} \\ & & & \text{kgv van noemers 3 en 13 is 39} \\\Leftrightarrow & \color{blue}{39} .(35x+\frac{35}{3})& = & (6x+\frac{2}{13}). \color{blue}{39} \\\Leftrightarrow & 1365x \color{red}{+455} & = & \color{red}{234x} +6 \\\Leftrightarrow & 1365x \color{red}{+455} \color{blue}{-455} \color{blue}{-234x} & = & \color{red}{234x} +6 \color{blue}{-234x} \color{blue}{-455} \\\Leftrightarrow & 1365x-234x& = & 6-455 \\\Leftrightarrow & \color{red}{1131} x& = & -449 \\\Leftrightarrow & x = \frac{-449}{1131} & & \\ & V = \left\{ \frac{-449}{1131} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{4}{3})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 6x+4& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 1 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(6x+4)& = & (5x+\frac{10}{7}). \color{blue}{7} \\\Leftrightarrow & 42x \color{red}{+28} & = & \color{red}{35x} +10 \\\Leftrightarrow & 42x \color{red}{+28} \color{blue}{-28} \color{blue}{-35x} & = & \color{red}{35x} +10 \color{blue}{-35x} \color{blue}{-28} \\\Leftrightarrow & 42x-35x& = & 10-28 \\\Leftrightarrow & \color{red}{7} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{7} & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{4}{11})& = & 10x+\frac{7}{3} \\\Leftrightarrow & 9x-\frac{12}{11}& = & 10x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(9x-\frac{12}{11})& = & (10x+\frac{7}{3}). \color{blue}{33} \\\Leftrightarrow & 297x \color{red}{-36} & = & \color{red}{330x} +77 \\\Leftrightarrow & 297x \color{red}{-36} \color{blue}{+36} \color{blue}{-330x} & = & \color{red}{330x} +77 \color{blue}{-330x} \color{blue}{+36} \\\Leftrightarrow & 297x-330x& = & 77+36 \\\Leftrightarrow & \color{red}{-33} x& = & 113 \\\Leftrightarrow & x = \frac{113}{-33} & & \\\Leftrightarrow & x = \frac{-113}{33} & & \\ & V = \left\{ \frac{-113}{33} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (x+\frac{4}{9})& = & 2x+\frac{3}{14} \\\Leftrightarrow & 7x+\frac{28}{9}& = & 2x+\frac{3}{14} \\ & & & \text{kgv van noemers 9 en 14 is 126} \\\Leftrightarrow & \color{blue}{126} .(7x+\frac{28}{9})& = & (2x+\frac{3}{14}). \color{blue}{126} \\\Leftrightarrow & 882x \color{red}{+392} & = & \color{red}{252x} +27 \\\Leftrightarrow & 882x \color{red}{+392} \color{blue}{-392} \color{blue}{-252x} & = & \color{red}{252x} +27 \color{blue}{-252x} \color{blue}{-392} \\\Leftrightarrow & 882x-252x& = & 27-392 \\\Leftrightarrow & \color{red}{630} x& = & -365 \\\Leftrightarrow & x = \frac{-365}{630} & & \\\Leftrightarrow & x = \frac{-73}{126} & & \\ & V = \left\{ \frac{-73}{126} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{5}{4})& = & -9x+\frac{3}{8} \\\Leftrightarrow & 10x-\frac{5}{2}& = & -9x+\frac{3}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(10x-\frac{5}{2})& = & (-9x+\frac{3}{8}). \color{blue}{8} \\\Leftrightarrow & 80x \color{red}{-20} & = & \color{red}{-72x} +3 \\\Leftrightarrow & 80x \color{red}{-20} \color{blue}{+20} \color{blue}{+72x} & = & \color{red}{-72x} +3 \color{blue}{+72x} \color{blue}{+20} \\\Leftrightarrow & 80x+72x& = & 3+20 \\\Leftrightarrow & \color{red}{152} x& = & 23 \\\Leftrightarrow & x = \frac{23}{152} & & \\ & V = \left\{ \frac{23}{152} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{3}{13})& = & x+\frac{6}{13} \\\Leftrightarrow & 12x+\frac{9}{13}& = & x+\frac{6}{13} \\ & & & \text{kgv van noemers 13 en 13 is 13} \\\Leftrightarrow & \color{blue}{13} .(12x+\frac{9}{13})& = & (x+\frac{6}{13}). \color{blue}{13} \\\Leftrightarrow & 156x \color{red}{+9} & = & \color{red}{13x} +6 \\\Leftrightarrow & 156x \color{red}{+9} \color{blue}{-9} \color{blue}{-13x} & = & \color{red}{13x} +6 \color{blue}{-13x} \color{blue}{-9} \\\Leftrightarrow & 156x-13x& = & 6-9 \\\Leftrightarrow & \color{red}{143} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{143} & & \\ & V = \left\{ \frac{-3}{143} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (x+\frac{3}{13})& = & 7x+\frac{3}{10} \\\Leftrightarrow & -4x-\frac{12}{13}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 13 en 10 is 130} \\\Leftrightarrow & \color{blue}{130} .(-4x-\frac{12}{13})& = & (7x+\frac{3}{10}). \color{blue}{130} \\\Leftrightarrow & -520x \color{red}{-120} & = & \color{red}{910x} +39 \\\Leftrightarrow & -520x \color{red}{-120} \color{blue}{+120} \color{blue}{-910x} & = & \color{red}{910x} +39 \color{blue}{-910x} \color{blue}{+120} \\\Leftrightarrow & -520x-910x& = & 39+120 \\\Leftrightarrow & \color{red}{-1430} x& = & 159 \\\Leftrightarrow & x = \frac{159}{-1430} & & \\\Leftrightarrow & x = \frac{-159}{1430} & & \\ & V = \left\{ \frac{-159}{1430} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (x+\frac{3}{4})& = & x+\frac{4}{15} \\\Leftrightarrow & 4x+3& = & x+\frac{4}{15} \\ & & & \text{kgv van noemers 1 en 15 is 15} \\\Leftrightarrow & \color{blue}{15} .(4x+3)& = & (x+\frac{4}{15}). \color{blue}{15} \\\Leftrightarrow & 60x \color{red}{+45} & = & \color{red}{15x} +4 \\\Leftrightarrow & 60x \color{red}{+45} \color{blue}{-45} \color{blue}{-15x} & = & \color{red}{15x} +4 \color{blue}{-15x} \color{blue}{-45} \\\Leftrightarrow & 60x-15x& = & 4-45 \\\Leftrightarrow & \color{red}{45} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{45} & & \\ & V = \left\{ \frac{-41}{45} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-04-23 22:37:31