Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

  1. \(3(x+\frac{5}{14})=5x+\frac{3}{4}\)
  2. \((2x+\frac{2}{15})=7x+\frac{5}{16}\)
  3. \(7(-4x+\frac{3}{11})=9x+\frac{8}{11}\)
  4. \(-(2x-\frac{4}{15})=x+\frac{7}{12}\)
  5. \(-5(-4x-\frac{4}{7})=19x+\frac{10}{11}\)
  6. \((-5x-\frac{5}{12})=9x+\frac{7}{8}\)
  7. \(3(-4x+\frac{5}{7})=11x+\frac{2}{11}\)
  8. \(3(-2x-\frac{4}{5})=7x+\frac{3}{11}\)
  9. \(-3(-3x+\frac{3}{16})=5x+\frac{10}{7}\)
  10. \(-2(-2x-\frac{4}{13})=5x+\frac{5}{16}\)
  11. \(-2(-x+\frac{2}{13})=5x+\frac{10}{9}\)
  12. \(3(4x-\frac{4}{5})=5x+\frac{9}{2}\)

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (x+\frac{5}{14})& = & 5x+\frac{3}{4} \\\Leftrightarrow & 3x+\frac{15}{14}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 14 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(3x+\frac{15}{14})& = & (5x+\frac{3}{4}). \color{blue}{28} \\\Leftrightarrow & 84x \color{red}{+30} & = & \color{red}{140x} +21 \\\Leftrightarrow & 84x \color{red}{+30} \color{blue}{-30} \color{blue}{-140x} & = & \color{red}{140x} +21 \color{blue}{-140x} \color{blue}{-30} \\\Leftrightarrow & 84x-140x& = & 21-30 \\\Leftrightarrow & \color{red}{-56} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-56} & & \\\Leftrightarrow & x = \frac{9}{56} & & \\ & V = \left\{ \frac{9}{56} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (2x+\frac{2}{15})& = & 7x+\frac{5}{16} \\\Leftrightarrow & 2x+\frac{2}{15}& = & 7x+\frac{5}{16} \\ & & & \text{kgv van noemers 15 en 16 is 240} \\\Leftrightarrow & \color{blue}{240} .(2x+\frac{2}{15})& = & (7x+\frac{5}{16}). \color{blue}{240} \\\Leftrightarrow & 480x \color{red}{+32} & = & \color{red}{1680x} +75 \\\Leftrightarrow & 480x \color{red}{+32} \color{blue}{-32} \color{blue}{-1680x} & = & \color{red}{1680x} +75 \color{blue}{-1680x} \color{blue}{-32} \\\Leftrightarrow & 480x-1680x& = & 75-32 \\\Leftrightarrow & \color{red}{-1200} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-1200} & & \\\Leftrightarrow & x = \frac{-43}{1200} & & \\ & V = \left\{ \frac{-43}{1200} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{11})& = & 9x+\frac{8}{11} \\\Leftrightarrow & -28x+\frac{21}{11}& = & 9x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(-28x+\frac{21}{11})& = & (9x+\frac{8}{11}). \color{blue}{11} \\\Leftrightarrow & -308x \color{red}{+21} & = & \color{red}{99x} +8 \\\Leftrightarrow & -308x \color{red}{+21} \color{blue}{-21} \color{blue}{-99x} & = & \color{red}{99x} +8 \color{blue}{-99x} \color{blue}{-21} \\\Leftrightarrow & -308x-99x& = & 8-21 \\\Leftrightarrow & \color{red}{-407} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-407} & & \\\Leftrightarrow & x = \frac{13}{407} & & \\ & V = \left\{ \frac{13}{407} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-} (2x-\frac{4}{15})& = & x+\frac{7}{12} \\\Leftrightarrow & -2x+\frac{4}{15}& = & x+\frac{7}{12} \\ & & & \text{kgv van noemers 15 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(-2x+\frac{4}{15})& = & (x+\frac{7}{12}). \color{blue}{60} \\\Leftrightarrow & -120x \color{red}{+16} & = & \color{red}{60x} +35 \\\Leftrightarrow & -120x \color{red}{+16} \color{blue}{-16} \color{blue}{-60x} & = & \color{red}{60x} +35 \color{blue}{-60x} \color{blue}{-16} \\\Leftrightarrow & -120x-60x& = & 35-16 \\\Leftrightarrow & \color{red}{-180} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-180} & & \\\Leftrightarrow & x = \frac{-19}{180} & & \\ & V = \left\{ \frac{-19}{180} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{7})& = & 19x+\frac{10}{11} \\\Leftrightarrow & 20x+\frac{20}{7}& = & 19x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(20x+\frac{20}{7})& = & (19x+\frac{10}{11}). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{+220} & = & \color{red}{1463x} +70 \\\Leftrightarrow & 1540x \color{red}{+220} \color{blue}{-220} \color{blue}{-1463x} & = & \color{red}{1463x} +70 \color{blue}{-1463x} \color{blue}{-220} \\\Leftrightarrow & 1540x-1463x& = & 70-220 \\\Leftrightarrow & \color{red}{77} x& = & -150 \\\Leftrightarrow & x = \frac{-150}{77} & & \\ & V = \left\{ \frac{-150}{77} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (-5x-\frac{5}{12})& = & 9x+\frac{7}{8} \\\Leftrightarrow & -5x-\frac{5}{12}& = & 9x+\frac{7}{8} \\ & & & \text{kgv van noemers 12 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(-5x-\frac{5}{12})& = & (9x+\frac{7}{8}). \color{blue}{24} \\\Leftrightarrow & -120x \color{red}{-10} & = & \color{red}{216x} +21 \\\Leftrightarrow & -120x \color{red}{-10} \color{blue}{+10} \color{blue}{-216x} & = & \color{red}{216x} +21 \color{blue}{-216x} \color{blue}{+10} \\\Leftrightarrow & -120x-216x& = & 21+10 \\\Leftrightarrow & \color{red}{-336} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-336} & & \\\Leftrightarrow & x = \frac{-31}{336} & & \\ & V = \left\{ \frac{-31}{336} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{5}{7})& = & 11x+\frac{2}{11} \\\Leftrightarrow & -12x+\frac{15}{7}& = & 11x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(-12x+\frac{15}{7})& = & (11x+\frac{2}{11}). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+165} & = & \color{red}{847x} +14 \\\Leftrightarrow & -924x \color{red}{+165} \color{blue}{-165} \color{blue}{-847x} & = & \color{red}{847x} +14 \color{blue}{-847x} \color{blue}{-165} \\\Leftrightarrow & -924x-847x& = & 14-165 \\\Leftrightarrow & \color{red}{-1771} x& = & -151 \\\Leftrightarrow & x = \frac{-151}{-1771} & & \\\Leftrightarrow & x = \frac{151}{1771} & & \\ & V = \left\{ \frac{151}{1771} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{4}{5})& = & 7x+\frac{3}{11} \\\Leftrightarrow & -6x-\frac{12}{5}& = & 7x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(-6x-\frac{12}{5})& = & (7x+\frac{3}{11}). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{-132} & = & \color{red}{385x} +15 \\\Leftrightarrow & -330x \color{red}{-132} \color{blue}{+132} \color{blue}{-385x} & = & \color{red}{385x} +15 \color{blue}{-385x} \color{blue}{+132} \\\Leftrightarrow & -330x-385x& = & 15+132 \\\Leftrightarrow & \color{red}{-715} x& = & 147 \\\Leftrightarrow & x = \frac{147}{-715} & & \\\Leftrightarrow & x = \frac{-147}{715} & & \\ & V = \left\{ \frac{-147}{715} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{3}{16})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 9x-\frac{9}{16}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 16 en 7 is 112} \\\Leftrightarrow & \color{blue}{112} .(9x-\frac{9}{16})& = & (5x+\frac{10}{7}). \color{blue}{112} \\\Leftrightarrow & 1008x \color{red}{-63} & = & \color{red}{560x} +160 \\\Leftrightarrow & 1008x \color{red}{-63} \color{blue}{+63} \color{blue}{-560x} & = & \color{red}{560x} +160 \color{blue}{-560x} \color{blue}{+63} \\\Leftrightarrow & 1008x-560x& = & 160+63 \\\Leftrightarrow & \color{red}{448} x& = & 223 \\\Leftrightarrow & x = \frac{223}{448} & & \\ & V = \left\{ \frac{223}{448} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{4}{13})& = & 5x+\frac{5}{16} \\\Leftrightarrow & 4x+\frac{8}{13}& = & 5x+\frac{5}{16} \\ & & & \text{kgv van noemers 13 en 16 is 208} \\\Leftrightarrow & \color{blue}{208} .(4x+\frac{8}{13})& = & (5x+\frac{5}{16}). \color{blue}{208} \\\Leftrightarrow & 832x \color{red}{+128} & = & \color{red}{1040x} +65 \\\Leftrightarrow & 832x \color{red}{+128} \color{blue}{-128} \color{blue}{-1040x} & = & \color{red}{1040x} +65 \color{blue}{-1040x} \color{blue}{-128} \\\Leftrightarrow & 832x-1040x& = & 65-128 \\\Leftrightarrow & \color{red}{-208} x& = & -63 \\\Leftrightarrow & x = \frac{-63}{-208} & & \\\Leftrightarrow & x = \frac{63}{208} & & \\ & V = \left\{ \frac{63}{208} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-x+\frac{2}{13})& = & 5x+\frac{10}{9} \\\Leftrightarrow & 2x-\frac{4}{13}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 13 en 9 is 117} \\\Leftrightarrow & \color{blue}{117} .(2x-\frac{4}{13})& = & (5x+\frac{10}{9}). \color{blue}{117} \\\Leftrightarrow & 234x \color{red}{-36} & = & \color{red}{585x} +130 \\\Leftrightarrow & 234x \color{red}{-36} \color{blue}{+36} \color{blue}{-585x} & = & \color{red}{585x} +130 \color{blue}{-585x} \color{blue}{+36} \\\Leftrightarrow & 234x-585x& = & 130+36 \\\Leftrightarrow & \color{red}{-351} x& = & 166 \\\Leftrightarrow & x = \frac{166}{-351} & & \\\Leftrightarrow & x = \frac{-166}{351} & & \\ & V = \left\{ \frac{-166}{351} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(12x-\frac{12}{5})& = & (5x+\frac{9}{2}). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-24} & = & \color{red}{50x} +45 \\\Leftrightarrow & 120x \color{red}{-24} \color{blue}{+24} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{+24} \\\Leftrightarrow & 120x-50x& = & 45+24 \\\Leftrightarrow & \color{red}{70} x& = & 69 \\\Leftrightarrow & x = \frac{69}{70} & & \\ & V = \left\{ \frac{69}{70} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-05-19 05:48:09