Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{2}{3})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -12x-\frac{8}{3}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-36}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -36x \color{red}{-8} & = & \color{red}{15x} +4 \\\Leftrightarrow & -36x \color{red}{-8} \color{blue}{+8} \color{blue}{-15x} & = & \color{red}{15x} +4 \color{blue}{-15x} \color{blue}{+8} \\\Leftrightarrow & -36x-15x& = & 4+8 \\\Leftrightarrow & \color{red}{-51} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-51} & & \\\Leftrightarrow & x = \frac{-4}{17} & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{2}{3})& = & 9x+\frac{9}{2} \\\Leftrightarrow & -35x+\frac{14}{3}& = & 9x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-210}{ \color{blue}{6} }x+ \frac{28}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -210x \color{red}{+28} & = & \color{red}{54x} +27 \\\Leftrightarrow & -210x \color{red}{+28} \color{blue}{-28} \color{blue}{-54x} & = & \color{red}{54x} +27 \color{blue}{-54x} \color{blue}{-28} \\\Leftrightarrow & -210x-54x& = & 27-28 \\\Leftrightarrow & \color{red}{-264} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-264} & & \\\Leftrightarrow & x = \frac{1}{264} & & \\ & V = \left\{ \frac{1}{264} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{2}{5})& = & 3x+\frac{3}{8} \\\Leftrightarrow & -14x-\frac{14}{5}& = & 3x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-560}{ \color{blue}{40} }x- \frac{112}{ \color{blue}{40} })& = & (\frac{120}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -560x \color{red}{-112} & = & \color{red}{120x} +15 \\\Leftrightarrow & -560x \color{red}{-112} \color{blue}{+112} \color{blue}{-120x} & = & \color{red}{120x} +15 \color{blue}{-120x} \color{blue}{+112} \\\Leftrightarrow & -560x-120x& = & 15+112 \\\Leftrightarrow & \color{red}{-680} x& = & 127 \\\Leftrightarrow & x = \frac{127}{-680} & & \\\Leftrightarrow & x = \frac{-127}{680} & & \\ & V = \left\{ \frac{-127}{680} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{2}{7})& = & 5x+\frac{7}{11} \\\Leftrightarrow & 18x+\frac{12}{7}& = & 5x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x+ \frac{132}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{+132} & = & \color{red}{385x} +49 \\\Leftrightarrow & 1386x \color{red}{+132} \color{blue}{-132} \color{blue}{-385x} & = & \color{red}{385x} +49 \color{blue}{-385x} \color{blue}{-132} \\\Leftrightarrow & 1386x-385x& = & 49-132 \\\Leftrightarrow & \color{red}{1001} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{1001} & & \\ & V = \left\{ \frac{-83}{1001} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{5}{9})& = & 7x+\frac{9}{11} \\\Leftrightarrow & -16x+\frac{20}{9}& = & 7x+\frac{9}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1584}{ \color{blue}{99} }x+ \frac{220}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{81}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1584x \color{red}{+220} & = & \color{red}{693x} +81 \\\Leftrightarrow & -1584x \color{red}{+220} \color{blue}{-220} \color{blue}{-693x} & = & \color{red}{693x} +81 \color{blue}{-693x} \color{blue}{-220} \\\Leftrightarrow & -1584x-693x& = & 81-220 \\\Leftrightarrow & \color{red}{-2277} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{-2277} & & \\\Leftrightarrow & x = \frac{139}{2277} & & \\ & V = \left\{ \frac{139}{2277} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{4}{11})& = & -5x+\frac{2}{11} \\\Leftrightarrow & -12x-\frac{24}{11}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x- \frac{24}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{-24} & = & \color{red}{-55x} +2 \\\Leftrightarrow & -132x \color{red}{-24} \color{blue}{+24} \color{blue}{+55x} & = & \color{red}{-55x} +2 \color{blue}{+55x} \color{blue}{+24} \\\Leftrightarrow & -132x+55x& = & 2+24 \\\Leftrightarrow & \color{red}{-77} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-77} & & \\\Leftrightarrow & x = \frac{-26}{77} & & \\ & V = \left\{ \frac{-26}{77} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{2}{9})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -12x+\frac{8}{9}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{+88} & = & \color{red}{495x} +45 \\\Leftrightarrow & -1188x \color{red}{+88} \color{blue}{-88} \color{blue}{-495x} & = & \color{red}{495x} +45 \color{blue}{-495x} \color{blue}{-88} \\\Leftrightarrow & -1188x-495x& = & 45-88 \\\Leftrightarrow & \color{red}{-1683} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-1683} & & \\\Leftrightarrow & x = \frac{43}{1683} & & \\ & V = \left\{ \frac{43}{1683} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{5}{2})& = & -8x+\frac{9}{2} \\\Leftrightarrow & -15x+\frac{25}{2}& = & -8x+\frac{9}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-30}{ \color{blue}{2} }x+ \frac{25}{ \color{blue}{2} })& = & (\frac{-16}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -30x \color{red}{+25} & = & \color{red}{-16x} +9 \\\Leftrightarrow & -30x \color{red}{+25} \color{blue}{-25} \color{blue}{+16x} & = & \color{red}{-16x} +9 \color{blue}{+16x} \color{blue}{-25} \\\Leftrightarrow & -30x+16x& = & 9-25 \\\Leftrightarrow & \color{red}{-14} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-14} & & \\\Leftrightarrow & x = \frac{8}{7} & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{4}{5})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 6x+\frac{12}{5}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{270}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 270x \color{red}{+108} & = & \color{red}{-225x} +40 \\\Leftrightarrow & 270x \color{red}{+108} \color{blue}{-108} \color{blue}{+225x} & = & \color{red}{-225x} +40 \color{blue}{+225x} \color{blue}{-108} \\\Leftrightarrow & 270x+225x& = & 40-108 \\\Leftrightarrow & \color{red}{495} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{495} & & \\ & V = \left\{ \frac{-68}{495} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{7})& = & 3x+\frac{7}{12} \\\Leftrightarrow & -20x-\frac{16}{7}& = & 3x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-1680}{ \color{blue}{84} }x- \frac{192}{ \color{blue}{84} })& = & (\frac{252}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -1680x \color{red}{-192} & = & \color{red}{252x} +49 \\\Leftrightarrow & -1680x \color{red}{-192} \color{blue}{+192} \color{blue}{-252x} & = & \color{red}{252x} +49 \color{blue}{-252x} \color{blue}{+192} \\\Leftrightarrow & -1680x-252x& = & 49+192 \\\Leftrightarrow & \color{red}{-1932} x& = & 241 \\\Leftrightarrow & x = \frac{241}{-1932} & & \\\Leftrightarrow & x = \frac{-241}{1932} & & \\ & V = \left\{ \frac{-241}{1932} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{4})& = & 7x+\frac{2}{11} \\\Leftrightarrow & 9x-\frac{15}{4}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{396}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{8}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 396x \color{red}{-165} & = & \color{red}{308x} +8 \\\Leftrightarrow & 396x \color{red}{-165} \color{blue}{+165} \color{blue}{-308x} & = & \color{red}{308x} +8 \color{blue}{-308x} \color{blue}{+165} \\\Leftrightarrow & 396x-308x& = & 8+165 \\\Leftrightarrow & \color{red}{88} x& = & 173 \\\Leftrightarrow & x = \frac{173}{88} & & \\ & V = \left\{ \frac{173}{88} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{2}{7})& = & 5x+\frac{9}{10} \\\Leftrightarrow & -12x-\frac{6}{7}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-840}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -840x \color{red}{-60} & = & \color{red}{350x} +63 \\\Leftrightarrow & -840x \color{red}{-60} \color{blue}{+60} \color{blue}{-350x} & = & \color{red}{350x} +63 \color{blue}{-350x} \color{blue}{+60} \\\Leftrightarrow & -840x-350x& = & 63+60 \\\Leftrightarrow & \color{red}{-1190} x& = & 123 \\\Leftrightarrow & x = \frac{123}{-1190} & & \\\Leftrightarrow & x = \frac{-123}{1190} & & \\ & V = \left\{ \frac{-123}{1190} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-13 09:12:59
Een site van Busleyden Atheneum Mechelen