Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{5}{3})& = & -8x+\frac{4}{11} \\\Leftrightarrow & -21x+\frac{35}{3}& = & -8x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-693}{ \color{blue}{33} }x+ \frac{385}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -693x \color{red}{+385} & = & \color{red}{-264x} +12 \\\Leftrightarrow & -693x \color{red}{+385} \color{blue}{-385} \color{blue}{+264x} & = & \color{red}{-264x} +12 \color{blue}{+264x} \color{blue}{-385} \\\Leftrightarrow & -693x+264x& = & 12-385 \\\Leftrightarrow & \color{red}{-429} x& = & -373 \\\Leftrightarrow & x = \frac{-373}{-429} & & \\\Leftrightarrow & x = \frac{373}{429} & & \\ & V = \left\{ \frac{373}{429} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{3}{4})& = & 7x+\frac{7}{4} \\\Leftrightarrow & -10x+\frac{15}{4}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-40}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{28}{ \color{blue}{4} }x+ \frac{7}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -40x \color{red}{+15} & = & \color{red}{28x} +7 \\\Leftrightarrow & -40x \color{red}{+15} \color{blue}{-15} \color{blue}{-28x} & = & \color{red}{28x} +7 \color{blue}{-28x} \color{blue}{-15} \\\Leftrightarrow & -40x-28x& = & 7-15 \\\Leftrightarrow & \color{red}{-68} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-68} & & \\\Leftrightarrow & x = \frac{2}{17} & & \\ & V = \left\{ \frac{2}{17} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{3}{7})& = & -5x+\frac{6}{7} \\\Leftrightarrow & -12x-\frac{18}{7}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x- \frac{18}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{-18} & = & \color{red}{-35x} +6 \\\Leftrightarrow & -84x \color{red}{-18} \color{blue}{+18} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{+18} \\\Leftrightarrow & -84x+35x& = & 6+18 \\\Leftrightarrow & \color{red}{-49} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-49} & & \\\Leftrightarrow & x = \frac{-24}{49} & & \\ & V = \left\{ \frac{-24}{49} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{2}{7})& = & -7x+\frac{4}{11} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-66} & = & \color{red}{-539x} +28 \\\Leftrightarrow & -462x \color{red}{-66} \color{blue}{+66} \color{blue}{+539x} & = & \color{red}{-539x} +28 \color{blue}{+539x} \color{blue}{+66} \\\Leftrightarrow & -462x+539x& = & 28+66 \\\Leftrightarrow & \color{red}{77} x& = & 94 \\\Leftrightarrow & x = \frac{94}{77} & & \\ & V = \left\{ \frac{94}{77} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{7})& = & -5x+\frac{9}{10} \\\Leftrightarrow & -12x-\frac{20}{7}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-840}{ \color{blue}{70} }x- \frac{200}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -840x \color{red}{-200} & = & \color{red}{-350x} +63 \\\Leftrightarrow & -840x \color{red}{-200} \color{blue}{+200} \color{blue}{+350x} & = & \color{red}{-350x} +63 \color{blue}{+350x} \color{blue}{+200} \\\Leftrightarrow & -840x+350x& = & 63+200 \\\Leftrightarrow & \color{red}{-490} x& = & 263 \\\Leftrightarrow & x = \frac{263}{-490} & & \\\Leftrightarrow & x = \frac{-263}{490} & & \\ & V = \left\{ \frac{-263}{490} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{11})& = & -5x+\frac{3}{4} \\\Leftrightarrow & 18x+\frac{24}{11}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{792}{ \color{blue}{44} }x+ \frac{96}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 792x \color{red}{+96} & = & \color{red}{-220x} +33 \\\Leftrightarrow & 792x \color{red}{+96} \color{blue}{-96} \color{blue}{+220x} & = & \color{red}{-220x} +33 \color{blue}{+220x} \color{blue}{-96} \\\Leftrightarrow & 792x+220x& = & 33-96 \\\Leftrightarrow & \color{red}{1012} x& = & -63 \\\Leftrightarrow & x = \frac{-63}{1012} & & \\ & V = \left\{ \frac{-63}{1012} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{2}{7})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 15x+\frac{10}{7}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{+30} & = & \color{red}{147x} +56 \\\Leftrightarrow & 315x \color{red}{+30} \color{blue}{-30} \color{blue}{-147x} & = & \color{red}{147x} +56 \color{blue}{-147x} \color{blue}{-30} \\\Leftrightarrow & 315x-147x& = & 56-30 \\\Leftrightarrow & \color{red}{168} x& = & 26 \\\Leftrightarrow & x = \frac{26}{168} & & \\\Leftrightarrow & x = \frac{13}{84} & & \\ & V = \left\{ \frac{13}{84} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{4}{7})& = & -5x+\frac{10}{9} \\\Leftrightarrow & -12x+\frac{16}{7}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x+ \frac{144}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{+144} & = & \color{red}{-315x} +70 \\\Leftrightarrow & -756x \color{red}{+144} \color{blue}{-144} \color{blue}{+315x} & = & \color{red}{-315x} +70 \color{blue}{+315x} \color{blue}{-144} \\\Leftrightarrow & -756x+315x& = & 70-144 \\\Leftrightarrow & \color{red}{-441} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{-441} & & \\\Leftrightarrow & x = \frac{74}{441} & & \\ & V = \left\{ \frac{74}{441} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{3}{5})& = & 3x+\frac{3}{11} \\\Leftrightarrow & 10x+\frac{6}{5}& = & 3x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{+66} & = & \color{red}{165x} +15 \\\Leftrightarrow & 550x \color{red}{+66} \color{blue}{-66} \color{blue}{-165x} & = & \color{red}{165x} +15 \color{blue}{-165x} \color{blue}{-66} \\\Leftrightarrow & 550x-165x& = & 15-66 \\\Leftrightarrow & \color{red}{385} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{385} & & \\ & V = \left\{ \frac{-51}{385} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{4}{5})& = & -6x+\frac{9}{2} \\\Leftrightarrow & -18x+\frac{24}{5}& = & -6x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-180}{ \color{blue}{10} }x+ \frac{48}{ \color{blue}{10} })& = & (\frac{-60}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -180x \color{red}{+48} & = & \color{red}{-60x} +45 \\\Leftrightarrow & -180x \color{red}{+48} \color{blue}{-48} \color{blue}{+60x} & = & \color{red}{-60x} +45 \color{blue}{+60x} \color{blue}{-48} \\\Leftrightarrow & -180x+60x& = & 45-48 \\\Leftrightarrow & \color{red}{-120} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-120} & & \\\Leftrightarrow & x = \frac{1}{40} & & \\ & V = \left\{ \frac{1}{40} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{11})& = & 5x+\frac{2}{9} \\\Leftrightarrow & 6x-\frac{6}{11}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{594}{ \color{blue}{99} }x- \frac{54}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 594x \color{red}{-54} & = & \color{red}{495x} +22 \\\Leftrightarrow & 594x \color{red}{-54} \color{blue}{+54} \color{blue}{-495x} & = & \color{red}{495x} +22 \color{blue}{-495x} \color{blue}{+54} \\\Leftrightarrow & 594x-495x& = & 22+54 \\\Leftrightarrow & \color{red}{99} x& = & 76 \\\Leftrightarrow & x = \frac{76}{99} & & \\ & V = \left\{ \frac{76}{99} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{4}{3})& = & -9x+\frac{3}{4} \\\Leftrightarrow & -25x+\frac{20}{3}& = & -9x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-300}{ \color{blue}{12} }x+ \frac{80}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -300x \color{red}{+80} & = & \color{red}{-108x} +9 \\\Leftrightarrow & -300x \color{red}{+80} \color{blue}{-80} \color{blue}{+108x} & = & \color{red}{-108x} +9 \color{blue}{+108x} \color{blue}{-80} \\\Leftrightarrow & -300x+108x& = & 9-80 \\\Leftrightarrow & \color{red}{-192} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{-192} & & \\\Leftrightarrow & x = \frac{71}{192} & & \\ & V = \left\{ \frac{71}{192} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-05 23:48:44
Een site van Busleyden Atheneum Mechelen