Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{2}{9})& = & -3x+\frac{9}{10} \\\Leftrightarrow & 8x-\frac{8}{9}& = & -3x+\frac{9}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{720}{ \color{blue}{90} }x- \frac{80}{ \color{blue}{90} })& = & (\frac{-270}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 720x \color{red}{-80} & = & \color{red}{-270x} +81 \\\Leftrightarrow & 720x \color{red}{-80} \color{blue}{+80} \color{blue}{+270x} & = & \color{red}{-270x} +81 \color{blue}{+270x} \color{blue}{+80} \\\Leftrightarrow & 720x+270x& = & 81+80 \\\Leftrightarrow & \color{red}{990} x& = & 161 \\\Leftrightarrow & x = \frac{161}{990} & & \\ & V = \left\{ \frac{161}{990} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{2}{5})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 20x-\frac{8}{5}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{100}{ \color{blue}{5} }x- \frac{8}{ \color{blue}{5} })& = & (\frac{-15}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 100x \color{red}{-8} & = & \color{red}{-15x} +6 \\\Leftrightarrow & 100x \color{red}{-8} \color{blue}{+8} \color{blue}{+15x} & = & \color{red}{-15x} +6 \color{blue}{+15x} \color{blue}{+8} \\\Leftrightarrow & 100x+15x& = & 6+8 \\\Leftrightarrow & \color{red}{115} x& = & 14 \\\Leftrightarrow & x = \frac{14}{115} & & \\ & V = \left\{ \frac{14}{115} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{4}{7})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{16}{7}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{48}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+48} & = & \color{red}{-105x} +56 \\\Leftrightarrow & 252x \color{red}{+48} \color{blue}{-48} \color{blue}{+105x} & = & \color{red}{-105x} +56 \color{blue}{+105x} \color{blue}{-48} \\\Leftrightarrow & 252x+105x& = & 56-48 \\\Leftrightarrow & \color{red}{357} x& = & 8 \\\Leftrightarrow & x = \frac{8}{357} & & \\ & V = \left\{ \frac{8}{357} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{3}{5})& = & 7x+\frac{5}{3} \\\Leftrightarrow & -6x+\frac{6}{5}& = & 7x+\frac{5}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{25}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{+18} & = & \color{red}{105x} +25 \\\Leftrightarrow & -90x \color{red}{+18} \color{blue}{-18} \color{blue}{-105x} & = & \color{red}{105x} +25 \color{blue}{-105x} \color{blue}{-18} \\\Leftrightarrow & -90x-105x& = & 25-18 \\\Leftrightarrow & \color{red}{-195} x& = & 7 \\\Leftrightarrow & x = \frac{7}{-195} & & \\\Leftrightarrow & x = \frac{-7}{195} & & \\ & V = \left\{ \frac{-7}{195} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{3}{7})& = & -5x+\frac{7}{10} \\\Leftrightarrow & -4x+\frac{6}{7}& = & -5x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-280}{ \color{blue}{70} }x+ \frac{60}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -280x \color{red}{+60} & = & \color{red}{-350x} +49 \\\Leftrightarrow & -280x \color{red}{+60} \color{blue}{-60} \color{blue}{+350x} & = & \color{red}{-350x} +49 \color{blue}{+350x} \color{blue}{-60} \\\Leftrightarrow & -280x+350x& = & 49-60 \\\Leftrightarrow & \color{red}{70} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{70} & & \\ & V = \left\{ \frac{-11}{70} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{4}{5})& = & -3x+\frac{9}{7} \\\Leftrightarrow & 10x-\frac{8}{5}& = & -3x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x- \frac{56}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{-56} & = & \color{red}{-105x} +45 \\\Leftrightarrow & 350x \color{red}{-56} \color{blue}{+56} \color{blue}{+105x} & = & \color{red}{-105x} +45 \color{blue}{+105x} \color{blue}{+56} \\\Leftrightarrow & 350x+105x& = & 45+56 \\\Leftrightarrow & \color{red}{455} x& = & 101 \\\Leftrightarrow & x = \frac{101}{455} & & \\ & V = \left\{ \frac{101}{455} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+1)& = & -8x+\frac{10}{7} \\\Leftrightarrow & 21x-7& = & -8x+\frac{10}{7} \\ & & & \text{kgv van noemers 1 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{147}{ \color{blue}{7} }x- \frac{49}{ \color{blue}{7} })& = & (\frac{-56}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 147x \color{red}{-49} & = & \color{red}{-56x} +10 \\\Leftrightarrow & 147x \color{red}{-49} \color{blue}{+49} \color{blue}{+56x} & = & \color{red}{-56x} +10 \color{blue}{+56x} \color{blue}{+49} \\\Leftrightarrow & 147x+56x& = & 10+49 \\\Leftrightarrow & \color{red}{203} x& = & 59 \\\Leftrightarrow & x = \frac{59}{203} & & \\ & V = \left\{ \frac{59}{203} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{4}{5})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -9x+\frac{12}{5}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{+84} & = & \color{red}{175x} +50 \\\Leftrightarrow & -315x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +50 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & -315x-175x& = & 50-84 \\\Leftrightarrow & \color{red}{-490} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-490} & & \\\Leftrightarrow & x = \frac{17}{245} & & \\ & V = \left\{ \frac{17}{245} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{3}{11})& = & 2x+\frac{9}{11} \\\Leftrightarrow & 15x-\frac{15}{11}& = & 2x+\frac{9}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{165}{ \color{blue}{11} }x- \frac{15}{ \color{blue}{11} })& = & (\frac{22}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 165x \color{red}{-15} & = & \color{red}{22x} +9 \\\Leftrightarrow & 165x \color{red}{-15} \color{blue}{+15} \color{blue}{-22x} & = & \color{red}{22x} +9 \color{blue}{-22x} \color{blue}{+15} \\\Leftrightarrow & 165x-22x& = & 9+15 \\\Leftrightarrow & \color{red}{143} x& = & 24 \\\Leftrightarrow & x = \frac{24}{143} & & \\ & V = \left\{ \frac{24}{143} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{2}{11})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -9x+\frac{6}{11}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-297}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -297x \color{red}{+18} & = & \color{red}{165x} +44 \\\Leftrightarrow & -297x \color{red}{+18} \color{blue}{-18} \color{blue}{-165x} & = & \color{red}{165x} +44 \color{blue}{-165x} \color{blue}{-18} \\\Leftrightarrow & -297x-165x& = & 44-18 \\\Leftrightarrow & \color{red}{-462} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-462} & & \\\Leftrightarrow & x = \frac{-13}{231} & & \\ & V = \left\{ \frac{-13}{231} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{4}{3})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 10x+\frac{20}{3}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{60}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 60x \color{red}{+40} & = & \color{red}{-42x} +9 \\\Leftrightarrow & 60x \color{red}{+40} \color{blue}{-40} \color{blue}{+42x} & = & \color{red}{-42x} +9 \color{blue}{+42x} \color{blue}{-40} \\\Leftrightarrow & 60x+42x& = & 9-40 \\\Leftrightarrow & \color{red}{102} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{102} & & \\ & V = \left\{ \frac{-31}{102} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{3}{4})& = & 2x+\frac{2}{7} \\\Leftrightarrow & 15x-\frac{15}{4}& = & 2x+\frac{2}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{420}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{56}{ \color{blue}{28} }x+ \frac{8}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 420x \color{red}{-105} & = & \color{red}{56x} +8 \\\Leftrightarrow & 420x \color{red}{-105} \color{blue}{+105} \color{blue}{-56x} & = & \color{red}{56x} +8 \color{blue}{-56x} \color{blue}{+105} \\\Leftrightarrow & 420x-56x& = & 8+105 \\\Leftrightarrow & \color{red}{364} x& = & 113 \\\Leftrightarrow & x = \frac{113}{364} & & \\ & V = \left\{ \frac{113}{364} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-12 23:29:31
Een site van Busleyden Atheneum Mechelen