Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{2}{3})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 21x-\frac{14}{3}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{63}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 63x \color{red}{-14} & = & \color{red}{15x} +4 \\\Leftrightarrow & 63x \color{red}{-14} \color{blue}{+14} \color{blue}{-15x} & = & \color{red}{15x} +4 \color{blue}{-15x} \color{blue}{+14} \\\Leftrightarrow & 63x-15x& = & 4+14 \\\Leftrightarrow & \color{red}{48} x& = & 18 \\\Leftrightarrow & x = \frac{18}{48} & & \\\Leftrightarrow & x = \frac{3}{8} & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{5}{11})& = & 5x+\frac{4}{7} \\\Leftrightarrow & -24x+\frac{30}{11}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x+ \frac{210}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{+210} & = & \color{red}{385x} +44 \\\Leftrightarrow & -1848x \color{red}{+210} \color{blue}{-210} \color{blue}{-385x} & = & \color{red}{385x} +44 \color{blue}{-385x} \color{blue}{-210} \\\Leftrightarrow & -1848x-385x& = & 44-210 \\\Leftrightarrow & \color{red}{-2233} x& = & -166 \\\Leftrightarrow & x = \frac{-166}{-2233} & & \\\Leftrightarrow & x = \frac{166}{2233} & & \\ & V = \left\{ \frac{166}{2233} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{2}{5})& = & -7x+\frac{7}{12} \\\Leftrightarrow & -24x-\frac{12}{5}& = & -7x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-1440}{ \color{blue}{60} }x- \frac{144}{ \color{blue}{60} })& = & (\frac{-420}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -1440x \color{red}{-144} & = & \color{red}{-420x} +35 \\\Leftrightarrow & -1440x \color{red}{-144} \color{blue}{+144} \color{blue}{+420x} & = & \color{red}{-420x} +35 \color{blue}{+420x} \color{blue}{+144} \\\Leftrightarrow & -1440x+420x& = & 35+144 \\\Leftrightarrow & \color{red}{-1020} x& = & 179 \\\Leftrightarrow & x = \frac{179}{-1020} & & \\\Leftrightarrow & x = \frac{-179}{1020} & & \\ & V = \left\{ \frac{-179}{1020} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{3}{7})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-66} & = & \color{red}{-539x} +35 \\\Leftrightarrow & -462x \color{red}{-66} \color{blue}{+66} \color{blue}{+539x} & = & \color{red}{-539x} +35 \color{blue}{+539x} \color{blue}{+66} \\\Leftrightarrow & -462x+539x& = & 35+66 \\\Leftrightarrow & \color{red}{77} x& = & 101 \\\Leftrightarrow & x = \frac{101}{77} & & \\ & V = \left\{ \frac{101}{77} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{2}{3})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -20x-\frac{10}{3}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{110}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-110} & = & \color{red}{-231x} +15 \\\Leftrightarrow & -660x \color{red}{-110} \color{blue}{+110} \color{blue}{+231x} & = & \color{red}{-231x} +15 \color{blue}{+231x} \color{blue}{+110} \\\Leftrightarrow & -660x+231x& = & 15+110 \\\Leftrightarrow & \color{red}{-429} x& = & 125 \\\Leftrightarrow & x = \frac{125}{-429} & & \\\Leftrightarrow & x = \frac{-125}{429} & & \\ & V = \left\{ \frac{-125}{429} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{5}{11})& = & 8x+\frac{6}{5} \\\Leftrightarrow & 25x+\frac{25}{11}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1375}{ \color{blue}{55} }x+ \frac{125}{ \color{blue}{55} })& = & (\frac{440}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1375x \color{red}{+125} & = & \color{red}{440x} +66 \\\Leftrightarrow & 1375x \color{red}{+125} \color{blue}{-125} \color{blue}{-440x} & = & \color{red}{440x} +66 \color{blue}{-440x} \color{blue}{-125} \\\Leftrightarrow & 1375x-440x& = & 66-125 \\\Leftrightarrow & \color{red}{935} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{935} & & \\ & V = \left\{ \frac{-59}{935} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{3})& = & -8x+\frac{5}{2} \\\Leftrightarrow & -21x-\frac{14}{3}& = & -8x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-126}{ \color{blue}{6} }x- \frac{28}{ \color{blue}{6} })& = & (\frac{-48}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -126x \color{red}{-28} & = & \color{red}{-48x} +15 \\\Leftrightarrow & -126x \color{red}{-28} \color{blue}{+28} \color{blue}{+48x} & = & \color{red}{-48x} +15 \color{blue}{+48x} \color{blue}{+28} \\\Leftrightarrow & -126x+48x& = & 15+28 \\\Leftrightarrow & \color{red}{-78} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-78} & & \\\Leftrightarrow & x = \frac{-43}{78} & & \\ & V = \left\{ \frac{-43}{78} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{2}{3})& = & 8x+\frac{5}{11} \\\Leftrightarrow & 35x-\frac{14}{3}& = & 8x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{264}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{-154} & = & \color{red}{264x} +15 \\\Leftrightarrow & 1155x \color{red}{-154} \color{blue}{+154} \color{blue}{-264x} & = & \color{red}{264x} +15 \color{blue}{-264x} \color{blue}{+154} \\\Leftrightarrow & 1155x-264x& = & 15+154 \\\Leftrightarrow & \color{red}{891} x& = & 169 \\\Leftrightarrow & x = \frac{169}{891} & & \\ & V = \left\{ \frac{169}{891} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{3}{5})& = & -3x+\frac{5}{2} \\\Leftrightarrow & -8x-\frac{12}{5}& = & -3x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{-24} & = & \color{red}{-30x} +25 \\\Leftrightarrow & -80x \color{red}{-24} \color{blue}{+24} \color{blue}{+30x} & = & \color{red}{-30x} +25 \color{blue}{+30x} \color{blue}{+24} \\\Leftrightarrow & -80x+30x& = & 25+24 \\\Leftrightarrow & \color{red}{-50} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-50} & & \\\Leftrightarrow & x = \frac{-49}{50} & & \\ & V = \left\{ \frac{-49}{50} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{3})& = & -3x+\frac{7}{8} \\\Leftrightarrow & 8x-\frac{4}{3}& = & -3x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{192}{ \color{blue}{24} }x- \frac{32}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 192x \color{red}{-32} & = & \color{red}{-72x} +21 \\\Leftrightarrow & 192x \color{red}{-32} \color{blue}{+32} \color{blue}{+72x} & = & \color{red}{-72x} +21 \color{blue}{+72x} \color{blue}{+32} \\\Leftrightarrow & 192x+72x& = & 21+32 \\\Leftrightarrow & \color{red}{264} x& = & 53 \\\Leftrightarrow & x = \frac{53}{264} & & \\ & V = \left\{ \frac{53}{264} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{2}{7})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{6}{7}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+18} & = & \color{red}{105x} +56 \\\Leftrightarrow & 252x \color{red}{+18} \color{blue}{-18} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{-18} \\\Leftrightarrow & 252x-105x& = & 56-18 \\\Leftrightarrow & \color{red}{147} x& = & 38 \\\Leftrightarrow & x = \frac{38}{147} & & \\ & V = \left\{ \frac{38}{147} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{2}{9})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 6x+\frac{4}{9}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{36}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{+28} & = & \color{red}{315x} +36 \\\Leftrightarrow & 378x \color{red}{+28} \color{blue}{-28} \color{blue}{-315x} & = & \color{red}{315x} +36 \color{blue}{-315x} \color{blue}{-28} \\\Leftrightarrow & 378x-315x& = & 36-28 \\\Leftrightarrow & \color{red}{63} x& = & 8 \\\Leftrightarrow & x = \frac{8}{63} & & \\ & V = \left\{ \frac{8}{63} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-03 14:36:52
Een site van Busleyden Atheneum Mechelen