Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{4}{7})& = & 4x+\frac{7}{5} \\\Leftrightarrow & -25x+\frac{20}{7}& = & 4x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-875}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{140}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -875x \color{red}{+100} & = & \color{red}{140x} +49 \\\Leftrightarrow & -875x \color{red}{+100} \color{blue}{-100} \color{blue}{-140x} & = & \color{red}{140x} +49 \color{blue}{-140x} \color{blue}{-100} \\\Leftrightarrow & -875x-140x& = & 49-100 \\\Leftrightarrow & \color{red}{-1015} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{-1015} & & \\\Leftrightarrow & x = \frac{51}{1015} & & \\ & V = \left\{ \frac{51}{1015} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{3}{2})& = & -8x+\frac{8}{11} \\\Leftrightarrow & -21x-\frac{21}{2}& = & -8x+\frac{8}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-462}{ \color{blue}{22} }x- \frac{231}{ \color{blue}{22} })& = & (\frac{-176}{ \color{blue}{22} }x+ \frac{16}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -462x \color{red}{-231} & = & \color{red}{-176x} +16 \\\Leftrightarrow & -462x \color{red}{-231} \color{blue}{+231} \color{blue}{+176x} & = & \color{red}{-176x} +16 \color{blue}{+176x} \color{blue}{+231} \\\Leftrightarrow & -462x+176x& = & 16+231 \\\Leftrightarrow & \color{red}{-286} x& = & 247 \\\Leftrightarrow & x = \frac{247}{-286} & & \\\Leftrightarrow & x = \frac{-19}{22} & & \\ & V = \left\{ \frac{-19}{22} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{4}{3})& = & 4x+\frac{3}{5} \\\Leftrightarrow & 21x+\frac{28}{3}& = & 4x+\frac{3}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x+ \frac{140}{ \color{blue}{15} })& = & (\frac{60}{ \color{blue}{15} }x+ \frac{9}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{+140} & = & \color{red}{60x} +9 \\\Leftrightarrow & 315x \color{red}{+140} \color{blue}{-140} \color{blue}{-60x} & = & \color{red}{60x} +9 \color{blue}{-60x} \color{blue}{-140} \\\Leftrightarrow & 315x-60x& = & 9-140 \\\Leftrightarrow & \color{red}{255} x& = & -131 \\\Leftrightarrow & x = \frac{-131}{255} & & \\ & V = \left\{ \frac{-131}{255} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{2}{5})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -10x+\frac{4}{5}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{+12} & = & \color{red}{105x} +50 \\\Leftrightarrow & -150x \color{red}{+12} \color{blue}{-12} \color{blue}{-105x} & = & \color{red}{105x} +50 \color{blue}{-105x} \color{blue}{-12} \\\Leftrightarrow & -150x-105x& = & 50-12 \\\Leftrightarrow & \color{red}{-255} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-255} & & \\\Leftrightarrow & x = \frac{-38}{255} & & \\ & V = \left\{ \frac{-38}{255} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{3}{7})& = & -9x+\frac{8}{3} \\\Leftrightarrow & -8x-\frac{6}{7}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{-18} & = & \color{red}{-189x} +56 \\\Leftrightarrow & -168x \color{red}{-18} \color{blue}{+18} \color{blue}{+189x} & = & \color{red}{-189x} +56 \color{blue}{+189x} \color{blue}{+18} \\\Leftrightarrow & -168x+189x& = & 56+18 \\\Leftrightarrow & \color{red}{21} x& = & 74 \\\Leftrightarrow & x = \frac{74}{21} & & \\ & V = \left\{ \frac{74}{21} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{5}{11})& = & 3x+\frac{10}{9} \\\Leftrightarrow & 14x+\frac{35}{11}& = & 3x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1386}{ \color{blue}{99} }x+ \frac{315}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1386x \color{red}{+315} & = & \color{red}{297x} +110 \\\Leftrightarrow & 1386x \color{red}{+315} \color{blue}{-315} \color{blue}{-297x} & = & \color{red}{297x} +110 \color{blue}{-297x} \color{blue}{-315} \\\Leftrightarrow & 1386x-297x& = & 110-315 \\\Leftrightarrow & \color{red}{1089} x& = & -205 \\\Leftrightarrow & x = \frac{-205}{1089} & & \\ & V = \left\{ \frac{-205}{1089} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{2}{3})& = & 6x+\frac{5}{12} \\\Leftrightarrow & 35x+\frac{14}{3}& = & 6x+\frac{5}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{420}{ \color{blue}{12} }x+ \frac{56}{ \color{blue}{12} })& = & (\frac{72}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 420x \color{red}{+56} & = & \color{red}{72x} +5 \\\Leftrightarrow & 420x \color{red}{+56} \color{blue}{-56} \color{blue}{-72x} & = & \color{red}{72x} +5 \color{blue}{-72x} \color{blue}{-56} \\\Leftrightarrow & 420x-72x& = & 5-56 \\\Leftrightarrow & \color{red}{348} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{348} & & \\\Leftrightarrow & x = \frac{-17}{116} & & \\ & V = \left\{ \frac{-17}{116} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{+12} & = & \color{red}{25x} +6 \\\Leftrightarrow & 60x \color{red}{+12} \color{blue}{-12} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{-12} \\\Leftrightarrow & 60x-25x& = & 6-12 \\\Leftrightarrow & \color{red}{35} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{35} & & \\ & V = \left\{ \frac{-6}{35} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{3}{4})& = & -8x+\frac{8}{7} \\\Leftrightarrow & -25x-\frac{15}{4}& = & -8x+\frac{8}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-700}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-224}{ \color{blue}{28} }x+ \frac{32}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -700x \color{red}{-105} & = & \color{red}{-224x} +32 \\\Leftrightarrow & -700x \color{red}{-105} \color{blue}{+105} \color{blue}{+224x} & = & \color{red}{-224x} +32 \color{blue}{+224x} \color{blue}{+105} \\\Leftrightarrow & -700x+224x& = & 32+105 \\\Leftrightarrow & \color{red}{-476} x& = & 137 \\\Leftrightarrow & x = \frac{137}{-476} & & \\\Leftrightarrow & x = \frac{-137}{476} & & \\ & V = \left\{ \frac{-137}{476} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{5}{9})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 8x+\frac{10}{9}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{360}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} })& = & (\frac{135}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 360x \color{red}{+50} & = & \color{red}{135x} +54 \\\Leftrightarrow & 360x \color{red}{+50} \color{blue}{-50} \color{blue}{-135x} & = & \color{red}{135x} +54 \color{blue}{-135x} \color{blue}{-50} \\\Leftrightarrow & 360x-135x& = & 54-50 \\\Leftrightarrow & \color{red}{225} x& = & 4 \\\Leftrightarrow & x = \frac{4}{225} & & \\ & V = \left\{ \frac{4}{225} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{4}{3})& = & 9x+\frac{8}{5} \\\Leftrightarrow & 25x+\frac{20}{3}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{375}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 375x \color{red}{+100} & = & \color{red}{135x} +24 \\\Leftrightarrow & 375x \color{red}{+100} \color{blue}{-100} \color{blue}{-135x} & = & \color{red}{135x} +24 \color{blue}{-135x} \color{blue}{-100} \\\Leftrightarrow & 375x-135x& = & 24-100 \\\Leftrightarrow & \color{red}{240} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{240} & & \\\Leftrightarrow & x = \frac{-19}{60} & & \\ & V = \left\{ \frac{-19}{60} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{3}{5})& = & -9x+\frac{7}{8} \\\Leftrightarrow & -8x-\frac{12}{5}& = & -9x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-320}{ \color{blue}{40} }x- \frac{96}{ \color{blue}{40} })& = & (\frac{-360}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -320x \color{red}{-96} & = & \color{red}{-360x} +35 \\\Leftrightarrow & -320x \color{red}{-96} \color{blue}{+96} \color{blue}{+360x} & = & \color{red}{-360x} +35 \color{blue}{+360x} \color{blue}{+96} \\\Leftrightarrow & -320x+360x& = & 35+96 \\\Leftrightarrow & \color{red}{40} x& = & 131 \\\Leftrightarrow & x = \frac{131}{40} & & \\ & V = \left\{ \frac{131}{40} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-04 16:45:39
Een site van Busleyden Atheneum Mechelen