Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{5}{11})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -30x+\frac{30}{11}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-330}{ \color{blue}{11} }x+ \frac{30}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -330x \color{red}{+30} & = & \color{red}{77x} +10 \\\Leftrightarrow & -330x \color{red}{+30} \color{blue}{-30} \color{blue}{-77x} & = & \color{red}{77x} +10 \color{blue}{-77x} \color{blue}{-30} \\\Leftrightarrow & -330x-77x& = & 10-30 \\\Leftrightarrow & \color{red}{-407} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-407} & & \\\Leftrightarrow & x = \frac{20}{407} & & \\ & V = \left\{ \frac{20}{407} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{2}{3})& = & 7x+\frac{4}{5} \\\Leftrightarrow & 8x+\frac{4}{3}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+20} & = & \color{red}{105x} +12 \\\Leftrightarrow & 120x \color{red}{+20} \color{blue}{-20} \color{blue}{-105x} & = & \color{red}{105x} +12 \color{blue}{-105x} \color{blue}{-20} \\\Leftrightarrow & 120x-105x& = & 12-20 \\\Leftrightarrow & \color{red}{15} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{15} & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{4}{3})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -16x+\frac{16}{3}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-96}{ \color{blue}{6} }x+ \frac{32}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -96x \color{red}{+32} & = & \color{red}{-42x} +9 \\\Leftrightarrow & -96x \color{red}{+32} \color{blue}{-32} \color{blue}{+42x} & = & \color{red}{-42x} +9 \color{blue}{+42x} \color{blue}{-32} \\\Leftrightarrow & -96x+42x& = & 9-32 \\\Leftrightarrow & \color{red}{-54} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-54} & & \\\Leftrightarrow & x = \frac{23}{54} & & \\ & V = \left\{ \frac{23}{54} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{2}{7})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -9x-\frac{6}{7}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-189}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -189x \color{red}{-18} & = & \color{red}{105x} +56 \\\Leftrightarrow & -189x \color{red}{-18} \color{blue}{+18} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{+18} \\\Leftrightarrow & -189x-105x& = & 56+18 \\\Leftrightarrow & \color{red}{-294} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-294} & & \\\Leftrightarrow & x = \frac{-37}{147} & & \\ & V = \left\{ \frac{-37}{147} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{11})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -6x+\frac{15}{11}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x+ \frac{135}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{+135} & = & \color{red}{-693x} +22 \\\Leftrightarrow & -594x \color{red}{+135} \color{blue}{-135} \color{blue}{+693x} & = & \color{red}{-693x} +22 \color{blue}{+693x} \color{blue}{-135} \\\Leftrightarrow & -594x+693x& = & 22-135 \\\Leftrightarrow & \color{red}{99} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{99} & & \\ & V = \left\{ \frac{-113}{99} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{4})& = & -4x+\frac{9}{5} \\\Leftrightarrow & -35x-\frac{35}{4}& = & -4x+\frac{9}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-700}{ \color{blue}{20} }x- \frac{175}{ \color{blue}{20} })& = & (\frac{-80}{ \color{blue}{20} }x+ \frac{36}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -700x \color{red}{-175} & = & \color{red}{-80x} +36 \\\Leftrightarrow & -700x \color{red}{-175} \color{blue}{+175} \color{blue}{+80x} & = & \color{red}{-80x} +36 \color{blue}{+80x} \color{blue}{+175} \\\Leftrightarrow & -700x+80x& = & 36+175 \\\Leftrightarrow & \color{red}{-620} x& = & 211 \\\Leftrightarrow & x = \frac{211}{-620} & & \\\Leftrightarrow & x = \frac{-211}{620} & & \\ & V = \left\{ \frac{-211}{620} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{4}{9})& = & 9x+\frac{9}{11} \\\Leftrightarrow & 10x+\frac{20}{9}& = & 9x+\frac{9}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{990}{ \color{blue}{99} }x+ \frac{220}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{81}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{+220} & = & \color{red}{891x} +81 \\\Leftrightarrow & 990x \color{red}{+220} \color{blue}{-220} \color{blue}{-891x} & = & \color{red}{891x} +81 \color{blue}{-891x} \color{blue}{-220} \\\Leftrightarrow & 990x-891x& = & 81-220 \\\Leftrightarrow & \color{red}{99} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{99} & & \\ & V = \left\{ \frac{-139}{99} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{3}{7})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 24x-\frac{18}{7}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{504}{ \color{blue}{21} }x- \frac{54}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 504x \color{red}{-54} & = & \color{red}{105x} +14 \\\Leftrightarrow & 504x \color{red}{-54} \color{blue}{+54} \color{blue}{-105x} & = & \color{red}{105x} +14 \color{blue}{-105x} \color{blue}{+54} \\\Leftrightarrow & 504x-105x& = & 14+54 \\\Leftrightarrow & \color{red}{399} x& = & 68 \\\Leftrightarrow & x = \frac{68}{399} & & \\ & V = \left\{ \frac{68}{399} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{7})& = & -8x+\frac{9}{10} \\\Leftrightarrow & -15x-\frac{6}{7}& = & -8x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1050}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{-560}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1050x \color{red}{-60} & = & \color{red}{-560x} +63 \\\Leftrightarrow & -1050x \color{red}{-60} \color{blue}{+60} \color{blue}{+560x} & = & \color{red}{-560x} +63 \color{blue}{+560x} \color{blue}{+60} \\\Leftrightarrow & -1050x+560x& = & 63+60 \\\Leftrightarrow & \color{red}{-490} x& = & 123 \\\Leftrightarrow & x = \frac{123}{-490} & & \\\Leftrightarrow & x = \frac{-123}{490} & & \\ & V = \left\{ \frac{-123}{490} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{5}{7})& = & -7x+\frac{2}{7} \\\Leftrightarrow & -6x+\frac{10}{7}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{+10} & = & \color{red}{-49x} +2 \\\Leftrightarrow & -42x \color{red}{+10} \color{blue}{-10} \color{blue}{+49x} & = & \color{red}{-49x} +2 \color{blue}{+49x} \color{blue}{-10} \\\Leftrightarrow & -42x+49x& = & 2-10 \\\Leftrightarrow & \color{red}{7} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{7} & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{2}{3})& = & -3x+\frac{4}{3} \\\Leftrightarrow & 28x-\frac{14}{3}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{84}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 84x \color{red}{-14} & = & \color{red}{-9x} +4 \\\Leftrightarrow & 84x \color{red}{-14} \color{blue}{+14} \color{blue}{+9x} & = & \color{red}{-9x} +4 \color{blue}{+9x} \color{blue}{+14} \\\Leftrightarrow & 84x+9x& = & 4+14 \\\Leftrightarrow & \color{red}{93} x& = & 18 \\\Leftrightarrow & x = \frac{18}{93} & & \\\Leftrightarrow & x = \frac{6}{31} & & \\ & V = \left\{ \frac{6}{31} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{4}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{24}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x+ \frac{24}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{+24} & = & \color{red}{25x} +6 \\\Leftrightarrow & -60x \color{red}{+24} \color{blue}{-24} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{-24} \\\Leftrightarrow & -60x-25x& = & 6-24 \\\Leftrightarrow & \color{red}{-85} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-85} & & \\\Leftrightarrow & x = \frac{18}{85} & & \\ & V = \left\{ \frac{18}{85} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-10-27 11:22:18
Een site van Busleyden Atheneum Mechelen