Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{3}{2})& = & 5x+\frac{10}{9} \\\Leftrightarrow & -12x+\frac{9}{2}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-216}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} })& = & (\frac{90}{ \color{blue}{18} }x+ \frac{20}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -216x \color{red}{+81} & = & \color{red}{90x} +20 \\\Leftrightarrow & -216x \color{red}{+81} \color{blue}{-81} \color{blue}{-90x} & = & \color{red}{90x} +20 \color{blue}{-90x} \color{blue}{-81} \\\Leftrightarrow & -216x-90x& = & 20-81 \\\Leftrightarrow & \color{red}{-306} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{-306} & & \\\Leftrightarrow & x = \frac{61}{306} & & \\ & V = \left\{ \frac{61}{306} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{2}{7})& = & -4x+\frac{5}{6} \\\Leftrightarrow & -15x+\frac{6}{7}& = & -4x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-630}{ \color{blue}{42} }x+ \frac{36}{ \color{blue}{42} })& = & (\frac{-168}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -630x \color{red}{+36} & = & \color{red}{-168x} +35 \\\Leftrightarrow & -630x \color{red}{+36} \color{blue}{-36} \color{blue}{+168x} & = & \color{red}{-168x} +35 \color{blue}{+168x} \color{blue}{-36} \\\Leftrightarrow & -630x+168x& = & 35-36 \\\Leftrightarrow & \color{red}{-462} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-462} & & \\\Leftrightarrow & x = \frac{1}{462} & & \\ & V = \left\{ \frac{1}{462} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{2}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{-12} & = & \color{red}{25x} +6 \\\Leftrightarrow & -60x \color{red}{-12} \color{blue}{+12} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{+12} \\\Leftrightarrow & -60x-25x& = & 6+12 \\\Leftrightarrow & \color{red}{-85} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-85} & & \\\Leftrightarrow & x = \frac{-18}{85} & & \\ & V = \left\{ \frac{-18}{85} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{5})& = & -5x+\frac{5}{11} \\\Leftrightarrow & -9x-\frac{9}{5}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x- \frac{99}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{-99} & = & \color{red}{-275x} +25 \\\Leftrightarrow & -495x \color{red}{-99} \color{blue}{+99} \color{blue}{+275x} & = & \color{red}{-275x} +25 \color{blue}{+275x} \color{blue}{+99} \\\Leftrightarrow & -495x+275x& = & 25+99 \\\Leftrightarrow & \color{red}{-220} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-220} & & \\\Leftrightarrow & x = \frac{-31}{55} & & \\ & V = \left\{ \frac{-31}{55} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{4}{7})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -20x+\frac{16}{7}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x+ \frac{48}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{+48} & = & \color{red}{147x} +70 \\\Leftrightarrow & -420x \color{red}{+48} \color{blue}{-48} \color{blue}{-147x} & = & \color{red}{147x} +70 \color{blue}{-147x} \color{blue}{-48} \\\Leftrightarrow & -420x-147x& = & 70-48 \\\Leftrightarrow & \color{red}{-567} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-567} & & \\\Leftrightarrow & x = \frac{-22}{567} & & \\ & V = \left\{ \frac{-22}{567} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{3}{7})& = & 9x+\frac{7}{9} \\\Leftrightarrow & 4x+\frac{6}{7}& = & 9x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{252}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 252x \color{red}{+54} & = & \color{red}{567x} +49 \\\Leftrightarrow & 252x \color{red}{+54} \color{blue}{-54} \color{blue}{-567x} & = & \color{red}{567x} +49 \color{blue}{-567x} \color{blue}{-54} \\\Leftrightarrow & 252x-567x& = & 49-54 \\\Leftrightarrow & \color{red}{-315} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-315} & & \\\Leftrightarrow & x = \frac{1}{63} & & \\ & V = \left\{ \frac{1}{63} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{4}{11})& = & 8x+\frac{9}{11} \\\Leftrightarrow & -21x+\frac{28}{11}& = & 8x+\frac{9}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-231}{ \color{blue}{11} }x+ \frac{28}{ \color{blue}{11} })& = & (\frac{88}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -231x \color{red}{+28} & = & \color{red}{88x} +9 \\\Leftrightarrow & -231x \color{red}{+28} \color{blue}{-28} \color{blue}{-88x} & = & \color{red}{88x} +9 \color{blue}{-88x} \color{blue}{-28} \\\Leftrightarrow & -231x-88x& = & 9-28 \\\Leftrightarrow & \color{red}{-319} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{-319} & & \\\Leftrightarrow & x = \frac{19}{319} & & \\ & V = \left\{ \frac{19}{319} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{5})& = & 9x+\frac{5}{6} \\\Leftrightarrow & -8x+\frac{8}{5}& = & 9x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-240}{ \color{blue}{30} }x+ \frac{48}{ \color{blue}{30} })& = & (\frac{270}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -240x \color{red}{+48} & = & \color{red}{270x} +25 \\\Leftrightarrow & -240x \color{red}{+48} \color{blue}{-48} \color{blue}{-270x} & = & \color{red}{270x} +25 \color{blue}{-270x} \color{blue}{-48} \\\Leftrightarrow & -240x-270x& = & 25-48 \\\Leftrightarrow & \color{red}{-510} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-510} & & \\\Leftrightarrow & x = \frac{23}{510} & & \\ & V = \left\{ \frac{23}{510} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{5}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -6x-\frac{10}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{-10} & = & \color{red}{-49x} +10 \\\Leftrightarrow & -42x \color{red}{-10} \color{blue}{+10} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{+10} \\\Leftrightarrow & -42x+49x& = & 10+10 \\\Leftrightarrow & \color{red}{7} x& = & 20 \\\Leftrightarrow & x = \frac{20}{7} & & \\ & V = \left\{ \frac{20}{7} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{5}{8})& = & -7x+\frac{7}{8} \\\Leftrightarrow & -25x+\frac{25}{8}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-200}{ \color{blue}{8} }x+ \frac{25}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -200x \color{red}{+25} & = & \color{red}{-56x} +7 \\\Leftrightarrow & -200x \color{red}{+25} \color{blue}{-25} \color{blue}{+56x} & = & \color{red}{-56x} +7 \color{blue}{+56x} \color{blue}{-25} \\\Leftrightarrow & -200x+56x& = & 7-25 \\\Leftrightarrow & \color{red}{-144} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-144} & & \\\Leftrightarrow & x = \frac{1}{8} & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{1}{3})& = & 5x+\frac{9}{8} \\\Leftrightarrow & -14x-\frac{7}{3}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-336}{ \color{blue}{24} }x- \frac{56}{ \color{blue}{24} })& = & (\frac{120}{ \color{blue}{24} }x+ \frac{27}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -336x \color{red}{-56} & = & \color{red}{120x} +27 \\\Leftrightarrow & -336x \color{red}{-56} \color{blue}{+56} \color{blue}{-120x} & = & \color{red}{120x} +27 \color{blue}{-120x} \color{blue}{+56} \\\Leftrightarrow & -336x-120x& = & 27+56 \\\Leftrightarrow & \color{red}{-456} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-456} & & \\\Leftrightarrow & x = \frac{-83}{456} & & \\ & V = \left\{ \frac{-83}{456} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{5})& = & -5x+\frac{4}{11} \\\Leftrightarrow & 6x-\frac{6}{5}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x- \frac{66}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{-66} & = & \color{red}{-275x} +20 \\\Leftrightarrow & 330x \color{red}{-66} \color{blue}{+66} \color{blue}{+275x} & = & \color{red}{-275x} +20 \color{blue}{+275x} \color{blue}{+66} \\\Leftrightarrow & 330x+275x& = & 20+66 \\\Leftrightarrow & \color{red}{605} x& = & 86 \\\Leftrightarrow & x = \frac{86}{605} & & \\ & V = \left\{ \frac{86}{605} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-05 08:22:44
Een site van Busleyden Atheneum Mechelen