Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{3}{2})& = & 7x+\frac{3}{7} \\\Leftrightarrow & -20x-\frac{15}{2}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-280}{ \color{blue}{14} }x- \frac{105}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{6}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -280x \color{red}{-105} & = & \color{red}{98x} +6 \\\Leftrightarrow & -280x \color{red}{-105} \color{blue}{+105} \color{blue}{-98x} & = & \color{red}{98x} +6 \color{blue}{-98x} \color{blue}{+105} \\\Leftrightarrow & -280x-98x& = & 6+105 \\\Leftrightarrow & \color{red}{-378} x& = & 111 \\\Leftrightarrow & x = \frac{111}{-378} & & \\\Leftrightarrow & x = \frac{-37}{126} & & \\ & V = \left\{ \frac{-37}{126} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{3}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -12x-\frac{18}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x- \frac{18}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{-18} & = & \color{red}{-25x} +6 \\\Leftrightarrow & -60x \color{red}{-18} \color{blue}{+18} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{+18} \\\Leftrightarrow & -60x+25x& = & 6+18 \\\Leftrightarrow & \color{red}{-35} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-35} & & \\\Leftrightarrow & x = \frac{-24}{35} & & \\ & V = \left\{ \frac{-24}{35} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{7})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x-\frac{20}{7}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-100} & = & \color{red}{175x} +42 \\\Leftrightarrow & -420x \color{red}{-100} \color{blue}{+100} \color{blue}{-175x} & = & \color{red}{175x} +42 \color{blue}{-175x} \color{blue}{+100} \\\Leftrightarrow & -420x-175x& = & 42+100 \\\Leftrightarrow & \color{red}{-595} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-595} & & \\\Leftrightarrow & x = \frac{-142}{595} & & \\ & V = \left\{ \frac{-142}{595} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{3}{5})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -6x-\frac{9}{5}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x- \frac{81}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{-81} & = & \color{red}{-315x} +50 \\\Leftrightarrow & -270x \color{red}{-81} \color{blue}{+81} \color{blue}{+315x} & = & \color{red}{-315x} +50 \color{blue}{+315x} \color{blue}{+81} \\\Leftrightarrow & -270x+315x& = & 50+81 \\\Leftrightarrow & \color{red}{45} x& = & 131 \\\Leftrightarrow & x = \frac{131}{45} & & \\ & V = \left\{ \frac{131}{45} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{3}{2})& = & -5x+\frac{7}{9} \\\Leftrightarrow & 9x+\frac{9}{2}& = & -5x+\frac{7}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{162}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{14}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 162x \color{red}{+81} & = & \color{red}{-90x} +14 \\\Leftrightarrow & 162x \color{red}{+81} \color{blue}{-81} \color{blue}{+90x} & = & \color{red}{-90x} +14 \color{blue}{+90x} \color{blue}{-81} \\\Leftrightarrow & 162x+90x& = & 14-81 \\\Leftrightarrow & \color{red}{252} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{252} & & \\ & V = \left\{ \frac{-67}{252} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{5})& = & 8x+\frac{8}{9} \\\Leftrightarrow & -28x-\frac{14}{5}& = & 8x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1260}{ \color{blue}{45} }x- \frac{126}{ \color{blue}{45} })& = & (\frac{360}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1260x \color{red}{-126} & = & \color{red}{360x} +40 \\\Leftrightarrow & -1260x \color{red}{-126} \color{blue}{+126} \color{blue}{-360x} & = & \color{red}{360x} +40 \color{blue}{-360x} \color{blue}{+126} \\\Leftrightarrow & -1260x-360x& = & 40+126 \\\Leftrightarrow & \color{red}{-1620} x& = & 166 \\\Leftrightarrow & x = \frac{166}{-1620} & & \\\Leftrightarrow & x = \frac{-83}{810} & & \\ & V = \left\{ \frac{-83}{810} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{4}{9})& = & -3x+\frac{6}{5} \\\Leftrightarrow & -35x-\frac{28}{9}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1575}{ \color{blue}{45} }x- \frac{140}{ \color{blue}{45} })& = & (\frac{-135}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1575x \color{red}{-140} & = & \color{red}{-135x} +54 \\\Leftrightarrow & -1575x \color{red}{-140} \color{blue}{+140} \color{blue}{+135x} & = & \color{red}{-135x} +54 \color{blue}{+135x} \color{blue}{+140} \\\Leftrightarrow & -1575x+135x& = & 54+140 \\\Leftrightarrow & \color{red}{-1440} x& = & 194 \\\Leftrightarrow & x = \frac{194}{-1440} & & \\\Leftrightarrow & x = \frac{-97}{720} & & \\ & V = \left\{ \frac{-97}{720} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{4}{3})& = & -8x+\frac{7}{3} \\\Leftrightarrow & -21x+\frac{28}{3}& = & -8x+\frac{7}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-63}{ \color{blue}{3} }x+ \frac{28}{ \color{blue}{3} })& = & (\frac{-24}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -63x \color{red}{+28} & = & \color{red}{-24x} +7 \\\Leftrightarrow & -63x \color{red}{+28} \color{blue}{-28} \color{blue}{+24x} & = & \color{red}{-24x} +7 \color{blue}{+24x} \color{blue}{-28} \\\Leftrightarrow & -63x+24x& = & 7-28 \\\Leftrightarrow & \color{red}{-39} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-39} & & \\\Leftrightarrow & x = \frac{7}{13} & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{5}{4})& = & 8x+\frac{5}{2} \\\Leftrightarrow & -15x-\frac{15}{4}& = & 8x+\frac{5}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-60}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{32}{ \color{blue}{4} }x+ \frac{10}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -60x \color{red}{-15} & = & \color{red}{32x} +10 \\\Leftrightarrow & -60x \color{red}{-15} \color{blue}{+15} \color{blue}{-32x} & = & \color{red}{32x} +10 \color{blue}{-32x} \color{blue}{+15} \\\Leftrightarrow & -60x-32x& = & 10+15 \\\Leftrightarrow & \color{red}{-92} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-92} & & \\\Leftrightarrow & x = \frac{-25}{92} & & \\ & V = \left\{ \frac{-25}{92} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{5}{4})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -6x-\frac{15}{4}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-120}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -120x \color{red}{-75} & = & \color{red}{-140x} +24 \\\Leftrightarrow & -120x \color{red}{-75} \color{blue}{+75} \color{blue}{+140x} & = & \color{red}{-140x} +24 \color{blue}{+140x} \color{blue}{+75} \\\Leftrightarrow & -120x+140x& = & 24+75 \\\Leftrightarrow & \color{red}{20} x& = & 99 \\\Leftrightarrow & x = \frac{99}{20} & & \\ & V = \left\{ \frac{99}{20} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{5}{4})& = & 8x+\frac{3}{5} \\\Leftrightarrow & 15x+\frac{15}{4}& = & 8x+\frac{3}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{300}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{160}{ \color{blue}{20} }x+ \frac{12}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 300x \color{red}{+75} & = & \color{red}{160x} +12 \\\Leftrightarrow & 300x \color{red}{+75} \color{blue}{-75} \color{blue}{-160x} & = & \color{red}{160x} +12 \color{blue}{-160x} \color{blue}{-75} \\\Leftrightarrow & 300x-160x& = & 12-75 \\\Leftrightarrow & \color{red}{140} x& = & -63 \\\Leftrightarrow & x = \frac{-63}{140} & & \\\Leftrightarrow & x = \frac{-9}{20} & & \\ & V = \left\{ \frac{-9}{20} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{4}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -6x-\frac{12}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-30}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -30x \color{red}{-12} & = & \color{red}{35x} +6 \\\Leftrightarrow & -30x \color{red}{-12} \color{blue}{+12} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{+12} \\\Leftrightarrow & -30x-35x& = & 6+12 \\\Leftrightarrow & \color{red}{-65} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-65} & & \\\Leftrightarrow & x = \frac{-18}{65} & & \\ & V = \left\{ \frac{-18}{65} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-04 08:37:55
Een site van Busleyden Atheneum Mechelen