Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{3}{2})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -6x-\frac{9}{2}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-12}{ \color{blue}{2} }x- \frac{9}{ \color{blue}{2} })& = & (\frac{-14}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -12x \color{red}{-9} & = & \color{red}{-14x} +9 \\\Leftrightarrow & -12x \color{red}{-9} \color{blue}{+9} \color{blue}{+14x} & = & \color{red}{-14x} +9 \color{blue}{+14x} \color{blue}{+9} \\\Leftrightarrow & -12x+14x& = & 9+9 \\\Leftrightarrow & \color{red}{2} x& = & 18 \\\Leftrightarrow & x = \frac{18}{2} & & \\\Leftrightarrow & x = 9 & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{5}{7})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 12x-\frac{20}{7}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x- \frac{40}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{-40} & = & \color{red}{-70x} +21 \\\Leftrightarrow & 168x \color{red}{-40} \color{blue}{+40} \color{blue}{+70x} & = & \color{red}{-70x} +21 \color{blue}{+70x} \color{blue}{+40} \\\Leftrightarrow & 168x+70x& = & 21+40 \\\Leftrightarrow & \color{red}{238} x& = & 61 \\\Leftrightarrow & x = \frac{61}{238} & & \\ & V = \left\{ \frac{61}{238} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{4}{5})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{75x} +50 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +50 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & -180x-75x& = & 50+36 \\\Leftrightarrow & \color{red}{-255} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-255} & & \\\Leftrightarrow & x = \frac{-86}{255} & & \\ & V = \left\{ \frac{-86}{255} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{3}{7})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 10x+\frac{6}{7}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{+30} & = & \color{red}{105x} +42 \\\Leftrightarrow & 350x \color{red}{+30} \color{blue}{-30} \color{blue}{-105x} & = & \color{red}{105x} +42 \color{blue}{-105x} \color{blue}{-30} \\\Leftrightarrow & 350x-105x& = & 42-30 \\\Leftrightarrow & \color{red}{245} x& = & 12 \\\Leftrightarrow & x = \frac{12}{245} & & \\ & V = \left\{ \frac{12}{245} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{2}{9})& = & -5x+\frac{2}{7} \\\Leftrightarrow & 12x-\frac{8}{9}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{18}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{-56} & = & \color{red}{-315x} +18 \\\Leftrightarrow & 756x \color{red}{-56} \color{blue}{+56} \color{blue}{+315x} & = & \color{red}{-315x} +18 \color{blue}{+315x} \color{blue}{+56} \\\Leftrightarrow & 756x+315x& = & 18+56 \\\Leftrightarrow & \color{red}{1071} x& = & 74 \\\Leftrightarrow & x = \frac{74}{1071} & & \\ & V = \left\{ \frac{74}{1071} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{2}{9})& = & -9x+\frac{6}{7} \\\Leftrightarrow & -20x+\frac{8}{9}& = & -9x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{+56} & = & \color{red}{-567x} +54 \\\Leftrightarrow & -1260x \color{red}{+56} \color{blue}{-56} \color{blue}{+567x} & = & \color{red}{-567x} +54 \color{blue}{+567x} \color{blue}{-56} \\\Leftrightarrow & -1260x+567x& = & 54-56 \\\Leftrightarrow & \color{red}{-693} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-693} & & \\\Leftrightarrow & x = \frac{2}{693} & & \\ & V = \left\{ \frac{2}{693} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{4}{7})& = & -9x+\frac{8}{5} \\\Leftrightarrow & -8x-\frac{16}{7}& = & -9x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x- \frac{80}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{-80} & = & \color{red}{-315x} +56 \\\Leftrightarrow & -280x \color{red}{-80} \color{blue}{+80} \color{blue}{+315x} & = & \color{red}{-315x} +56 \color{blue}{+315x} \color{blue}{+80} \\\Leftrightarrow & -280x+315x& = & 56+80 \\\Leftrightarrow & \color{red}{35} x& = & 136 \\\Leftrightarrow & x = \frac{136}{35} & & \\ & V = \left\{ \frac{136}{35} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{4}{11})& = & 5x+\frac{8}{11} \\\Leftrightarrow & -9x-\frac{12}{11}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-99}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -99x \color{red}{-12} & = & \color{red}{55x} +8 \\\Leftrightarrow & -99x \color{red}{-12} \color{blue}{+12} \color{blue}{-55x} & = & \color{red}{55x} +8 \color{blue}{-55x} \color{blue}{+12} \\\Leftrightarrow & -99x-55x& = & 8+12 \\\Leftrightarrow & \color{red}{-154} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-154} & & \\\Leftrightarrow & x = \frac{-10}{77} & & \\ & V = \left\{ \frac{-10}{77} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{5}{12})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -35x+\frac{35}{12}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 12 en 5 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-2100}{ \color{blue}{60} }x+ \frac{175}{ \color{blue}{60} })& = & (\frac{-540}{ \color{blue}{60} }x+ \frac{72}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -2100x \color{red}{+175} & = & \color{red}{-540x} +72 \\\Leftrightarrow & -2100x \color{red}{+175} \color{blue}{-175} \color{blue}{+540x} & = & \color{red}{-540x} +72 \color{blue}{+540x} \color{blue}{-175} \\\Leftrightarrow & -2100x+540x& = & 72-175 \\\Leftrightarrow & \color{red}{-1560} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{-1560} & & \\\Leftrightarrow & x = \frac{103}{1560} & & \\ & V = \left\{ \frac{103}{1560} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{1}{3})& = & 3x+\frac{3}{10} \\\Leftrightarrow & 28x+\frac{7}{3}& = & 3x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{840}{ \color{blue}{30} }x+ \frac{70}{ \color{blue}{30} })& = & (\frac{90}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 840x \color{red}{+70} & = & \color{red}{90x} +9 \\\Leftrightarrow & 840x \color{red}{+70} \color{blue}{-70} \color{blue}{-90x} & = & \color{red}{90x} +9 \color{blue}{-90x} \color{blue}{-70} \\\Leftrightarrow & 840x-90x& = & 9-70 \\\Leftrightarrow & \color{red}{750} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{750} & & \\ & V = \left\{ \frac{-61}{750} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{2}{3})& = & -4x+\frac{2}{9} \\\Leftrightarrow & 15x-\frac{10}{3}& = & -4x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{135}{ \color{blue}{9} }x- \frac{30}{ \color{blue}{9} })& = & (\frac{-36}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 135x \color{red}{-30} & = & \color{red}{-36x} +2 \\\Leftrightarrow & 135x \color{red}{-30} \color{blue}{+30} \color{blue}{+36x} & = & \color{red}{-36x} +2 \color{blue}{+36x} \color{blue}{+30} \\\Leftrightarrow & 135x+36x& = & 2+30 \\\Leftrightarrow & \color{red}{171} x& = & 32 \\\Leftrightarrow & x = \frac{32}{171} & & \\ & V = \left\{ \frac{32}{171} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{5}{12})& = & -8x+\frac{3}{2} \\\Leftrightarrow & -15x-\frac{25}{12}& = & -8x+\frac{3}{2} \\ & & & \text{kgv van noemers 12 en 2 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x- \frac{25}{ \color{blue}{12} })& = & (\frac{-96}{ \color{blue}{12} }x+ \frac{18}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{-25} & = & \color{red}{-96x} +18 \\\Leftrightarrow & -180x \color{red}{-25} \color{blue}{+25} \color{blue}{+96x} & = & \color{red}{-96x} +18 \color{blue}{+96x} \color{blue}{+25} \\\Leftrightarrow & -180x+96x& = & 18+25 \\\Leftrightarrow & \color{red}{-84} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-84} & & \\\Leftrightarrow & x = \frac{-43}{84} & & \\ & V = \left\{ \frac{-43}{84} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-18 14:37:32
Een site van Busleyden Atheneum Mechelen