Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{2}{3})& = & 6x+\frac{7}{11} \\\Leftrightarrow & -25x-\frac{10}{3}& = & 6x+\frac{7}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-825}{ \color{blue}{33} }x- \frac{110}{ \color{blue}{33} })& = & (\frac{198}{ \color{blue}{33} }x+ \frac{21}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -825x \color{red}{-110} & = & \color{red}{198x} +21 \\\Leftrightarrow & -825x \color{red}{-110} \color{blue}{+110} \color{blue}{-198x} & = & \color{red}{198x} +21 \color{blue}{-198x} \color{blue}{+110} \\\Leftrightarrow & -825x-198x& = & 21+110 \\\Leftrightarrow & \color{red}{-1023} x& = & 131 \\\Leftrightarrow & x = \frac{131}{-1023} & & \\\Leftrightarrow & x = \frac{-131}{1023} & & \\ & V = \left\{ \frac{-131}{1023} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{5}{7})& = & -9x+\frac{7}{2} \\\Leftrightarrow & 8x-\frac{10}{7}& = & -9x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{112}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{-126}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 112x \color{red}{-20} & = & \color{red}{-126x} +49 \\\Leftrightarrow & 112x \color{red}{-20} \color{blue}{+20} \color{blue}{+126x} & = & \color{red}{-126x} +49 \color{blue}{+126x} \color{blue}{+20} \\\Leftrightarrow & 112x+126x& = & 49+20 \\\Leftrightarrow & \color{red}{238} x& = & 69 \\\Leftrightarrow & x = \frac{69}{238} & & \\ & V = \left\{ \frac{69}{238} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{8})& = & -2x+\frac{2}{5} \\\Leftrightarrow & 21x+\frac{21}{8}& = & -2x+\frac{2}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{840}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{-80}{ \color{blue}{40} }x+ \frac{16}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 840x \color{red}{+105} & = & \color{red}{-80x} +16 \\\Leftrightarrow & 840x \color{red}{+105} \color{blue}{-105} \color{blue}{+80x} & = & \color{red}{-80x} +16 \color{blue}{+80x} \color{blue}{-105} \\\Leftrightarrow & 840x+80x& = & 16-105 \\\Leftrightarrow & \color{red}{920} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{920} & & \\ & V = \left\{ \frac{-89}{920} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{11})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -10x-\frac{6}{11}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-220}{ \color{blue}{22} }x- \frac{12}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -220x \color{red}{-12} & = & \color{red}{-154x} +33 \\\Leftrightarrow & -220x \color{red}{-12} \color{blue}{+12} \color{blue}{+154x} & = & \color{red}{-154x} +33 \color{blue}{+154x} \color{blue}{+12} \\\Leftrightarrow & -220x+154x& = & 33+12 \\\Leftrightarrow & \color{red}{-66} x& = & 45 \\\Leftrightarrow & x = \frac{45}{-66} & & \\\Leftrightarrow & x = \frac{-15}{22} & & \\ & V = \left\{ \frac{-15}{22} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{4}{5})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -30x+\frac{24}{5}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-300}{ \color{blue}{10} }x+ \frac{48}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -300x \color{red}{+48} & = & \color{red}{-70x} +15 \\\Leftrightarrow & -300x \color{red}{+48} \color{blue}{-48} \color{blue}{+70x} & = & \color{red}{-70x} +15 \color{blue}{+70x} \color{blue}{-48} \\\Leftrightarrow & -300x+70x& = & 15-48 \\\Leftrightarrow & \color{red}{-230} x& = & -33 \\\Leftrightarrow & x = \frac{-33}{-230} & & \\\Leftrightarrow & x = \frac{33}{230} & & \\ & V = \left\{ \frac{33}{230} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{5})& = & 7x+\frac{10}{9} \\\Leftrightarrow & -9x-\frac{9}{5}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-405}{ \color{blue}{45} }x- \frac{81}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -405x \color{red}{-81} & = & \color{red}{315x} +50 \\\Leftrightarrow & -405x \color{red}{-81} \color{blue}{+81} \color{blue}{-315x} & = & \color{red}{315x} +50 \color{blue}{-315x} \color{blue}{+81} \\\Leftrightarrow & -405x-315x& = & 50+81 \\\Leftrightarrow & \color{red}{-720} x& = & 131 \\\Leftrightarrow & x = \frac{131}{-720} & & \\\Leftrightarrow & x = \frac{-131}{720} & & \\ & V = \left\{ \frac{-131}{720} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{11})& = & -5x+\frac{4}{11} \\\Leftrightarrow & -12x-\frac{30}{11}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x- \frac{30}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{-30} & = & \color{red}{-55x} +4 \\\Leftrightarrow & -132x \color{red}{-30} \color{blue}{+30} \color{blue}{+55x} & = & \color{red}{-55x} +4 \color{blue}{+55x} \color{blue}{+30} \\\Leftrightarrow & -132x+55x& = & 4+30 \\\Leftrightarrow & \color{red}{-77} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-77} & & \\\Leftrightarrow & x = \frac{-34}{77} & & \\ & V = \left\{ \frac{-34}{77} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{3}{7})& = & -5x+\frac{7}{2} \\\Leftrightarrow & -4x-\frac{6}{7}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-56}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -56x \color{red}{-12} & = & \color{red}{-70x} +49 \\\Leftrightarrow & -56x \color{red}{-12} \color{blue}{+12} \color{blue}{+70x} & = & \color{red}{-70x} +49 \color{blue}{+70x} \color{blue}{+12} \\\Leftrightarrow & -56x+70x& = & 49+12 \\\Leftrightarrow & \color{red}{14} x& = & 61 \\\Leftrightarrow & x = \frac{61}{14} & & \\ & V = \left\{ \frac{61}{14} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{4}{5})& = & 5x+\frac{3}{11} \\\Leftrightarrow & 24x+\frac{24}{5}& = & 5x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{+264} & = & \color{red}{275x} +15 \\\Leftrightarrow & 1320x \color{red}{+264} \color{blue}{-264} \color{blue}{-275x} & = & \color{red}{275x} +15 \color{blue}{-275x} \color{blue}{-264} \\\Leftrightarrow & 1320x-275x& = & 15-264 \\\Leftrightarrow & \color{red}{1045} x& = & -249 \\\Leftrightarrow & x = \frac{-249}{1045} & & \\ & V = \left\{ \frac{-249}{1045} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{2}{7})& = & 2x+\frac{10}{9} \\\Leftrightarrow & 15x+\frac{6}{7}& = & 2x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{126}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{+54} & = & \color{red}{126x} +70 \\\Leftrightarrow & 945x \color{red}{+54} \color{blue}{-54} \color{blue}{-126x} & = & \color{red}{126x} +70 \color{blue}{-126x} \color{blue}{-54} \\\Leftrightarrow & 945x-126x& = & 70-54 \\\Leftrightarrow & \color{red}{819} x& = & 16 \\\Leftrightarrow & x = \frac{16}{819} & & \\ & V = \left\{ \frac{16}{819} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{3}{11})& = & 7x+\frac{5}{8} \\\Leftrightarrow & -30x-\frac{18}{11}& = & 7x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2640}{ \color{blue}{88} }x- \frac{144}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2640x \color{red}{-144} & = & \color{red}{616x} +55 \\\Leftrightarrow & -2640x \color{red}{-144} \color{blue}{+144} \color{blue}{-616x} & = & \color{red}{616x} +55 \color{blue}{-616x} \color{blue}{+144} \\\Leftrightarrow & -2640x-616x& = & 55+144 \\\Leftrightarrow & \color{red}{-3256} x& = & 199 \\\Leftrightarrow & x = \frac{199}{-3256} & & \\\Leftrightarrow & x = \frac{-199}{3256} & & \\ & V = \left\{ \frac{-199}{3256} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{4}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -16x-\frac{16}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-336}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -336x \color{red}{-48} & = & \color{red}{-147x} +70 \\\Leftrightarrow & -336x \color{red}{-48} \color{blue}{+48} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{+48} \\\Leftrightarrow & -336x+147x& = & 70+48 \\\Leftrightarrow & \color{red}{-189} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-189} & & \\\Leftrightarrow & x = \frac{-118}{189} & & \\ & V = \left\{ \frac{-118}{189} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-17 11:32:02
Een site van Busleyden Atheneum Mechelen