Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{3})& = & -7x+\frac{4}{9} \\\Leftrightarrow & 8x+\frac{8}{3}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{+24} & = & \color{red}{-63x} +4 \\\Leftrightarrow & 72x \color{red}{+24} \color{blue}{-24} \color{blue}{+63x} & = & \color{red}{-63x} +4 \color{blue}{+63x} \color{blue}{-24} \\\Leftrightarrow & 72x+63x& = & 4-24 \\\Leftrightarrow & \color{red}{135} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{135} & & \\\Leftrightarrow & x = \frac{-4}{27} & & \\ & V = \left\{ \frac{-4}{27} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{3}{5})& = & -5x+\frac{7}{11} \\\Leftrightarrow & 16x-\frac{12}{5}& = & -5x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{880}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 880x \color{red}{-132} & = & \color{red}{-275x} +35 \\\Leftrightarrow & 880x \color{red}{-132} \color{blue}{+132} \color{blue}{+275x} & = & \color{red}{-275x} +35 \color{blue}{+275x} \color{blue}{+132} \\\Leftrightarrow & 880x+275x& = & 35+132 \\\Leftrightarrow & \color{red}{1155} x& = & 167 \\\Leftrightarrow & x = \frac{167}{1155} & & \\ & V = \left\{ \frac{167}{1155} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{11})& = & -2x+\frac{8}{9} \\\Leftrightarrow & 21x+\frac{21}{11}& = & -2x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2079}{ \color{blue}{99} }x+ \frac{189}{ \color{blue}{99} })& = & (\frac{-198}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2079x \color{red}{+189} & = & \color{red}{-198x} +88 \\\Leftrightarrow & 2079x \color{red}{+189} \color{blue}{-189} \color{blue}{+198x} & = & \color{red}{-198x} +88 \color{blue}{+198x} \color{blue}{-189} \\\Leftrightarrow & 2079x+198x& = & 88-189 \\\Leftrightarrow & \color{red}{2277} x& = & -101 \\\Leftrightarrow & x = \frac{-101}{2277} & & \\ & V = \left\{ \frac{-101}{2277} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{5}{7})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 12x-\frac{20}{7}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{-60} & = & \color{red}{105x} +56 \\\Leftrightarrow & 252x \color{red}{-60} \color{blue}{+60} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{+60} \\\Leftrightarrow & 252x-105x& = & 56+60 \\\Leftrightarrow & \color{red}{147} x& = & 116 \\\Leftrightarrow & x = \frac{116}{147} & & \\ & V = \left\{ \frac{116}{147} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{2}{3})& = & 5x+\frac{2}{5} \\\Leftrightarrow & -12x+\frac{8}{3}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+40} & = & \color{red}{75x} +6 \\\Leftrightarrow & -180x \color{red}{+40} \color{blue}{-40} \color{blue}{-75x} & = & \color{red}{75x} +6 \color{blue}{-75x} \color{blue}{-40} \\\Leftrightarrow & -180x-75x& = & 6-40 \\\Leftrightarrow & \color{red}{-255} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-255} & & \\\Leftrightarrow & x = \frac{2}{15} & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{4}{5})& = & 8x+\frac{2}{9} \\\Leftrightarrow & -15x-\frac{12}{5}& = & 8x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-675}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{360}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -675x \color{red}{-108} & = & \color{red}{360x} +10 \\\Leftrightarrow & -675x \color{red}{-108} \color{blue}{+108} \color{blue}{-360x} & = & \color{red}{360x} +10 \color{blue}{-360x} \color{blue}{+108} \\\Leftrightarrow & -675x-360x& = & 10+108 \\\Leftrightarrow & \color{red}{-1035} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-1035} & & \\\Leftrightarrow & x = \frac{-118}{1035} & & \\ & V = \left\{ \frac{-118}{1035} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{5}{11})& = & 9x+\frac{9}{4} \\\Leftrightarrow & -25x-\frac{25}{11}& = & 9x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1100}{ \color{blue}{44} }x- \frac{100}{ \color{blue}{44} })& = & (\frac{396}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1100x \color{red}{-100} & = & \color{red}{396x} +99 \\\Leftrightarrow & -1100x \color{red}{-100} \color{blue}{+100} \color{blue}{-396x} & = & \color{red}{396x} +99 \color{blue}{-396x} \color{blue}{+100} \\\Leftrightarrow & -1100x-396x& = & 99+100 \\\Leftrightarrow & \color{red}{-1496} x& = & 199 \\\Leftrightarrow & x = \frac{199}{-1496} & & \\\Leftrightarrow & x = \frac{-199}{1496} & & \\ & V = \left\{ \frac{-199}{1496} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{2}{7})& = & -7x+\frac{9}{8} \\\Leftrightarrow & -10x+\frac{10}{7}& = & -7x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-560}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -560x \color{red}{+80} & = & \color{red}{-392x} +63 \\\Leftrightarrow & -560x \color{red}{+80} \color{blue}{-80} \color{blue}{+392x} & = & \color{red}{-392x} +63 \color{blue}{+392x} \color{blue}{-80} \\\Leftrightarrow & -560x+392x& = & 63-80 \\\Leftrightarrow & \color{red}{-168} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-168} & & \\\Leftrightarrow & x = \frac{17}{168} & & \\ & V = \left\{ \frac{17}{168} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{3}{11})& = & 7x+\frac{10}{9} \\\Leftrightarrow & -30x-\frac{18}{11}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2970}{ \color{blue}{99} }x- \frac{162}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2970x \color{red}{-162} & = & \color{red}{693x} +110 \\\Leftrightarrow & -2970x \color{red}{-162} \color{blue}{+162} \color{blue}{-693x} & = & \color{red}{693x} +110 \color{blue}{-693x} \color{blue}{+162} \\\Leftrightarrow & -2970x-693x& = & 110+162 \\\Leftrightarrow & \color{red}{-3663} x& = & 272 \\\Leftrightarrow & x = \frac{272}{-3663} & & \\\Leftrightarrow & x = \frac{-272}{3663} & & \\ & V = \left\{ \frac{-272}{3663} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{8})& = & -3x+\frac{4}{11} \\\Leftrightarrow & -14x-\frac{21}{8}& = & -3x+\frac{4}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1232}{ \color{blue}{88} }x- \frac{231}{ \color{blue}{88} })& = & (\frac{-264}{ \color{blue}{88} }x+ \frac{32}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1232x \color{red}{-231} & = & \color{red}{-264x} +32 \\\Leftrightarrow & -1232x \color{red}{-231} \color{blue}{+231} \color{blue}{+264x} & = & \color{red}{-264x} +32 \color{blue}{+264x} \color{blue}{+231} \\\Leftrightarrow & -1232x+264x& = & 32+231 \\\Leftrightarrow & \color{red}{-968} x& = & 263 \\\Leftrightarrow & x = \frac{263}{-968} & & \\\Leftrightarrow & x = \frac{-263}{968} & & \\ & V = \left\{ \frac{-263}{968} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{3})& = & 2x+\frac{9}{2} \\\Leftrightarrow & 15x-\frac{20}{3}& = & 2x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{90}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{12}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 90x \color{red}{-40} & = & \color{red}{12x} +27 \\\Leftrightarrow & 90x \color{red}{-40} \color{blue}{+40} \color{blue}{-12x} & = & \color{red}{12x} +27 \color{blue}{-12x} \color{blue}{+40} \\\Leftrightarrow & 90x-12x& = & 27+40 \\\Leftrightarrow & \color{red}{78} x& = & 67 \\\Leftrightarrow & x = \frac{67}{78} & & \\ & V = \left\{ \frac{67}{78} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{2}{5})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -10x+\frac{4}{5}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{+44} & = & \color{red}{385x} +30 \\\Leftrightarrow & -550x \color{red}{+44} \color{blue}{-44} \color{blue}{-385x} & = & \color{red}{385x} +30 \color{blue}{-385x} \color{blue}{-44} \\\Leftrightarrow & -550x-385x& = & 30-44 \\\Leftrightarrow & \color{red}{-935} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-935} & & \\\Leftrightarrow & x = \frac{14}{935} & & \\ & V = \left\{ \frac{14}{935} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-05-14 01:02:09
Een site van Busleyden Atheneum Mechelen