Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{3}{11})& = & 7x+\frac{7}{4} \\\Leftrightarrow & 10x-\frac{15}{11}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{440}{ \color{blue}{44} }x- \frac{60}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 440x \color{red}{-60} & = & \color{red}{308x} +77 \\\Leftrightarrow & 440x \color{red}{-60} \color{blue}{+60} \color{blue}{-308x} & = & \color{red}{308x} +77 \color{blue}{-308x} \color{blue}{+60} \\\Leftrightarrow & 440x-308x& = & 77+60 \\\Leftrightarrow & \color{red}{132} x& = & 137 \\\Leftrightarrow & x = \frac{137}{132} & & \\ & V = \left\{ \frac{137}{132} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{2}{5})& = & 7x+\frac{3}{10} \\\Leftrightarrow & 30x-\frac{12}{5}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{300}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 300x \color{red}{-24} & = & \color{red}{70x} +3 \\\Leftrightarrow & 300x \color{red}{-24} \color{blue}{+24} \color{blue}{-70x} & = & \color{red}{70x} +3 \color{blue}{-70x} \color{blue}{+24} \\\Leftrightarrow & 300x-70x& = & 3+24 \\\Leftrightarrow & \color{red}{230} x& = & 27 \\\Leftrightarrow & x = \frac{27}{230} & & \\ & V = \left\{ \frac{27}{230} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{2}{11})& = & -9x+\frac{2}{5} \\\Leftrightarrow & -18x-\frac{12}{11}& = & -9x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{-60} & = & \color{red}{-495x} +22 \\\Leftrightarrow & -990x \color{red}{-60} \color{blue}{+60} \color{blue}{+495x} & = & \color{red}{-495x} +22 \color{blue}{+495x} \color{blue}{+60} \\\Leftrightarrow & -990x+495x& = & 22+60 \\\Leftrightarrow & \color{red}{-495} x& = & 82 \\\Leftrightarrow & x = \frac{82}{-495} & & \\\Leftrightarrow & x = \frac{-82}{495} & & \\ & V = \left\{ \frac{-82}{495} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{7})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -10x-\frac{6}{7}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-140}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -140x \color{red}{-12} & = & \color{red}{98x} +63 \\\Leftrightarrow & -140x \color{red}{-12} \color{blue}{+12} \color{blue}{-98x} & = & \color{red}{98x} +63 \color{blue}{-98x} \color{blue}{+12} \\\Leftrightarrow & -140x-98x& = & 63+12 \\\Leftrightarrow & \color{red}{-238} x& = & 75 \\\Leftrightarrow & x = \frac{75}{-238} & & \\\Leftrightarrow & x = \frac{-75}{238} & & \\ & V = \left\{ \frac{-75}{238} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{9})& = & 9x+\frac{9}{4} \\\Leftrightarrow & 28x-\frac{14}{9}& = & 9x+\frac{9}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{1008}{ \color{blue}{36} }x- \frac{56}{ \color{blue}{36} })& = & (\frac{324}{ \color{blue}{36} }x+ \frac{81}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 1008x \color{red}{-56} & = & \color{red}{324x} +81 \\\Leftrightarrow & 1008x \color{red}{-56} \color{blue}{+56} \color{blue}{-324x} & = & \color{red}{324x} +81 \color{blue}{-324x} \color{blue}{+56} \\\Leftrightarrow & 1008x-324x& = & 81+56 \\\Leftrightarrow & \color{red}{684} x& = & 137 \\\Leftrightarrow & x = \frac{137}{684} & & \\ & V = \left\{ \frac{137}{684} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{3})& = & -3x+\frac{5}{9} \\\Leftrightarrow & -35x-\frac{14}{3}& = & -3x+\frac{5}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-315}{ \color{blue}{9} }x- \frac{42}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -315x \color{red}{-42} & = & \color{red}{-27x} +5 \\\Leftrightarrow & -315x \color{red}{-42} \color{blue}{+42} \color{blue}{+27x} & = & \color{red}{-27x} +5 \color{blue}{+27x} \color{blue}{+42} \\\Leftrightarrow & -315x+27x& = & 5+42 \\\Leftrightarrow & \color{red}{-288} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-288} & & \\\Leftrightarrow & x = \frac{-47}{288} & & \\ & V = \left\{ \frac{-47}{288} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{10})& = & 8x+\frac{7}{11} \\\Leftrightarrow & 21x+\frac{21}{10}& = & 8x+\frac{7}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{2310}{ \color{blue}{110} }x+ \frac{231}{ \color{blue}{110} })& = & (\frac{880}{ \color{blue}{110} }x+ \frac{70}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 2310x \color{red}{+231} & = & \color{red}{880x} +70 \\\Leftrightarrow & 2310x \color{red}{+231} \color{blue}{-231} \color{blue}{-880x} & = & \color{red}{880x} +70 \color{blue}{-880x} \color{blue}{-231} \\\Leftrightarrow & 2310x-880x& = & 70-231 \\\Leftrightarrow & \color{red}{1430} x& = & -161 \\\Leftrightarrow & x = \frac{-161}{1430} & & \\ & V = \left\{ \frac{-161}{1430} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{8})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -20x+\frac{15}{8}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-160}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{36}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -160x \color{red}{+15} & = & \color{red}{-56x} +36 \\\Leftrightarrow & -160x \color{red}{+15} \color{blue}{-15} \color{blue}{+56x} & = & \color{red}{-56x} +36 \color{blue}{+56x} \color{blue}{-15} \\\Leftrightarrow & -160x+56x& = & 36-15 \\\Leftrightarrow & \color{red}{-104} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-104} & & \\\Leftrightarrow & x = \frac{-21}{104} & & \\ & V = \left\{ \frac{-21}{104} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{2}{7})& = & -5x+\frac{10}{3} \\\Leftrightarrow & -12x-\frac{6}{7}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-18} & = & \color{red}{-105x} +70 \\\Leftrightarrow & -252x \color{red}{-18} \color{blue}{+18} \color{blue}{+105x} & = & \color{red}{-105x} +70 \color{blue}{+105x} \color{blue}{+18} \\\Leftrightarrow & -252x+105x& = & 70+18 \\\Leftrightarrow & \color{red}{-147} x& = & 88 \\\Leftrightarrow & x = \frac{88}{-147} & & \\\Leftrightarrow & x = \frac{-88}{147} & & \\ & V = \left\{ \frac{-88}{147} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{11})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -30x-\frac{18}{11}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-990}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -990x \color{red}{-54} & = & \color{red}{-231x} +22 \\\Leftrightarrow & -990x \color{red}{-54} \color{blue}{+54} \color{blue}{+231x} & = & \color{red}{-231x} +22 \color{blue}{+231x} \color{blue}{+54} \\\Leftrightarrow & -990x+231x& = & 22+54 \\\Leftrightarrow & \color{red}{-759} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-759} & & \\\Leftrightarrow & x = \frac{-76}{759} & & \\ & V = \left\{ \frac{-76}{759} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{4}{9})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 6x-\frac{8}{9}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{108}{ \color{blue}{18} }x- \frac{16}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 108x \color{red}{-16} & = & \color{red}{-90x} +27 \\\Leftrightarrow & 108x \color{red}{-16} \color{blue}{+16} \color{blue}{+90x} & = & \color{red}{-90x} +27 \color{blue}{+90x} \color{blue}{+16} \\\Leftrightarrow & 108x+90x& = & 27+16 \\\Leftrightarrow & \color{red}{198} x& = & 43 \\\Leftrightarrow & x = \frac{43}{198} & & \\ & V = \left\{ \frac{43}{198} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{2}{5})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 24x-\frac{12}{5}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{240}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 240x \color{red}{-24} & = & \color{red}{-50x} +45 \\\Leftrightarrow & 240x \color{red}{-24} \color{blue}{+24} \color{blue}{+50x} & = & \color{red}{-50x} +45 \color{blue}{+50x} \color{blue}{+24} \\\Leftrightarrow & 240x+50x& = & 45+24 \\\Leftrightarrow & \color{red}{290} x& = & 69 \\\Leftrightarrow & x = \frac{69}{290} & & \\ & V = \left\{ \frac{69}{290} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-01 08:14:19
Een site van Busleyden Atheneum Mechelen