Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{2}{5})& = & 2x+\frac{9}{5} \\\Leftrightarrow & -18x+\frac{12}{5}& = & 2x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-90}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{10}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -90x \color{red}{+12} & = & \color{red}{10x} +9 \\\Leftrightarrow & -90x \color{red}{+12} \color{blue}{-12} \color{blue}{-10x} & = & \color{red}{10x} +9 \color{blue}{-10x} \color{blue}{-12} \\\Leftrightarrow & -90x-10x& = & 9-12 \\\Leftrightarrow & \color{red}{-100} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-100} & & \\\Leftrightarrow & x = \frac{3}{100} & & \\ & V = \left\{ \frac{3}{100} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{5}{3})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -6x-\frac{10}{3}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-18}{ \color{blue}{3} }x- \frac{10}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -18x \color{red}{-10} & = & \color{red}{-21x} +2 \\\Leftrightarrow & -18x \color{red}{-10} \color{blue}{+10} \color{blue}{+21x} & = & \color{red}{-21x} +2 \color{blue}{+21x} \color{blue}{+10} \\\Leftrightarrow & -18x+21x& = & 2+10 \\\Leftrightarrow & \color{red}{3} x& = & 12 \\\Leftrightarrow & x = \frac{12}{3} & & \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{7})& = & 5x+\frac{7}{12} \\\Leftrightarrow & 18x+\frac{24}{7}& = & 5x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{1512}{ \color{blue}{84} }x+ \frac{288}{ \color{blue}{84} })& = & (\frac{420}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 1512x \color{red}{+288} & = & \color{red}{420x} +49 \\\Leftrightarrow & 1512x \color{red}{+288} \color{blue}{-288} \color{blue}{-420x} & = & \color{red}{420x} +49 \color{blue}{-420x} \color{blue}{-288} \\\Leftrightarrow & 1512x-420x& = & 49-288 \\\Leftrightarrow & \color{red}{1092} x& = & -239 \\\Leftrightarrow & x = \frac{-239}{1092} & & \\ & V = \left\{ \frac{-239}{1092} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{3}{5})& = & -3x+\frac{3}{7} \\\Leftrightarrow & 20x+\frac{12}{5}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{+84} & = & \color{red}{-105x} +15 \\\Leftrightarrow & 700x \color{red}{+84} \color{blue}{-84} \color{blue}{+105x} & = & \color{red}{-105x} +15 \color{blue}{+105x} \color{blue}{-84} \\\Leftrightarrow & 700x+105x& = & 15-84 \\\Leftrightarrow & \color{red}{805} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{805} & & \\\Leftrightarrow & x = \frac{-3}{35} & & \\ & V = \left\{ \frac{-3}{35} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{7})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -20x-\frac{16}{7}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-140}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -140x \color{red}{-16} & = & \color{red}{49x} +4 \\\Leftrightarrow & -140x \color{red}{-16} \color{blue}{+16} \color{blue}{-49x} & = & \color{red}{49x} +4 \color{blue}{-49x} \color{blue}{+16} \\\Leftrightarrow & -140x-49x& = & 4+16 \\\Leftrightarrow & \color{red}{-189} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-189} & & \\\Leftrightarrow & x = \frac{-20}{189} & & \\ & V = \left\{ \frac{-20}{189} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{5}{3})& = & -5x+\frac{10}{9} \\\Leftrightarrow & 12x-\frac{20}{3}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{108}{ \color{blue}{9} }x- \frac{60}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 108x \color{red}{-60} & = & \color{red}{-45x} +10 \\\Leftrightarrow & 108x \color{red}{-60} \color{blue}{+60} \color{blue}{+45x} & = & \color{red}{-45x} +10 \color{blue}{+45x} \color{blue}{+60} \\\Leftrightarrow & 108x+45x& = & 10+60 \\\Leftrightarrow & \color{red}{153} x& = & 70 \\\Leftrightarrow & x = \frac{70}{153} & & \\ & V = \left\{ \frac{70}{153} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{3}{5})& = & 7x+\frac{8}{9} \\\Leftrightarrow & -9x+\frac{9}{5}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-405}{ \color{blue}{45} }x+ \frac{81}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -405x \color{red}{+81} & = & \color{red}{315x} +40 \\\Leftrightarrow & -405x \color{red}{+81} \color{blue}{-81} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{-81} \\\Leftrightarrow & -405x-315x& = & 40-81 \\\Leftrightarrow & \color{red}{-720} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{-720} & & \\\Leftrightarrow & x = \frac{41}{720} & & \\ & V = \left\{ \frac{41}{720} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{4}{7})& = & 2x+\frac{3}{4} \\\Leftrightarrow & 21x+4& = & 2x+\frac{3}{4} \\ & & & \text{kgv van noemers 1 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{84}{ \color{blue}{4} }x+ \frac{16}{ \color{blue}{4} })& = & (\frac{8}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 84x \color{red}{+16} & = & \color{red}{8x} +3 \\\Leftrightarrow & 84x \color{red}{+16} \color{blue}{-16} \color{blue}{-8x} & = & \color{red}{8x} +3 \color{blue}{-8x} \color{blue}{-16} \\\Leftrightarrow & 84x-8x& = & 3-16 \\\Leftrightarrow & \color{red}{76} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{76} & & \\ & V = \left\{ \frac{-13}{76} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{3}{4})& = & 7x+\frac{7}{8} \\\Leftrightarrow & 20x+\frac{15}{4}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{160}{ \color{blue}{8} }x+ \frac{30}{ \color{blue}{8} })& = & (\frac{56}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 160x \color{red}{+30} & = & \color{red}{56x} +7 \\\Leftrightarrow & 160x \color{red}{+30} \color{blue}{-30} \color{blue}{-56x} & = & \color{red}{56x} +7 \color{blue}{-56x} \color{blue}{-30} \\\Leftrightarrow & 160x-56x& = & 7-30 \\\Leftrightarrow & \color{red}{104} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{104} & & \\ & V = \left\{ \frac{-23}{104} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{2}{11})& = & 8x+\frac{9}{7} \\\Leftrightarrow & 35x-\frac{14}{11}& = & 8x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2695}{ \color{blue}{77} }x- \frac{98}{ \color{blue}{77} })& = & (\frac{616}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2695x \color{red}{-98} & = & \color{red}{616x} +99 \\\Leftrightarrow & 2695x \color{red}{-98} \color{blue}{+98} \color{blue}{-616x} & = & \color{red}{616x} +99 \color{blue}{-616x} \color{blue}{+98} \\\Leftrightarrow & 2695x-616x& = & 99+98 \\\Leftrightarrow & \color{red}{2079} x& = & 197 \\\Leftrightarrow & x = \frac{197}{2079} & & \\ & V = \left\{ \frac{197}{2079} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{4}{7})& = & -5x+\frac{5}{3} \\\Leftrightarrow & 24x-\frac{24}{7}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{504}{ \color{blue}{21} }x- \frac{72}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 504x \color{red}{-72} & = & \color{red}{-105x} +35 \\\Leftrightarrow & 504x \color{red}{-72} \color{blue}{+72} \color{blue}{+105x} & = & \color{red}{-105x} +35 \color{blue}{+105x} \color{blue}{+72} \\\Leftrightarrow & 504x+105x& = & 35+72 \\\Leftrightarrow & \color{red}{609} x& = & 107 \\\Leftrightarrow & x = \frac{107}{609} & & \\ & V = \left\{ \frac{107}{609} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{3}{7})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 6x+\frac{9}{7}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{+27} & = & \color{red}{105x} +70 \\\Leftrightarrow & 126x \color{red}{+27} \color{blue}{-27} \color{blue}{-105x} & = & \color{red}{105x} +70 \color{blue}{-105x} \color{blue}{-27} \\\Leftrightarrow & 126x-105x& = & 70-27 \\\Leftrightarrow & \color{red}{21} x& = & 43 \\\Leftrightarrow & x = \frac{43}{21} & & \\ & V = \left\{ \frac{43}{21} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-20 18:46:21
Een site van Busleyden Atheneum Mechelen