Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

  1. \(-7(-5x-\frac{3}{10})=8x+\frac{5}{4}\)
  2. \(-4(4x+\frac{2}{5})=-9x+\frac{10}{3}\)
  3. \(-7(4x-\frac{4}{5})=-9x+\frac{4}{5}\)
  4. \(4(-3x-\frac{5}{12})=7x+\frac{5}{11}\)
  5. \(3(x-\frac{4}{15})=5x+\frac{3}{16}\)
  6. \(-(-3x-\frac{5}{11})=-2x+\frac{7}{12}\)
  7. \(-5(4x+\frac{2}{5})=9x+\frac{8}{13}\)
  8. \(6(5x-\frac{5}{6})=7x+\frac{8}{13}\)
  9. \(6(5x-\frac{2}{15})=x+\frac{8}{13}\)
  10. \(-3(-4x+\frac{5}{13})=-7x+\frac{8}{3}\)
  11. \(-2(-2x-\frac{2}{9})=3x+\frac{4}{13}\)
  12. \(-4(4x+\frac{4}{5})=-3x+\frac{4}{3}\)

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{3}{10})& = & 8x+\frac{5}{4} \\\Leftrightarrow & 35x+\frac{21}{10}& = & 8x+\frac{5}{4} \\ & & & \text{kgv van noemers 10 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(35x+\frac{21}{10})& = & (8x+\frac{5}{4}). \color{blue}{20} \\\Leftrightarrow & 700x \color{red}{+42} & = & \color{red}{160x} +25 \\\Leftrightarrow & 700x \color{red}{+42} \color{blue}{-42} \color{blue}{-160x} & = & \color{red}{160x} +25 \color{blue}{-160x} \color{blue}{-42} \\\Leftrightarrow & 700x-160x& = & 25-42 \\\Leftrightarrow & \color{red}{540} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{540} & & \\ & V = \left\{ \frac{-17}{540} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{2}{5})& = & -9x+\frac{10}{3} \\\Leftrightarrow & -16x-\frac{8}{5}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(-16x-\frac{8}{5})& = & (-9x+\frac{10}{3}). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{-24} & = & \color{red}{-135x} +50 \\\Leftrightarrow & -240x \color{red}{-24} \color{blue}{+24} \color{blue}{+135x} & = & \color{red}{-135x} +50 \color{blue}{+135x} \color{blue}{+24} \\\Leftrightarrow & -240x+135x& = & 50+24 \\\Leftrightarrow & \color{red}{-105} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-105} & & \\\Leftrightarrow & x = \frac{-74}{105} & & \\ & V = \left\{ \frac{-74}{105} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{4}{5})& = & -9x+\frac{4}{5} \\\Leftrightarrow & -28x+\frac{28}{5}& = & -9x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(-28x+\frac{28}{5})& = & (-9x+\frac{4}{5}). \color{blue}{5} \\\Leftrightarrow & -140x \color{red}{+28} & = & \color{red}{-45x} +4 \\\Leftrightarrow & -140x \color{red}{+28} \color{blue}{-28} \color{blue}{+45x} & = & \color{red}{-45x} +4 \color{blue}{+45x} \color{blue}{-28} \\\Leftrightarrow & -140x+45x& = & 4-28 \\\Leftrightarrow & \color{red}{-95} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{-95} & & \\\Leftrightarrow & x = \frac{24}{95} & & \\ & V = \left\{ \frac{24}{95} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{12})& = & 7x+\frac{5}{11} \\\Leftrightarrow & -12x-\frac{5}{3}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(-12x-\frac{5}{3})& = & (7x+\frac{5}{11}). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-55} & = & \color{red}{231x} +15 \\\Leftrightarrow & -396x \color{red}{-55} \color{blue}{+55} \color{blue}{-231x} & = & \color{red}{231x} +15 \color{blue}{-231x} \color{blue}{+55} \\\Leftrightarrow & -396x-231x& = & 15+55 \\\Leftrightarrow & \color{red}{-627} x& = & 70 \\\Leftrightarrow & x = \frac{70}{-627} & & \\\Leftrightarrow & x = \frac{-70}{627} & & \\ & V = \left\{ \frac{-70}{627} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (x-\frac{4}{15})& = & 5x+\frac{3}{16} \\\Leftrightarrow & 3x-\frac{4}{5}& = & 5x+\frac{3}{16} \\ & & & \text{kgv van noemers 5 en 16 is 80} \\\Leftrightarrow & \color{blue}{80} .(3x-\frac{4}{5})& = & (5x+\frac{3}{16}). \color{blue}{80} \\\Leftrightarrow & 240x \color{red}{-64} & = & \color{red}{400x} +15 \\\Leftrightarrow & 240x \color{red}{-64} \color{blue}{+64} \color{blue}{-400x} & = & \color{red}{400x} +15 \color{blue}{-400x} \color{blue}{+64} \\\Leftrightarrow & 240x-400x& = & 15+64 \\\Leftrightarrow & \color{red}{-160} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-160} & & \\\Leftrightarrow & x = \frac{-79}{160} & & \\ & V = \left\{ \frac{-79}{160} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-} (-3x-\frac{5}{11})& = & -2x+\frac{7}{12} \\\Leftrightarrow & 3x+\frac{5}{11}& = & -2x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(3x+\frac{5}{11})& = & (-2x+\frac{7}{12}). \color{blue}{132} \\\Leftrightarrow & 396x \color{red}{+60} & = & \color{red}{-264x} +77 \\\Leftrightarrow & 396x \color{red}{+60} \color{blue}{-60} \color{blue}{+264x} & = & \color{red}{-264x} +77 \color{blue}{+264x} \color{blue}{-60} \\\Leftrightarrow & 396x+264x& = & 77-60 \\\Leftrightarrow & \color{red}{660} x& = & 17 \\\Leftrightarrow & x = \frac{17}{660} & & \\ & V = \left\{ \frac{17}{660} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{5})& = & 9x+\frac{8}{13} \\\Leftrightarrow & -20x-2& = & 9x+\frac{8}{13} \\ & & & \text{kgv van noemers 1 en 13 is 13} \\\Leftrightarrow & \color{blue}{13} .(-20x-2)& = & (9x+\frac{8}{13}). \color{blue}{13} \\\Leftrightarrow & -260x \color{red}{-26} & = & \color{red}{117x} +8 \\\Leftrightarrow & -260x \color{red}{-26} \color{blue}{+26} \color{blue}{-117x} & = & \color{red}{117x} +8 \color{blue}{-117x} \color{blue}{+26} \\\Leftrightarrow & -260x-117x& = & 8+26 \\\Leftrightarrow & \color{red}{-377} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-377} & & \\\Leftrightarrow & x = \frac{-34}{377} & & \\ & V = \left\{ \frac{-34}{377} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{5}{6})& = & 7x+\frac{8}{13} \\\Leftrightarrow & 30x-5& = & 7x+\frac{8}{13} \\ & & & \text{kgv van noemers 1 en 13 is 13} \\\Leftrightarrow & \color{blue}{13} .(30x-5)& = & (7x+\frac{8}{13}). \color{blue}{13} \\\Leftrightarrow & 390x \color{red}{-65} & = & \color{red}{91x} +8 \\\Leftrightarrow & 390x \color{red}{-65} \color{blue}{+65} \color{blue}{-91x} & = & \color{red}{91x} +8 \color{blue}{-91x} \color{blue}{+65} \\\Leftrightarrow & 390x-91x& = & 8+65 \\\Leftrightarrow & \color{red}{299} x& = & 73 \\\Leftrightarrow & x = \frac{73}{299} & & \\ & V = \left\{ \frac{73}{299} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{2}{15})& = & x+\frac{8}{13} \\\Leftrightarrow & 30x-\frac{4}{5}& = & x+\frac{8}{13} \\ & & & \text{kgv van noemers 5 en 13 is 65} \\\Leftrightarrow & \color{blue}{65} .(30x-\frac{4}{5})& = & (x+\frac{8}{13}). \color{blue}{65} \\\Leftrightarrow & 1950x \color{red}{-52} & = & \color{red}{65x} +40 \\\Leftrightarrow & 1950x \color{red}{-52} \color{blue}{+52} \color{blue}{-65x} & = & \color{red}{65x} +40 \color{blue}{-65x} \color{blue}{+52} \\\Leftrightarrow & 1950x-65x& = & 40+52 \\\Leftrightarrow & \color{red}{1885} x& = & 92 \\\Leftrightarrow & x = \frac{92}{1885} & & \\ & V = \left\{ \frac{92}{1885} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{5}{13})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 12x-\frac{15}{13}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 13 en 3 is 39} \\\Leftrightarrow & \color{blue}{39} .(12x-\frac{15}{13})& = & (-7x+\frac{8}{3}). \color{blue}{39} \\\Leftrightarrow & 468x \color{red}{-45} & = & \color{red}{-273x} +104 \\\Leftrightarrow & 468x \color{red}{-45} \color{blue}{+45} \color{blue}{+273x} & = & \color{red}{-273x} +104 \color{blue}{+273x} \color{blue}{+45} \\\Leftrightarrow & 468x+273x& = & 104+45 \\\Leftrightarrow & \color{red}{741} x& = & 149 \\\Leftrightarrow & x = \frac{149}{741} & & \\ & V = \left\{ \frac{149}{741} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{2}{9})& = & 3x+\frac{4}{13} \\\Leftrightarrow & 4x+\frac{4}{9}& = & 3x+\frac{4}{13} \\ & & & \text{kgv van noemers 9 en 13 is 117} \\\Leftrightarrow & \color{blue}{117} .(4x+\frac{4}{9})& = & (3x+\frac{4}{13}). \color{blue}{117} \\\Leftrightarrow & 468x \color{red}{+52} & = & \color{red}{351x} +36 \\\Leftrightarrow & 468x \color{red}{+52} \color{blue}{-52} \color{blue}{-351x} & = & \color{red}{351x} +36 \color{blue}{-351x} \color{blue}{-52} \\\Leftrightarrow & 468x-351x& = & 36-52 \\\Leftrightarrow & \color{red}{117} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{117} & & \\ & V = \left\{ \frac{-16}{117} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{4}{5})& = & -3x+\frac{4}{3} \\\Leftrightarrow & -16x-\frac{16}{5}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(-16x-\frac{16}{5})& = & (-3x+\frac{4}{3}). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{-48} & = & \color{red}{-45x} +20 \\\Leftrightarrow & -240x \color{red}{-48} \color{blue}{+48} \color{blue}{+45x} & = & \color{red}{-45x} +20 \color{blue}{+45x} \color{blue}{+48} \\\Leftrightarrow & -240x+45x& = & 20+48 \\\Leftrightarrow & \color{red}{-195} x& = & 68 \\\Leftrightarrow & x = \frac{68}{-195} & & \\\Leftrightarrow & x = \frac{-68}{195} & & \\ & V = \left\{ \frac{-68}{195} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2024-11-21 09:56:12