Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{2}{3})& = & -8x+\frac{3}{8} \\\Leftrightarrow & -21x+\frac{14}{3}& = & -8x+\frac{3}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-504}{ \color{blue}{24} }x+ \frac{112}{ \color{blue}{24} })& = & (\frac{-192}{ \color{blue}{24} }x+ \frac{9}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -504x \color{red}{+112} & = & \color{red}{-192x} +9 \\\Leftrightarrow & -504x \color{red}{+112} \color{blue}{-112} \color{blue}{+192x} & = & \color{red}{-192x} +9 \color{blue}{+192x} \color{blue}{-112} \\\Leftrightarrow & -504x+192x& = & 9-112 \\\Leftrightarrow & \color{red}{-312} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{-312} & & \\\Leftrightarrow & x = \frac{103}{312} & & \\ & V = \left\{ \frac{103}{312} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{4}{3})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 6x+\frac{8}{3}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{18}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 18x \color{red}{+8} & = & \color{red}{-21x} +10 \\\Leftrightarrow & 18x \color{red}{+8} \color{blue}{-8} \color{blue}{+21x} & = & \color{red}{-21x} +10 \color{blue}{+21x} \color{blue}{-8} \\\Leftrightarrow & 18x+21x& = & 10-8 \\\Leftrightarrow & \color{red}{39} x& = & 2 \\\Leftrightarrow & x = \frac{2}{39} & & \\ & V = \left\{ \frac{2}{39} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{2}{11})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 8x-\frac{8}{11}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{176}{ \color{blue}{22} }x- \frac{16}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 176x \color{red}{-16} & = & \color{red}{-110x} +33 \\\Leftrightarrow & 176x \color{red}{-16} \color{blue}{+16} \color{blue}{+110x} & = & \color{red}{-110x} +33 \color{blue}{+110x} \color{blue}{+16} \\\Leftrightarrow & 176x+110x& = & 33+16 \\\Leftrightarrow & \color{red}{286} x& = & 49 \\\Leftrightarrow & x = \frac{49}{286} & & \\ & V = \left\{ \frac{49}{286} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{3}{5})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -12x-\frac{9}{5}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{63}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-63} & = & \color{red}{-175x} +50 \\\Leftrightarrow & -420x \color{red}{-63} \color{blue}{+63} \color{blue}{+175x} & = & \color{red}{-175x} +50 \color{blue}{+175x} \color{blue}{+63} \\\Leftrightarrow & -420x+175x& = & 50+63 \\\Leftrightarrow & \color{red}{-245} x& = & 113 \\\Leftrightarrow & x = \frac{113}{-245} & & \\\Leftrightarrow & x = \frac{-113}{245} & & \\ & V = \left\{ \frac{-113}{245} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{5})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -30x+\frac{18}{5}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x+ \frac{126}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{+126} & = & \color{red}{-245x} +50 \\\Leftrightarrow & -1050x \color{red}{+126} \color{blue}{-126} \color{blue}{+245x} & = & \color{red}{-245x} +50 \color{blue}{+245x} \color{blue}{-126} \\\Leftrightarrow & -1050x+245x& = & 50-126 \\\Leftrightarrow & \color{red}{-805} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{-805} & & \\\Leftrightarrow & x = \frac{76}{805} & & \\ & V = \left\{ \frac{76}{805} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{11})& = & -5x+\frac{9}{2} \\\Leftrightarrow & -4x-\frac{8}{11}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-88}{ \color{blue}{22} }x- \frac{16}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -88x \color{red}{-16} & = & \color{red}{-110x} +99 \\\Leftrightarrow & -88x \color{red}{-16} \color{blue}{+16} \color{blue}{+110x} & = & \color{red}{-110x} +99 \color{blue}{+110x} \color{blue}{+16} \\\Leftrightarrow & -88x+110x& = & 99+16 \\\Leftrightarrow & \color{red}{22} x& = & 115 \\\Leftrightarrow & x = \frac{115}{22} & & \\ & V = \left\{ \frac{115}{22} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{5}{4})& = & -9x+\frac{6}{11} \\\Leftrightarrow & -28x+\frac{35}{4}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1232}{ \color{blue}{44} }x+ \frac{385}{ \color{blue}{44} })& = & (\frac{-396}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1232x \color{red}{+385} & = & \color{red}{-396x} +24 \\\Leftrightarrow & -1232x \color{red}{+385} \color{blue}{-385} \color{blue}{+396x} & = & \color{red}{-396x} +24 \color{blue}{+396x} \color{blue}{-385} \\\Leftrightarrow & -1232x+396x& = & 24-385 \\\Leftrightarrow & \color{red}{-836} x& = & -361 \\\Leftrightarrow & x = \frac{-361}{-836} & & \\\Leftrightarrow & x = \frac{19}{44} & & \\ & V = \left\{ \frac{19}{44} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{4}{3})& = & -3x+\frac{8}{11} \\\Leftrightarrow & -25x+\frac{20}{3}& = & -3x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-825}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -825x \color{red}{+220} & = & \color{red}{-99x} +24 \\\Leftrightarrow & -825x \color{red}{+220} \color{blue}{-220} \color{blue}{+99x} & = & \color{red}{-99x} +24 \color{blue}{+99x} \color{blue}{-220} \\\Leftrightarrow & -825x+99x& = & 24-220 \\\Leftrightarrow & \color{red}{-726} x& = & -196 \\\Leftrightarrow & x = \frac{-196}{-726} & & \\\Leftrightarrow & x = \frac{98}{363} & & \\ & V = \left\{ \frac{98}{363} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{1}{2})& = & 4x+\frac{8}{7} \\\Leftrightarrow & 15x+\frac{5}{2}& = & 4x+\frac{8}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{210}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} })& = & (\frac{56}{ \color{blue}{14} }x+ \frac{16}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 210x \color{red}{+35} & = & \color{red}{56x} +16 \\\Leftrightarrow & 210x \color{red}{+35} \color{blue}{-35} \color{blue}{-56x} & = & \color{red}{56x} +16 \color{blue}{-56x} \color{blue}{-35} \\\Leftrightarrow & 210x-56x& = & 16-35 \\\Leftrightarrow & \color{red}{154} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{154} & & \\ & V = \left\{ \frac{-19}{154} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{3}{5})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -24x+\frac{18}{5}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-360}{ \color{blue}{15} }x+ \frac{54}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -360x \color{red}{+54} & = & \color{red}{75x} +10 \\\Leftrightarrow & -360x \color{red}{+54} \color{blue}{-54} \color{blue}{-75x} & = & \color{red}{75x} +10 \color{blue}{-75x} \color{blue}{-54} \\\Leftrightarrow & -360x-75x& = & 10-54 \\\Leftrightarrow & \color{red}{-435} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{-435} & & \\\Leftrightarrow & x = \frac{44}{435} & & \\ & V = \left\{ \frac{44}{435} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{3}{5})& = & 7x+\frac{8}{5} \\\Leftrightarrow & 12x-\frac{18}{5}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x- \frac{18}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{-18} & = & \color{red}{35x} +8 \\\Leftrightarrow & 60x \color{red}{-18} \color{blue}{+18} \color{blue}{-35x} & = & \color{red}{35x} +8 \color{blue}{-35x} \color{blue}{+18} \\\Leftrightarrow & 60x-35x& = & 8+18 \\\Leftrightarrow & \color{red}{25} x& = & 26 \\\Leftrightarrow & x = \frac{26}{25} & & \\ & V = \left\{ \frac{26}{25} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{3}{10})& = & -9x+\frac{2}{5} \\\Leftrightarrow & 14x+\frac{21}{10}& = & -9x+\frac{2}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{140}{ \color{blue}{10} }x+ \frac{21}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{4}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 140x \color{red}{+21} & = & \color{red}{-90x} +4 \\\Leftrightarrow & 140x \color{red}{+21} \color{blue}{-21} \color{blue}{+90x} & = & \color{red}{-90x} +4 \color{blue}{+90x} \color{blue}{-21} \\\Leftrightarrow & 140x+90x& = & 4-21 \\\Leftrightarrow & \color{red}{230} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{230} & & \\ & V = \left\{ \frac{-17}{230} \right\} & \\\end{align}\)
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