Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{2}{3})& = & -3x+\frac{5}{6} \\\Leftrightarrow & 16x-\frac{8}{3}& = & -3x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{96}{ \color{blue}{6} }x- \frac{16}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 96x \color{red}{-16} & = & \color{red}{-18x} +5 \\\Leftrightarrow & 96x \color{red}{-16} \color{blue}{+16} \color{blue}{+18x} & = & \color{red}{-18x} +5 \color{blue}{+18x} \color{blue}{+16} \\\Leftrightarrow & 96x+18x& = & 5+16 \\\Leftrightarrow & \color{red}{114} x& = & 21 \\\Leftrightarrow & x = \frac{21}{114} & & \\\Leftrightarrow & x = \frac{7}{38} & & \\ & V = \left\{ \frac{7}{38} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{4}{11})& = & 7x+\frac{7}{8} \\\Leftrightarrow & -30x-\frac{24}{11}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2640}{ \color{blue}{88} }x- \frac{192}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2640x \color{red}{-192} & = & \color{red}{616x} +77 \\\Leftrightarrow & -2640x \color{red}{-192} \color{blue}{+192} \color{blue}{-616x} & = & \color{red}{616x} +77 \color{blue}{-616x} \color{blue}{+192} \\\Leftrightarrow & -2640x-616x& = & 77+192 \\\Leftrightarrow & \color{red}{-3256} x& = & 269 \\\Leftrightarrow & x = \frac{269}{-3256} & & \\\Leftrightarrow & x = \frac{-269}{3256} & & \\ & V = \left\{ \frac{-269}{3256} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{4}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 15x-\frac{20}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{-100} & = & \color{red}{-245x} +42 \\\Leftrightarrow & 525x \color{red}{-100} \color{blue}{+100} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{+100} \\\Leftrightarrow & 525x+245x& = & 42+100 \\\Leftrightarrow & \color{red}{770} x& = & 142 \\\Leftrightarrow & x = \frac{142}{770} & & \\\Leftrightarrow & x = \frac{71}{385} & & \\ & V = \left\{ \frac{71}{385} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{3}{5})& = & -5x+\frac{2}{3} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+36} & = & \color{red}{-75x} +10 \\\Leftrightarrow & -180x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +10 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & -180x+75x& = & 10-36 \\\Leftrightarrow & \color{red}{-105} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-105} & & \\\Leftrightarrow & x = \frac{26}{105} & & \\ & V = \left\{ \frac{26}{105} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{3}{5})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-132} & = & \color{red}{275x} +40 \\\Leftrightarrow & 660x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +40 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & 660x-275x& = & 40+132 \\\Leftrightarrow & \color{red}{385} x& = & 172 \\\Leftrightarrow & x = \frac{172}{385} & & \\ & V = \left\{ \frac{172}{385} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{3}{11})& = & 9x+\frac{3}{7} \\\Leftrightarrow & -18x-\frac{18}{11}& = & 9x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{-126} & = & \color{red}{693x} +33 \\\Leftrightarrow & -1386x \color{red}{-126} \color{blue}{+126} \color{blue}{-693x} & = & \color{red}{693x} +33 \color{blue}{-693x} \color{blue}{+126} \\\Leftrightarrow & -1386x-693x& = & 33+126 \\\Leftrightarrow & \color{red}{-2079} x& = & 159 \\\Leftrightarrow & x = \frac{159}{-2079} & & \\\Leftrightarrow & x = \frac{-53}{693} & & \\ & V = \left\{ \frac{-53}{693} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{3}{5})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 6x-\frac{9}{5}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x- \frac{18}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{-18} & = & \color{red}{70x} +45 \\\Leftrightarrow & 60x \color{red}{-18} \color{blue}{+18} \color{blue}{-70x} & = & \color{red}{70x} +45 \color{blue}{-70x} \color{blue}{+18} \\\Leftrightarrow & 60x-70x& = & 45+18 \\\Leftrightarrow & \color{red}{-10} x& = & 63 \\\Leftrightarrow & x = \frac{63}{-10} & & \\\Leftrightarrow & x = \frac{-63}{10} & & \\ & V = \left\{ \frac{-63}{10} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{5}{4})& = & 7x+\frac{3}{7} \\\Leftrightarrow & 15x+\frac{15}{4}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{420}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{12}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 420x \color{red}{+105} & = & \color{red}{196x} +12 \\\Leftrightarrow & 420x \color{red}{+105} \color{blue}{-105} \color{blue}{-196x} & = & \color{red}{196x} +12 \color{blue}{-196x} \color{blue}{-105} \\\Leftrightarrow & 420x-196x& = & 12-105 \\\Leftrightarrow & \color{red}{224} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{224} & & \\ & V = \left\{ \frac{-93}{224} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{2}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x-\frac{8}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x- \frac{8}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{-8} & = & \color{red}{25x} +6 \\\Leftrightarrow & -60x \color{red}{-8} \color{blue}{+8} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{+8} \\\Leftrightarrow & -60x-25x& = & 6+8 \\\Leftrightarrow & \color{red}{-85} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-85} & & \\\Leftrightarrow & x = \frac{-14}{85} & & \\ & V = \left\{ \frac{-14}{85} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{3}{5})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 8x-\frac{12}{5}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{40}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 40x \color{red}{-12} & = & \color{red}{-25x} +4 \\\Leftrightarrow & 40x \color{red}{-12} \color{blue}{+12} \color{blue}{+25x} & = & \color{red}{-25x} +4 \color{blue}{+25x} \color{blue}{+12} \\\Leftrightarrow & 40x+25x& = & 4+12 \\\Leftrightarrow & \color{red}{65} x& = & 16 \\\Leftrightarrow & x = \frac{16}{65} & & \\ & V = \left\{ \frac{16}{65} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{7})& = & 3x+\frac{5}{11} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 3x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-110} & = & \color{red}{231x} +35 \\\Leftrightarrow & 770x \color{red}{-110} \color{blue}{+110} \color{blue}{-231x} & = & \color{red}{231x} +35 \color{blue}{-231x} \color{blue}{+110} \\\Leftrightarrow & 770x-231x& = & 35+110 \\\Leftrightarrow & \color{red}{539} x& = & 145 \\\Leftrightarrow & x = \frac{145}{539} & & \\ & V = \left\{ \frac{145}{539} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{3}{5})& = & 5x+\frac{3}{7} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-84} & = & \color{red}{175x} +15 \\\Leftrightarrow & 420x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +15 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & 420x-175x& = & 15+84 \\\Leftrightarrow & \color{red}{245} x& = & 99 \\\Leftrightarrow & x = \frac{99}{245} & & \\ & V = \left\{ \frac{99}{245} \right\} & \\\end{align}\)
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