Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{7})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -12x-\frac{30}{7}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-330} & = & \color{red}{-385x} +42 \\\Leftrightarrow & -924x \color{red}{-330} \color{blue}{+330} \color{blue}{+385x} & = & \color{red}{-385x} +42 \color{blue}{+385x} \color{blue}{+330} \\\Leftrightarrow & -924x+385x& = & 42+330 \\\Leftrightarrow & \color{red}{-539} x& = & 372 \\\Leftrightarrow & x = \frac{372}{-539} & & \\\Leftrightarrow & x = \frac{-372}{539} & & \\ & V = \left\{ \frac{-372}{539} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{2}{5})& = & 5x+\frac{4}{9} \\\Leftrightarrow & -24x+\frac{12}{5}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1080}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1080x \color{red}{+108} & = & \color{red}{225x} +20 \\\Leftrightarrow & -1080x \color{red}{+108} \color{blue}{-108} \color{blue}{-225x} & = & \color{red}{225x} +20 \color{blue}{-225x} \color{blue}{-108} \\\Leftrightarrow & -1080x-225x& = & 20-108 \\\Leftrightarrow & \color{red}{-1305} x& = & -88 \\\Leftrightarrow & x = \frac{-88}{-1305} & & \\\Leftrightarrow & x = \frac{88}{1305} & & \\ & V = \left\{ \frac{88}{1305} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{3}{7})& = & -5x+\frac{7}{6} \\\Leftrightarrow & -4x-\frac{6}{7}& = & -5x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-168}{ \color{blue}{42} }x- \frac{36}{ \color{blue}{42} })& = & (\frac{-210}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -168x \color{red}{-36} & = & \color{red}{-210x} +49 \\\Leftrightarrow & -168x \color{red}{-36} \color{blue}{+36} \color{blue}{+210x} & = & \color{red}{-210x} +49 \color{blue}{+210x} \color{blue}{+36} \\\Leftrightarrow & -168x+210x& = & 49+36 \\\Leftrightarrow & \color{red}{42} x& = & 85 \\\Leftrightarrow & x = \frac{85}{42} & & \\ & V = \left\{ \frac{85}{42} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{5}{4})& = & -8x+\frac{4}{7} \\\Leftrightarrow & -15x+\frac{15}{4}& = & -8x+\frac{4}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-420}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{-224}{ \color{blue}{28} }x+ \frac{16}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -420x \color{red}{+105} & = & \color{red}{-224x} +16 \\\Leftrightarrow & -420x \color{red}{+105} \color{blue}{-105} \color{blue}{+224x} & = & \color{red}{-224x} +16 \color{blue}{+224x} \color{blue}{-105} \\\Leftrightarrow & -420x+224x& = & 16-105 \\\Leftrightarrow & \color{red}{-196} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{-196} & & \\\Leftrightarrow & x = \frac{89}{196} & & \\ & V = \left\{ \frac{89}{196} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{5}{7})& = & -7x+\frac{4}{11} \\\Leftrightarrow & -6x+\frac{10}{7}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+110} & = & \color{red}{-539x} +28 \\\Leftrightarrow & -462x \color{red}{+110} \color{blue}{-110} \color{blue}{+539x} & = & \color{red}{-539x} +28 \color{blue}{+539x} \color{blue}{-110} \\\Leftrightarrow & -462x+539x& = & 28-110 \\\Leftrightarrow & \color{red}{77} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{77} & & \\ & V = \left\{ \frac{-82}{77} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{4}{7})& = & 7x+\frac{5}{8} \\\Leftrightarrow & 10x+\frac{20}{7}& = & 7x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{560}{ \color{blue}{56} }x+ \frac{160}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 560x \color{red}{+160} & = & \color{red}{392x} +35 \\\Leftrightarrow & 560x \color{red}{+160} \color{blue}{-160} \color{blue}{-392x} & = & \color{red}{392x} +35 \color{blue}{-392x} \color{blue}{-160} \\\Leftrightarrow & 560x-392x& = & 35-160 \\\Leftrightarrow & \color{red}{168} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{168} & & \\ & V = \left\{ \frac{-125}{168} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{3}{11})& = & 5x+\frac{3}{10} \\\Leftrightarrow & 24x-\frac{18}{11}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{2640}{ \color{blue}{110} }x- \frac{180}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 2640x \color{red}{-180} & = & \color{red}{550x} +33 \\\Leftrightarrow & 2640x \color{red}{-180} \color{blue}{+180} \color{blue}{-550x} & = & \color{red}{550x} +33 \color{blue}{-550x} \color{blue}{+180} \\\Leftrightarrow & 2640x-550x& = & 33+180 \\\Leftrightarrow & \color{red}{2090} x& = & 213 \\\Leftrightarrow & x = \frac{213}{2090} & & \\ & V = \left\{ \frac{213}{2090} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{3}{5})& = & 5x+\frac{9}{8} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x+ \frac{96}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{+96} & = & \color{red}{200x} +45 \\\Leftrightarrow & 480x \color{red}{+96} \color{blue}{-96} \color{blue}{-200x} & = & \color{red}{200x} +45 \color{blue}{-200x} \color{blue}{-96} \\\Leftrightarrow & 480x-200x& = & 45-96 \\\Leftrightarrow & \color{red}{280} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{280} & & \\ & V = \left\{ \frac{-51}{280} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{5}{12})& = & 2x+\frac{7}{8} \\\Leftrightarrow & 25x+\frac{25}{12}& = & 2x+\frac{7}{8} \\ & & & \text{kgv van noemers 12 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{600}{ \color{blue}{24} }x+ \frac{50}{ \color{blue}{24} })& = & (\frac{48}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 600x \color{red}{+50} & = & \color{red}{48x} +21 \\\Leftrightarrow & 600x \color{red}{+50} \color{blue}{-50} \color{blue}{-48x} & = & \color{red}{48x} +21 \color{blue}{-48x} \color{blue}{-50} \\\Leftrightarrow & 600x-48x& = & 21-50 \\\Leftrightarrow & \color{red}{552} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{552} & & \\ & V = \left\{ \frac{-29}{552} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{5}{4})& = & 8x+\frac{2}{11} \\\Leftrightarrow & 9x-\frac{15}{4}& = & 8x+\frac{2}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{396}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{352}{ \color{blue}{44} }x+ \frac{8}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 396x \color{red}{-165} & = & \color{red}{352x} +8 \\\Leftrightarrow & 396x \color{red}{-165} \color{blue}{+165} \color{blue}{-352x} & = & \color{red}{352x} +8 \color{blue}{-352x} \color{blue}{+165} \\\Leftrightarrow & 396x-352x& = & 8+165 \\\Leftrightarrow & \color{red}{44} x& = & 173 \\\Leftrightarrow & x = \frac{173}{44} & & \\ & V = \left\{ \frac{173}{44} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{3}{7})& = & -9x+\frac{4}{3} \\\Leftrightarrow & -4x+\frac{6}{7}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-84}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -84x \color{red}{+18} & = & \color{red}{-189x} +28 \\\Leftrightarrow & -84x \color{red}{+18} \color{blue}{-18} \color{blue}{+189x} & = & \color{red}{-189x} +28 \color{blue}{+189x} \color{blue}{-18} \\\Leftrightarrow & -84x+189x& = & 28-18 \\\Leftrightarrow & \color{red}{105} x& = & 10 \\\Leftrightarrow & x = \frac{10}{105} & & \\\Leftrightarrow & x = \frac{2}{21} & & \\ & V = \left\{ \frac{2}{21} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{5}{3})& = & 9x+\frac{9}{10} \\\Leftrightarrow & 8x-\frac{20}{3}& = & 9x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{240}{ \color{blue}{30} }x- \frac{200}{ \color{blue}{30} })& = & (\frac{270}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 240x \color{red}{-200} & = & \color{red}{270x} +27 \\\Leftrightarrow & 240x \color{red}{-200} \color{blue}{+200} \color{blue}{-270x} & = & \color{red}{270x} +27 \color{blue}{-270x} \color{blue}{+200} \\\Leftrightarrow & 240x-270x& = & 27+200 \\\Leftrightarrow & \color{red}{-30} x& = & 227 \\\Leftrightarrow & x = \frac{227}{-30} & & \\\Leftrightarrow & x = \frac{-227}{30} & & \\ & V = \left\{ \frac{-227}{30} \right\} & \\\end{align}\)
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