Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{4}{9})& = & 8x+\frac{9}{5} \\\Leftrightarrow & -21x-\frac{28}{9}& = & 8x+\frac{9}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-945}{ \color{blue}{45} }x- \frac{140}{ \color{blue}{45} })& = & (\frac{360}{ \color{blue}{45} }x+ \frac{81}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -945x \color{red}{-140} & = & \color{red}{360x} +81 \\\Leftrightarrow & -945x \color{red}{-140} \color{blue}{+140} \color{blue}{-360x} & = & \color{red}{360x} +81 \color{blue}{-360x} \color{blue}{+140} \\\Leftrightarrow & -945x-360x& = & 81+140 \\\Leftrightarrow & \color{red}{-1305} x& = & 221 \\\Leftrightarrow & x = \frac{221}{-1305} & & \\\Leftrightarrow & x = \frac{-221}{1305} & & \\ & V = \left\{ \frac{-221}{1305} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{4}{5})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 18x+\frac{24}{5}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{+72} & = & \color{red}{-75x} +20 \\\Leftrightarrow & 270x \color{red}{+72} \color{blue}{-72} \color{blue}{+75x} & = & \color{red}{-75x} +20 \color{blue}{+75x} \color{blue}{-72} \\\Leftrightarrow & 270x+75x& = & 20-72 \\\Leftrightarrow & \color{red}{345} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{345} & & \\ & V = \left\{ \frac{-52}{345} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 6x+\frac{6}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{30}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 30x \color{red}{+6} & = & \color{red}{-35x} +6 \\\Leftrightarrow & 30x \color{red}{+6} \color{blue}{-6} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{-6} \\\Leftrightarrow & 30x+35x& = & 6-6 \\\Leftrightarrow & \color{red}{65} x& = & 0 \\\Leftrightarrow & x = \frac{0}{65} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{3}{5})& = & 9x+\frac{6}{11} \\\Leftrightarrow & 16x-\frac{12}{5}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{880}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 880x \color{red}{-132} & = & \color{red}{495x} +30 \\\Leftrightarrow & 880x \color{red}{-132} \color{blue}{+132} \color{blue}{-495x} & = & \color{red}{495x} +30 \color{blue}{-495x} \color{blue}{+132} \\\Leftrightarrow & 880x-495x& = & 30+132 \\\Leftrightarrow & \color{red}{385} x& = & 162 \\\Leftrightarrow & x = \frac{162}{385} & & \\ & V = \left\{ \frac{162}{385} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{2}{5})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 6x+\frac{4}{5}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{90}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 90x \color{red}{+12} & = & \color{red}{-75x} +40 \\\Leftrightarrow & 90x \color{red}{+12} \color{blue}{-12} \color{blue}{+75x} & = & \color{red}{-75x} +40 \color{blue}{+75x} \color{blue}{-12} \\\Leftrightarrow & 90x+75x& = & 40-12 \\\Leftrightarrow & \color{red}{165} x& = & 28 \\\Leftrightarrow & x = \frac{28}{165} & & \\ & V = \left\{ \frac{28}{165} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{2}{3})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -12x+\frac{8}{3}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-36}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -36x \color{red}{+8} & = & \color{red}{15x} +10 \\\Leftrightarrow & -36x \color{red}{+8} \color{blue}{-8} \color{blue}{-15x} & = & \color{red}{15x} +10 \color{blue}{-15x} \color{blue}{-8} \\\Leftrightarrow & -36x-15x& = & 10-8 \\\Leftrightarrow & \color{red}{-51} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-51} & & \\\Leftrightarrow & x = \frac{-2}{51} & & \\ & V = \left\{ \frac{-2}{51} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{4}{7})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -16x-\frac{16}{7}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1232}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{-176} & = & \color{red}{539x} +42 \\\Leftrightarrow & -1232x \color{red}{-176} \color{blue}{+176} \color{blue}{-539x} & = & \color{red}{539x} +42 \color{blue}{-539x} \color{blue}{+176} \\\Leftrightarrow & -1232x-539x& = & 42+176 \\\Leftrightarrow & \color{red}{-1771} x& = & 218 \\\Leftrightarrow & x = \frac{218}{-1771} & & \\\Leftrightarrow & x = \frac{-218}{1771} & & \\ & V = \left\{ \frac{-218}{1771} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{5}{6})& = & 9x+\frac{8}{9} \\\Leftrightarrow & 28x-\frac{35}{6}& = & 9x+\frac{8}{9} \\ & & & \text{kgv van noemers 6 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{504}{ \color{blue}{18} }x- \frac{105}{ \color{blue}{18} })& = & (\frac{162}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 504x \color{red}{-105} & = & \color{red}{162x} +16 \\\Leftrightarrow & 504x \color{red}{-105} \color{blue}{+105} \color{blue}{-162x} & = & \color{red}{162x} +16 \color{blue}{-162x} \color{blue}{+105} \\\Leftrightarrow & 504x-162x& = & 16+105 \\\Leftrightarrow & \color{red}{342} x& = & 121 \\\Leftrightarrow & x = \frac{121}{342} & & \\ & V = \left\{ \frac{121}{342} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{5}{2})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 20x+\frac{25}{2}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{200}{ \color{blue}{10} }x+ \frac{125}{ \color{blue}{10} })& = & (\frac{30}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 200x \color{red}{+125} & = & \color{red}{30x} +12 \\\Leftrightarrow & 200x \color{red}{+125} \color{blue}{-125} \color{blue}{-30x} & = & \color{red}{30x} +12 \color{blue}{-30x} \color{blue}{-125} \\\Leftrightarrow & 200x-30x& = & 12-125 \\\Leftrightarrow & \color{red}{170} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{170} & & \\ & V = \left\{ \frac{-113}{170} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{4})& = & 5x+\frac{5}{8} \\\Leftrightarrow & 9x-\frac{15}{4}& = & 5x+\frac{5}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{72}{ \color{blue}{8} }x- \frac{30}{ \color{blue}{8} })& = & (\frac{40}{ \color{blue}{8} }x+ \frac{5}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 72x \color{red}{-30} & = & \color{red}{40x} +5 \\\Leftrightarrow & 72x \color{red}{-30} \color{blue}{+30} \color{blue}{-40x} & = & \color{red}{40x} +5 \color{blue}{-40x} \color{blue}{+30} \\\Leftrightarrow & 72x-40x& = & 5+30 \\\Leftrightarrow & \color{red}{32} x& = & 35 \\\Leftrightarrow & x = \frac{35}{32} & & \\ & V = \left\{ \frac{35}{32} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{4}{9})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -16x+\frac{16}{9}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-144}{ \color{blue}{9} }x+ \frac{16}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -144x \color{red}{+16} & = & \color{red}{-63x} +30 \\\Leftrightarrow & -144x \color{red}{+16} \color{blue}{-16} \color{blue}{+63x} & = & \color{red}{-63x} +30 \color{blue}{+63x} \color{blue}{-16} \\\Leftrightarrow & -144x+63x& = & 30-16 \\\Leftrightarrow & \color{red}{-81} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-81} & & \\\Leftrightarrow & x = \frac{-14}{81} & & \\ & V = \left\{ \frac{-14}{81} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{5}{8})& = & -9x+\frac{4}{7} \\\Leftrightarrow & 20x-\frac{25}{8}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1120}{ \color{blue}{56} }x- \frac{175}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{32}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1120x \color{red}{-175} & = & \color{red}{-504x} +32 \\\Leftrightarrow & 1120x \color{red}{-175} \color{blue}{+175} \color{blue}{+504x} & = & \color{red}{-504x} +32 \color{blue}{+504x} \color{blue}{+175} \\\Leftrightarrow & 1120x+504x& = & 32+175 \\\Leftrightarrow & \color{red}{1624} x& = & 207 \\\Leftrightarrow & x = \frac{207}{1624} & & \\ & V = \left\{ \frac{207}{1624} \right\} & \\\end{align}\)
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