Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{2}{5})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -18x-\frac{12}{5}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-270}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -270x \color{red}{-36} & = & \color{red}{-135x} +10 \\\Leftrightarrow & -270x \color{red}{-36} \color{blue}{+36} \color{blue}{+135x} & = & \color{red}{-135x} +10 \color{blue}{+135x} \color{blue}{+36} \\\Leftrightarrow & -270x+135x& = & 10+36 \\\Leftrightarrow & \color{red}{-135} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-135} & & \\\Leftrightarrow & x = \frac{-46}{135} & & \\ & V = \left\{ \frac{-46}{135} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{4}{7})& = & -6x+\frac{4}{11} \\\Leftrightarrow & 25x+\frac{20}{7}& = & -6x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1925}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{-462}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1925x \color{red}{+220} & = & \color{red}{-462x} +28 \\\Leftrightarrow & 1925x \color{red}{+220} \color{blue}{-220} \color{blue}{+462x} & = & \color{red}{-462x} +28 \color{blue}{+462x} \color{blue}{-220} \\\Leftrightarrow & 1925x+462x& = & 28-220 \\\Leftrightarrow & \color{red}{2387} x& = & -192 \\\Leftrightarrow & x = \frac{-192}{2387} & & \\ & V = \left\{ \frac{-192}{2387} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{8})& = & -5x+\frac{4}{11} \\\Leftrightarrow & -12x-\frac{15}{8}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1056}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{-440}{ \color{blue}{88} }x+ \frac{32}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1056x \color{red}{-165} & = & \color{red}{-440x} +32 \\\Leftrightarrow & -1056x \color{red}{-165} \color{blue}{+165} \color{blue}{+440x} & = & \color{red}{-440x} +32 \color{blue}{+440x} \color{blue}{+165} \\\Leftrightarrow & -1056x+440x& = & 32+165 \\\Leftrightarrow & \color{red}{-616} x& = & 197 \\\Leftrightarrow & x = \frac{197}{-616} & & \\\Leftrightarrow & x = \frac{-197}{616} & & \\ & V = \left\{ \frac{-197}{616} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{3}{11})& = & -9x+\frac{8}{3} \\\Leftrightarrow & -35x+\frac{21}{11}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x+ \frac{63}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{+63} & = & \color{red}{-297x} +88 \\\Leftrightarrow & -1155x \color{red}{+63} \color{blue}{-63} \color{blue}{+297x} & = & \color{red}{-297x} +88 \color{blue}{+297x} \color{blue}{-63} \\\Leftrightarrow & -1155x+297x& = & 88-63 \\\Leftrightarrow & \color{red}{-858} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-858} & & \\\Leftrightarrow & x = \frac{-25}{858} & & \\ & V = \left\{ \frac{-25}{858} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{5}{11})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 24x+\frac{30}{11}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{528}{ \color{blue}{22} }x+ \frac{60}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 528x \color{red}{+60} & = & \color{red}{110x} +99 \\\Leftrightarrow & 528x \color{red}{+60} \color{blue}{-60} \color{blue}{-110x} & = & \color{red}{110x} +99 \color{blue}{-110x} \color{blue}{-60} \\\Leftrightarrow & 528x-110x& = & 99-60 \\\Leftrightarrow & \color{red}{418} x& = & 39 \\\Leftrightarrow & x = \frac{39}{418} & & \\ & V = \left\{ \frac{39}{418} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{2}{5})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -10x-\frac{4}{5}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-450}{ \color{blue}{45} }x- \frac{36}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -450x \color{red}{-36} & = & \color{red}{-315x} +20 \\\Leftrightarrow & -450x \color{red}{-36} \color{blue}{+36} \color{blue}{+315x} & = & \color{red}{-315x} +20 \color{blue}{+315x} \color{blue}{+36} \\\Leftrightarrow & -450x+315x& = & 20+36 \\\Leftrightarrow & \color{red}{-135} x& = & 56 \\\Leftrightarrow & x = \frac{56}{-135} & & \\\Leftrightarrow & x = \frac{-56}{135} & & \\ & V = \left\{ \frac{-56}{135} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{5}{7})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 4x-\frac{10}{7}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{28}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 28x \color{red}{-10} & = & \color{red}{35x} +10 \\\Leftrightarrow & 28x \color{red}{-10} \color{blue}{+10} \color{blue}{-35x} & = & \color{red}{35x} +10 \color{blue}{-35x} \color{blue}{+10} \\\Leftrightarrow & 28x-35x& = & 10+10 \\\Leftrightarrow & \color{red}{-7} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-7} & & \\\Leftrightarrow & x = \frac{-20}{7} & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{11})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -20x-\frac{16}{11}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{48}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-48} & = & \color{red}{-99x} +88 \\\Leftrightarrow & -660x \color{red}{-48} \color{blue}{+48} \color{blue}{+99x} & = & \color{red}{-99x} +88 \color{blue}{+99x} \color{blue}{+48} \\\Leftrightarrow & -660x+99x& = & 88+48 \\\Leftrightarrow & \color{red}{-561} x& = & 136 \\\Leftrightarrow & x = \frac{136}{-561} & & \\\Leftrightarrow & x = \frac{-8}{33} & & \\ & V = \left\{ \frac{-8}{33} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{4}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{24}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x- \frac{24}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{-24} & = & \color{red}{25x} +6 \\\Leftrightarrow & 60x \color{red}{-24} \color{blue}{+24} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{+24} \\\Leftrightarrow & 60x-25x& = & 6+24 \\\Leftrightarrow & \color{red}{35} x& = & 30 \\\Leftrightarrow & x = \frac{30}{35} & & \\\Leftrightarrow & x = \frac{6}{7} & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{2}{7})& = & -5x+\frac{5}{7} \\\Leftrightarrow & -9x+\frac{6}{7}& = & -5x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-63}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -63x \color{red}{+6} & = & \color{red}{-35x} +5 \\\Leftrightarrow & -63x \color{red}{+6} \color{blue}{-6} \color{blue}{+35x} & = & \color{red}{-35x} +5 \color{blue}{+35x} \color{blue}{-6} \\\Leftrightarrow & -63x+35x& = & 5-6 \\\Leftrightarrow & \color{red}{-28} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-28} & & \\\Leftrightarrow & x = \frac{1}{28} & & \\ & V = \left\{ \frac{1}{28} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{3}{7})& = & 9x+\frac{3}{8} \\\Leftrightarrow & 10x+\frac{6}{7}& = & 9x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{560}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} })& = & (\frac{504}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 560x \color{red}{+48} & = & \color{red}{504x} +21 \\\Leftrightarrow & 560x \color{red}{+48} \color{blue}{-48} \color{blue}{-504x} & = & \color{red}{504x} +21 \color{blue}{-504x} \color{blue}{-48} \\\Leftrightarrow & 560x-504x& = & 21-48 \\\Leftrightarrow & \color{red}{56} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{56} & & \\ & V = \left\{ \frac{-27}{56} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{3}{11})& = & -7x+\frac{9}{10} \\\Leftrightarrow & -16x+\frac{12}{11}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1760}{ \color{blue}{110} }x+ \frac{120}{ \color{blue}{110} })& = & (\frac{-770}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1760x \color{red}{+120} & = & \color{red}{-770x} +99 \\\Leftrightarrow & -1760x \color{red}{+120} \color{blue}{-120} \color{blue}{+770x} & = & \color{red}{-770x} +99 \color{blue}{+770x} \color{blue}{-120} \\\Leftrightarrow & -1760x+770x& = & 99-120 \\\Leftrightarrow & \color{red}{-990} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-990} & & \\\Leftrightarrow & x = \frac{7}{330} & & \\ & V = \left\{ \frac{7}{330} \right\} & \\\end{align}\)
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