Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{3}{7})& = & 5x+\frac{3}{8} \\\Leftrightarrow & -12x-\frac{9}{7}& = & 5x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-672}{ \color{blue}{56} }x- \frac{72}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -672x \color{red}{-72} & = & \color{red}{280x} +21 \\\Leftrightarrow & -672x \color{red}{-72} \color{blue}{+72} \color{blue}{-280x} & = & \color{red}{280x} +21 \color{blue}{-280x} \color{blue}{+72} \\\Leftrightarrow & -672x-280x& = & 21+72 \\\Leftrightarrow & \color{red}{-952} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-952} & & \\\Leftrightarrow & x = \frac{-93}{952} & & \\ & V = \left\{ \frac{-93}{952} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{4}{5})& = & -8x+\frac{7}{3} \\\Leftrightarrow & 9x+\frac{12}{5}& = & -8x+\frac{7}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{135}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{35}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 135x \color{red}{+36} & = & \color{red}{-120x} +35 \\\Leftrightarrow & 135x \color{red}{+36} \color{blue}{-36} \color{blue}{+120x} & = & \color{red}{-120x} +35 \color{blue}{+120x} \color{blue}{-36} \\\Leftrightarrow & 135x+120x& = & 35-36 \\\Leftrightarrow & \color{red}{255} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{255} & & \\ & V = \left\{ \frac{-1}{255} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{4}{11})& = & -4x+\frac{6}{5} \\\Leftrightarrow & 21x-\frac{28}{11}& = & -4x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1155}{ \color{blue}{55} }x- \frac{140}{ \color{blue}{55} })& = & (\frac{-220}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1155x \color{red}{-140} & = & \color{red}{-220x} +66 \\\Leftrightarrow & 1155x \color{red}{-140} \color{blue}{+140} \color{blue}{+220x} & = & \color{red}{-220x} +66 \color{blue}{+220x} \color{blue}{+140} \\\Leftrightarrow & 1155x+220x& = & 66+140 \\\Leftrightarrow & \color{red}{1375} x& = & 206 \\\Leftrightarrow & x = \frac{206}{1375} & & \\ & V = \left\{ \frac{206}{1375} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{4}{5})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 12x-\frac{16}{5}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{360}{ \color{blue}{30} }x- \frac{96}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 360x \color{red}{-96} & = & \color{red}{-150x} +25 \\\Leftrightarrow & 360x \color{red}{-96} \color{blue}{+96} \color{blue}{+150x} & = & \color{red}{-150x} +25 \color{blue}{+150x} \color{blue}{+96} \\\Leftrightarrow & 360x+150x& = & 25+96 \\\Leftrightarrow & \color{red}{510} x& = & 121 \\\Leftrightarrow & x = \frac{121}{510} & & \\ & V = \left\{ \frac{121}{510} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{2}{5})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 24x-\frac{12}{5}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{360}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 360x \color{red}{-36} & = & \color{red}{75x} +50 \\\Leftrightarrow & 360x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +50 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & 360x-75x& = & 50+36 \\\Leftrightarrow & \color{red}{285} x& = & 86 \\\Leftrightarrow & x = \frac{86}{285} & & \\ & V = \left\{ \frac{86}{285} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & -9x+\frac{5}{2} \\\Leftrightarrow & -28x+\frac{21}{8}& = & -9x+\frac{5}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-224}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{-72}{ \color{blue}{8} }x+ \frac{20}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -224x \color{red}{+21} & = & \color{red}{-72x} +20 \\\Leftrightarrow & -224x \color{red}{+21} \color{blue}{-21} \color{blue}{+72x} & = & \color{red}{-72x} +20 \color{blue}{+72x} \color{blue}{-21} \\\Leftrightarrow & -224x+72x& = & 20-21 \\\Leftrightarrow & \color{red}{-152} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-152} & & \\\Leftrightarrow & x = \frac{1}{152} & & \\ & V = \left\{ \frac{1}{152} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{4}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 12x-\frac{24}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x- \frac{72}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{-72} & = & \color{red}{231x} +22 \\\Leftrightarrow & 396x \color{red}{-72} \color{blue}{+72} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{+72} \\\Leftrightarrow & 396x-231x& = & 22+72 \\\Leftrightarrow & \color{red}{165} x& = & 94 \\\Leftrightarrow & x = \frac{94}{165} & & \\ & V = \left\{ \frac{94}{165} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{4}{9})& = & -9x+\frac{9}{8} \\\Leftrightarrow & 8x+\frac{8}{9}& = & -9x+\frac{9}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{576}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} })& = & (\frac{-648}{ \color{blue}{72} }x+ \frac{81}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 576x \color{red}{+64} & = & \color{red}{-648x} +81 \\\Leftrightarrow & 576x \color{red}{+64} \color{blue}{-64} \color{blue}{+648x} & = & \color{red}{-648x} +81 \color{blue}{+648x} \color{blue}{-64} \\\Leftrightarrow & 576x+648x& = & 81-64 \\\Leftrightarrow & \color{red}{1224} x& = & 17 \\\Leftrightarrow & x = \frac{17}{1224} & & \\\Leftrightarrow & x = \frac{1}{72} & & \\ & V = \left\{ \frac{1}{72} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{2}{3})& = & 7x+\frac{6}{11} \\\Leftrightarrow & 8x-\frac{8}{3}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{-88} & = & \color{red}{231x} +18 \\\Leftrightarrow & 264x \color{red}{-88} \color{blue}{+88} \color{blue}{-231x} & = & \color{red}{231x} +18 \color{blue}{-231x} \color{blue}{+88} \\\Leftrightarrow & 264x-231x& = & 18+88 \\\Leftrightarrow & \color{red}{33} x& = & 106 \\\Leftrightarrow & x = \frac{106}{33} & & \\ & V = \left\{ \frac{106}{33} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{5}{7})& = & 5x+\frac{4}{5} \\\Leftrightarrow & 18x-\frac{30}{7}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{-150} & = & \color{red}{175x} +28 \\\Leftrightarrow & 630x \color{red}{-150} \color{blue}{+150} \color{blue}{-175x} & = & \color{red}{175x} +28 \color{blue}{-175x} \color{blue}{+150} \\\Leftrightarrow & 630x-175x& = & 28+150 \\\Leftrightarrow & \color{red}{455} x& = & 178 \\\Leftrightarrow & x = \frac{178}{455} & & \\ & V = \left\{ \frac{178}{455} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{10})& = & 5x+\frac{5}{8} \\\Leftrightarrow & -9x-\frac{9}{10}& = & 5x+\frac{5}{8} \\ & & & \text{kgv van noemers 10 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-360}{ \color{blue}{40} }x- \frac{36}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{25}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -360x \color{red}{-36} & = & \color{red}{200x} +25 \\\Leftrightarrow & -360x \color{red}{-36} \color{blue}{+36} \color{blue}{-200x} & = & \color{red}{200x} +25 \color{blue}{-200x} \color{blue}{+36} \\\Leftrightarrow & -360x-200x& = & 25+36 \\\Leftrightarrow & \color{red}{-560} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-560} & & \\\Leftrightarrow & x = \frac{-61}{560} & & \\ & V = \left\{ \frac{-61}{560} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{5}{3})& = & -7x+\frac{3}{8} \\\Leftrightarrow & 15x+\frac{25}{3}& = & -7x+\frac{3}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{360}{ \color{blue}{24} }x+ \frac{200}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{9}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 360x \color{red}{+200} & = & \color{red}{-168x} +9 \\\Leftrightarrow & 360x \color{red}{+200} \color{blue}{-200} \color{blue}{+168x} & = & \color{red}{-168x} +9 \color{blue}{+168x} \color{blue}{-200} \\\Leftrightarrow & 360x+168x& = & 9-200 \\\Leftrightarrow & \color{red}{528} x& = & -191 \\\Leftrightarrow & x = \frac{-191}{528} & & \\ & V = \left\{ \frac{-191}{528} \right\} & \\\end{align}\)
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