Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{5}{3})& = & 9x+\frac{7}{12} \\\Leftrightarrow & 8x-\frac{20}{3}& = & 9x+\frac{7}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{96}{ \color{blue}{12} }x- \frac{80}{ \color{blue}{12} })& = & (\frac{108}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 96x \color{red}{-80} & = & \color{red}{108x} +7 \\\Leftrightarrow & 96x \color{red}{-80} \color{blue}{+80} \color{blue}{-108x} & = & \color{red}{108x} +7 \color{blue}{-108x} \color{blue}{+80} \\\Leftrightarrow & 96x-108x& = & 7+80 \\\Leftrightarrow & \color{red}{-12} x& = & 87 \\\Leftrightarrow & x = \frac{87}{-12} & & \\\Leftrightarrow & x = \frac{-29}{4} & & \\ & V = \left\{ \frac{-29}{4} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{2}{11})& = & -3x+\frac{6}{11} \\\Leftrightarrow & -8x-\frac{8}{11}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-88}{ \color{blue}{11} }x- \frac{8}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -88x \color{red}{-8} & = & \color{red}{-33x} +6 \\\Leftrightarrow & -88x \color{red}{-8} \color{blue}{+8} \color{blue}{+33x} & = & \color{red}{-33x} +6 \color{blue}{+33x} \color{blue}{+8} \\\Leftrightarrow & -88x+33x& = & 6+8 \\\Leftrightarrow & \color{red}{-55} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-55} & & \\\Leftrightarrow & x = \frac{-14}{55} & & \\ & V = \left\{ \frac{-14}{55} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{2}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 30x+\frac{12}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x+ \frac{60}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{+60} & = & \color{red}{-385x} +66 \\\Leftrightarrow & 1650x \color{red}{+60} \color{blue}{-60} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{-60} \\\Leftrightarrow & 1650x+385x& = & 66-60 \\\Leftrightarrow & \color{red}{2035} x& = & 6 \\\Leftrightarrow & x = \frac{6}{2035} & & \\ & V = \left\{ \frac{6}{2035} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{3}{8})& = & 4x+\frac{6}{5} \\\Leftrightarrow & -15x-\frac{15}{8}& = & 4x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-600}{ \color{blue}{40} }x- \frac{75}{ \color{blue}{40} })& = & (\frac{160}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -600x \color{red}{-75} & = & \color{red}{160x} +48 \\\Leftrightarrow & -600x \color{red}{-75} \color{blue}{+75} \color{blue}{-160x} & = & \color{red}{160x} +48 \color{blue}{-160x} \color{blue}{+75} \\\Leftrightarrow & -600x-160x& = & 48+75 \\\Leftrightarrow & \color{red}{-760} x& = & 123 \\\Leftrightarrow & x = \frac{123}{-760} & & \\\Leftrightarrow & x = \frac{-123}{760} & & \\ & V = \left\{ \frac{-123}{760} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{3}{5})& = & -5x+\frac{9}{11} \\\Leftrightarrow & 18x-\frac{18}{5}& = & -5x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x- \frac{198}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{-198} & = & \color{red}{-275x} +45 \\\Leftrightarrow & 990x \color{red}{-198} \color{blue}{+198} \color{blue}{+275x} & = & \color{red}{-275x} +45 \color{blue}{+275x} \color{blue}{+198} \\\Leftrightarrow & 990x+275x& = & 45+198 \\\Leftrightarrow & \color{red}{1265} x& = & 243 \\\Leftrightarrow & x = \frac{243}{1265} & & \\ & V = \left\{ \frac{243}{1265} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{3})& = & 9x+\frac{7}{2} \\\Leftrightarrow & 20x-\frac{20}{3}& = & 9x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{-40} & = & \color{red}{54x} +21 \\\Leftrightarrow & 120x \color{red}{-40} \color{blue}{+40} \color{blue}{-54x} & = & \color{red}{54x} +21 \color{blue}{-54x} \color{blue}{+40} \\\Leftrightarrow & 120x-54x& = & 21+40 \\\Leftrightarrow & \color{red}{66} x& = & 61 \\\Leftrightarrow & x = \frac{61}{66} & & \\ & V = \left\{ \frac{61}{66} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{3})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -12x-\frac{20}{3}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{100}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-100} & = & \color{red}{-75x} +18 \\\Leftrightarrow & -180x \color{red}{-100} \color{blue}{+100} \color{blue}{+75x} & = & \color{red}{-75x} +18 \color{blue}{+75x} \color{blue}{+100} \\\Leftrightarrow & -180x+75x& = & 18+100 \\\Leftrightarrow & \color{red}{-105} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-105} & & \\\Leftrightarrow & x = \frac{-118}{105} & & \\ & V = \left\{ \frac{-118}{105} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{3}{4})& = & 5x+\frac{7}{9} \\\Leftrightarrow & 12x-\frac{9}{4}& = & 5x+\frac{7}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{432}{ \color{blue}{36} }x- \frac{81}{ \color{blue}{36} })& = & (\frac{180}{ \color{blue}{36} }x+ \frac{28}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 432x \color{red}{-81} & = & \color{red}{180x} +28 \\\Leftrightarrow & 432x \color{red}{-81} \color{blue}{+81} \color{blue}{-180x} & = & \color{red}{180x} +28 \color{blue}{-180x} \color{blue}{+81} \\\Leftrightarrow & 432x-180x& = & 28+81 \\\Leftrightarrow & \color{red}{252} x& = & 109 \\\Leftrightarrow & x = \frac{109}{252} & & \\ & V = \left\{ \frac{109}{252} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{4}{3})& = & -9x+\frac{6}{11} \\\Leftrightarrow & -8x+\frac{16}{3}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{176}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+176} & = & \color{red}{-297x} +18 \\\Leftrightarrow & -264x \color{red}{+176} \color{blue}{-176} \color{blue}{+297x} & = & \color{red}{-297x} +18 \color{blue}{+297x} \color{blue}{-176} \\\Leftrightarrow & -264x+297x& = & 18-176 \\\Leftrightarrow & \color{red}{33} x& = & -158 \\\Leftrightarrow & x = \frac{-158}{33} & & \\ & V = \left\{ \frac{-158}{33} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{3}{7})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -6x-\frac{6}{7}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-18} & = & \color{red}{147x} +56 \\\Leftrightarrow & -126x \color{red}{-18} \color{blue}{+18} \color{blue}{-147x} & = & \color{red}{147x} +56 \color{blue}{-147x} \color{blue}{+18} \\\Leftrightarrow & -126x-147x& = & 56+18 \\\Leftrightarrow & \color{red}{-273} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-273} & & \\\Leftrightarrow & x = \frac{-74}{273} & & \\ & V = \left\{ \frac{-74}{273} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{5}{3})& = & -7x+\frac{5}{4} \\\Leftrightarrow & 20x+\frac{25}{3}& = & -7x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{240}{ \color{blue}{12} }x+ \frac{100}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 240x \color{red}{+100} & = & \color{red}{-84x} +15 \\\Leftrightarrow & 240x \color{red}{+100} \color{blue}{-100} \color{blue}{+84x} & = & \color{red}{-84x} +15 \color{blue}{+84x} \color{blue}{-100} \\\Leftrightarrow & 240x+84x& = & 15-100 \\\Leftrightarrow & \color{red}{324} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{324} & & \\ & V = \left\{ \frac{-85}{324} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{3})& = & 9x+\frac{4}{11} \\\Leftrightarrow & 28x-\frac{14}{3}& = & 9x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{924}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 924x \color{red}{-154} & = & \color{red}{297x} +12 \\\Leftrightarrow & 924x \color{red}{-154} \color{blue}{+154} \color{blue}{-297x} & = & \color{red}{297x} +12 \color{blue}{-297x} \color{blue}{+154} \\\Leftrightarrow & 924x-297x& = & 12+154 \\\Leftrightarrow & \color{red}{627} x& = & 166 \\\Leftrightarrow & x = \frac{166}{627} & & \\ & V = \left\{ \frac{166}{627} \right\} & \\\end{align}\)
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